Non-Standard Heavy Mesons and Baryons, an Experimental Review

Stephen Lars Olsen,1 Tomasz Skwarnicki,2 and Daria Zieminska3 1Center for Underground Physics, Institute for Basic Science, Daejeon 305-811 Korea 2Department of Physics, Syracuse University, Syracuse, NY 13244 U.S.A. 3Department of Physics, Indiana University, Bloomington, IN 47405-71055 U.S.A. (Dated: August 13, 2017)

Quantum Chromodynamics (QCD), the generally accepted theory for the strong interactions, describes the interactions between quarks and gluons. The strongly interacting particles that are seen in nature are hadrons, which are composites of quarks and gluons. Since QCD is a strongly coupled theory at distance scales that are characteristic of observable hadrons, there are no rigorous, ﬁrst-principle methods to derive the spectrum and properties of the hadrons from the QCD Lagrangian, except for Lattice QCD simulations that are not yet able to cope with all aspects of complex and short-lived states. Instead, a variety of “QCD inspired” phenomenological models have been proposed. Common features of these models are predictions for the existence of hadrons with substructures that are more complex than the standard quark-antiquark mesons and the three quark baryons of the original quark model that provides a concise description of most of the low-mass hadrons. Recently, an assortment of candidates for non-standard multi-quark mesons, meson-gluon hybrids and pentaquark baryons that contain heavy (charm or bottom) quarks have been discovered. Here we review the experimental evidence for these states and make some general comparisons of their measured properties with standard quark-model expectations and predictions of various models for non-standard hadrons. We conclude that the spectroscopy of all but simplest hadrons is not yet understood. Submitted to Reviews of Modern Physics.

CONTENTS 2. The BESIII experiment in the τ-charm threshold region 17 I. Introduction 2 3. Future prospects 18 A. Color charges, gluons and QCD 2 B. High-pT detectors at high-energy hadron colliders 19 1. Asymptotic freedom and conﬁnement 3 1. The Tevatron experiments 19 B. The QCD dilemma 3 2. The LHC experiments 20 C. Searches for light “non-standard” hadrons 4 C. LHCb - forward detector at LHC 20 D. Heavy quarks and the quarkonium spectra 5 1. The b quark and the spectrum of bottomonium IV. Heavy-light exotic hadron candidates 22 mesons 6 A. Charm 22 2. Non-standard quarkonium-like mesons and B. Bottom 24 arXiv:1708.04012v1 [hep-ph] 14 Aug 2017 quarkonium pentaquarks 6 3. Comments on units, terminology and notation 7 V. Neutral exotic hadron candidates 26 A. X(3872) 26 II. Models for non-standard hadrons 7 B. X(3915) 30 A. QCD-color-motivated models 9 1. Is the X(3915) the χc0 charmonium state? 30 1. QCD diquarks 9 2. Is the X(3915) a ccs¯ s¯ four-quark state? 31 2. QCD hybrids 9 3. Discussion 31 B. Other models 10 C. Y (4260) and other JPC = 1−− states 31 1. Hadronic molecules 10 1. BESIII as a “Y (4260)-Factory” 33 2. Hadrocharmonium 11 2. Discussion 35 3. Born-Oppenheimer model 11 D. X(4140) and other J/ψφ structures 36 4. Kinematically induced resonance-like mass peaks 11 1. The 6-dimensional LHCb Amplitude Analysis 37 C. Lattice QCD 12 2. Charmonium Assignments for the J/ψφ states? 38 E. X∗(3860), X(3940) and X(4160) 39 ∗ III. Heavy Flavor Experiments 14 1. X (3860) → DD¯; an alternative χc0(2P) A. Experiments at e+e− colliders 14 candidate? 40 1. The B-factory experiments 15 2. X(3940) → DD¯ ∗ 40 2

3. X(4160) → D∗D¯ ∗ 40 A. Color charges, gluons and QCD 4. Discussion 40

VI. Charged non-standard hadron candidates 41 The original quark model implied pretty grievous vi- A. Z(4430)+ and similar structures in B decays 41 olations of the Pauli Exclusion Principle. For example, 1. The Z(4430)+ → ψ0π+ in B → ψ0π+K decays 41 the quark model identifies the J = 3/2 Ω− baryon as a + + ¯0 + − 2. The Z(4200) → J/ψπ in B → J/ψπ K state that contains three s quarks that are all in a relative decays 43 + 0 + − S-wave and with parallel spins; i.e., the three s quarks oc- 3. Charged χc1π resonances in B¯ → χc1π K decays 44 cupy the same quantum state, in violation of Pauli’s prin- 4. Discussion 44 ciple. This inspired a suggestion by Greenberg (3) that B. Charged Z+ and Z+ states produced in e+e− b c quarks were not fermions but, instead, “parafermions” processes 44 of order three, with an additional, hidden quantum num- 1. The Zb charged bottomonium-like mesons 44 2. The Zc charged charmonium-like mesons 46 ber that made them distinct. In this picture, the three s quarks in the Ω− have different values of this hidden VII. Pentaquark candidates 50 quantum number and are, therefore, non-identical parti- VIII. Summary and Future Prospects 53 cles. A. Theory 53 In the following year, Han and Nambu (4) proposed 1. Molecules 53 2. Diquarks 57 a model in which each of the quarks are SU(3) triplets 3. QCD hybrids 58 in flavor-space (and with integer electric charges) with 4. Hadrocharmonium 59 strong-interaction “charges” that are a triplet in an- 5. Kinematically induced resonance-like peaks 59 other SU(3) space. They identified Greenberg’s hid- 6. Comments 59 B. Experiment 60 den quantum numbers with three different varieties of C. Final remark 61 strong charges, q → qi, i = 1, 2, 3, and associated the observable hadrons as singlets in the space of this addi- References 61 tional SU(3) symmetry group. This can be done with three-quark combinations in which each quark has a dif- I. INTRODUCTION ferent strong charge (baryons = ijkqiqjqk) or quark- antiquark combinations, where the quark’s strong charge The major breakthrough in our understanding of the and the antiquark’s strong anticharge are the same type i j spectrum of subatomic hadrons was the nearly simultane- (mesons = δjqiq¯ ). Because of the uncanny correspon- ous realization in 1964 by Gell-Mann (1) and Zweig (2) dence between these prescriptions with the rules for hu- that hadrons could be succinctly described as compos- man color perception, where white can be produced ites of fractionally charged fermions with baryon num- either by triplets of three primary colors or by color ber B = 1/3, called “quarks” by Gell-Mann and “aces” plus complementary-color pairs, the strong-interaction by Zweig. The original quark model had three differ- charges were soon dubbed “color” charges: red, green and ent flavored quarks: q = u+2/3, d−1/3, s−1/3 (now called blue, with anticharges that are the corresponding com- the light flavors)1 and their B = −1/3 antiparticles plementary colors: cyan, magenta and yellow. The color q¯ =u ¯−2/3, d¯+1/3, s¯+1/3. The most economical quark neutral combinations that form baryons, antibaryons and combinations for producing B = 0 mesons and B = 1 mesons are illustrated in Fig. 1a. baryons, are qq¯ and qqq,2 respectively, and these combinations reproduce the pseudoscalar and vector meson a) baryon anbaryon b) octets and the spin-1/2 and spin-3/2 baryon octet and de- red blue an- an- gluon exchange cuplet that were known at that time. Nevertheless, both blue green q green q authors noted in their original papers that more com- an- plex structures with integer charges and B = 0 or B = 1 red could exist, such as qqq¯q¯ “tetraquark” mesons and qqqqq¯ meson “pentaquark” baryons. However, no candidates for these red an- q q more complicated configurations were known at the time. red

FIG. 1 a) The color makeup of baryons, antibaryons and a meson. 1 The u and d quark form an isospin doublet: u with I3 = 1/2 and b) Single gluon exchange between two quarks. Gluons have two d with I3 = −1/2. The s-quark has a non-zero additive flavor color indices that can be viewed as two color charges that propagate quantum number called strangeness; for historical reasons the in opposite directions. s quark has negative strangeness S = −1 and thes ¯ quark has positive strangeness S = +1. 2 For simplicity of notation, flavor indices are suppressed. In com- Measurements of the total cross section for binations, such as qqq and qq¯, it is implicitly assumed that each e+e− → hadrons were consistent with the exis- q can have any one of the three light quark flavors. tence of the three color degrees of freedom (5). The 3 generalization of the Han-Nambu idea to a gauge theory αs ∼ O(1) and perturbation expansions do not converge. with quarks of fractional electric charge was done in This increase in the coupling strength for large quark sep- 1973 (6) and is called Quantum Chromodynamics or arations is the source of “confinement,” i.e., the reason QCD. This is now the generally accepted theory for the that isolated colored particles, be they quarks or gluons, strong interactions. are never seen. The only strongly interacting particles that can exist in isolation are color-charge-neutral (i.e. white) hadrons. 1. Asymptotic freedom and confinement

In QCD, the color force is mediated by eight massless vector particles called gluons, which are the the generalization of the photon in QED. Unlike QED in which the confinement photons are electrically neutral and do not interact with each other, the gluons of QCD have color charges and, αs αs thus, interact with each other. Figure 1b shows a single αs gluon exchange between two colored quarks. In QED, the vacuum polarization diagram, shown in Fig. 2(a), results in a modiﬁcation of the QED coupling strength αQED that makes it decrease with increasing distance. For distance scales of order 1 meter, αQED ' 1/137; at a asymptotic distance scale of 0.002 fm, comparable to the Compton freedom 0 wavelength of the Z weak vector boson, αQED ' 1/125.

a) QED

e FIG. 3 The behavior of the QCD coupling strength αs as a func- _ e e tion of the inverse momentum transfer 1/Q or, equivalently, the α γ γ quark separation distance r. Descriptions of the data points and QED αQED the associated references are provided in ref. (9). e e e

b) QCD B. The QCD dilemma

q q_ q q g q g g g g In QCD, the component of the Standard Model (SM) αS αS αS αS of elementary processes that deals with the strong in- q q q q g q teraction, the elementary particles are the color-charged quarks and gluons. However, a consequence of confinement is that these particles are never seen in experiments. FIG. 2 a) The lowest-order QED vacuum polarization diagram for electron-electron scattering. b) The lowest-order QCD vacuum Although the QCD Lagrangian is expected, in principle, polarization diagrams for quark-quark scattering. to completely describe the spectrum of hadrons and all of their properties, there is no rigorous first-principle trans- In QCD, the gluon-gluon interaction includes addi- lation of this into any useful mathematical expressions. tional vacuum polarization diagrams that have virtual The quark and gluon composition of hadrons can be gluon loops as shown in Fig. 2(b). These gluon loops hopelessly complex, as illustrated in the inset on the right modify the QCD coupling strength αs in a way that side of Fig. 3. For distance scales on the order 1 fm, the is opposite to that of its QED counterpart: they cause typical size of a hadron, αs ∼ 1 and the pattern illus- αs to decrease at short distances and increase at long trated in the figure is just one of an infinite number of distances (7; 8) as illustrated in Fig. 3. The relatively possible quark-gluon configurations that are only subject small value of the coupling strength at short distances: to the constraints that they have appropriate quantum αs = 0.1185 ± 0.0006 at r ' 0.002 fm, results in what numbers and are color neutral. In fact, while the tra- is called “asymptotic freedom,” and facilitates the use ditional three quarks form baryons and quark-antiquark of perturbation expansions to make reliable (albeit diffi- pairs form mesons prescription works well for the meson cult) first-principle calculations for short-distance, high- octets and the baryon octet & decuplet that were known momentum-transfer processes such as those studied in at the time quarks were first introduced, it fails in a num- the high-pT detectors at CERN’s Large Hadron Collider ber of other areas. Soon after the quark model was pro- (LHC). In contrast, for distance scales of that approach posed, it was realized that these simple rules failed to r ∼ 1 fm, which are characteristic of the sizes of hadrons, provide a satisfactory explanation for the properties of 4 the lowest-mass scalar-meson octet (10) and were unable latter are hadronic contributions to the predicted value to provide a simple explanation for the positive parity of of the muon anomalous magnetic moment (14). the lowest-lying excitation of the proton, the J P = 1/2+ N ∗(1440) (the “Roper resonance”) (11) or the mass of the P − lowest-lying excitation of the Λ hyperon, the J = 1/2 C. Searches for light “non-standard” hadrons Λ(1405) (12). A fundamental process that can be computed with A possible way experiments may be able to con- perturbative QCD is quark-quark elastic scattering at tribute to these improvements is by identifying patterns high-momentum transfer. This shows up in high energy in hadron physics that may help guide the development pp collider experiments as events with two high trans- of improved theoretical mdoels. One peculiar pattern, verse momentum jets of hadrons that are nearly back- and a long-standing puzzle, has been the lack of any to-back in azimuth. The theoretical description of this evidence for light-flavored hadrons with substructures process is based on calculations of the diagram shown in that are more complex than the three-quark baryons the inset on the left side of Fig. 3. Here, in lieu of a and quark-antiquark mesons of the original quark model. beam or target of isolated quarks, the beam and target During the fifty years that have ensued since the birth of particles are quarks contained inside the colliding pro- the quark idea, numerous experiments have searched for tons. The momentum distribution of quarks inside the pentaquark baryons and light-flavored mesons with J PC proton is governed by long-distance QCD and approx- quantum numbers that are not accessible in qq¯ systems. imated by universal parton distribution functions that Although during the same time period a large number are taken from fits to data from hadron collider mea- of additional qqq baryon and qq¯ meson resonances were surements at lower center of mass (c.m.) energies, deep- found, no unambiguous examples of light hadrons with inelastic lepton-proton scattering experiments, etc. The non-standard structures have emerged. fundamental QCD qq → qq process at the core of the In particular, from the very earliest days of the quark 3 diagram has been computed up to O(αs), but the prop- model, K+p and K+d cross section data were scoured for erties of the final-state quarks cannot be directly mea- evidence of resonances with positive strangeness (S = sured and, instead, have to be inferred from the jets of +1) quantum numbers in either the isospin I = 1 or hadrons that they produce; for this, empirical “fragmen- I = 0 channels that would necessarily contain ans ¯ tation functions” are employed. Thus, even processes quark in a minimal qudsu¯ (q = u or d) five-quark (“pen- that are amenable to perturbative QCD calculations in- taquark”) array.4 Candidates for baryon states with pos- volve significant long-distance QCD effects both in the itive strangeness, two with I = 0, dubbed the Z0(1780) initial and final state. and Z0(1865), and three with I = 1, the Z1(1900), This nearly total disconnect between the hadrons that Z1(2150) and Z1(2500), appeared in the 1976 Particle we observe in experiments and the quarks and gluons that data Group (PDG) tables (15), but were absent by the appear in the theory is a problem of huge proportions in time of the 1994 (16) and subsequent versions. History 3 particle physics. This is what we refer to as the “QCD repeated itself in 2003, when an experiment studying Dilemma.” In addition to the intellectual dissatisfaction γn → K+K−n reactions using a beam of energy-tagged with a theory that is not directly applicable to the par- γ rays impinging on a 12C target, reported a “sharp ticles that are used and detected in experiments, there baryon resonance peak” in the K+n invariant mass dis- is also a practical problem in that many SM tests and tribution with a mass and width, M = 1.54 ± 0.01 GeV searches for New Physics (NP) involve strongly interact- and Γ < 25 MeV (17), that closely matched the 1.53 GeV ing hadrons in the initial and/or final states of the asso- mass and 15 MeV width that was predicted for an S = +1 ciated measurements. Even experiments that do not use pentaquark in a 1997 paper by Diakonov et al. (18). The initial or final states that contain hadrons are still subject observation of this peak, which was called the Θ+, started to their effects from virtual quantum fluctuations. As a a great flurry of activity that produced a number of con- result, the sensitivities of many NP search experiments flicting experimental results. This ended three years later are ultimately limited by hadron-related theoretical un- when results from some definitive experiments became certainties. Because of this, as the experimental sensi- available. Based on these, the PDG 2006 report (19) de- tivities of NP searches improve, commensurate improve- clared that “The conclusion that pentaquarks in general, ments in our understanding of long-distance QCD be- and the Θ+, in particular, do not exist, appears com- come more and more important. A good example of the pelling.” Instructive reviews of this recent pentaquark

3 As Frank Wilczek, put it in a recent interview (13): “We have something called a standard model, but its foundations are kind 4 Since the s quark has S = −1, conventional three quark baryons of scandalous. We have not known how to define an important that contain one or more s quarks have negative strangeness; the part of it mathematically rigorously,...” K+ meson contains ans ¯ quark and has S = +1. 5 episode and references to the many related experimental D. Heavy quarks and the quarkonium spectra reports are provided in refs. (20; 21; 22). During the decade that immediately followed the in- Searches for non-standard mesons have mostly con- troduction of the notion of fractionally charged quarks, centrated on looking for meson resonances with “exotic” their actual existence was met with considerable skepti- PC quantum numbers, i.e. J values that cannot be formed cism. Although fractionally charged particles produced −− +− from a fermion-antifermion pair, namely 0 & 0 , in high energy particle collisions would have very distinct −+ +− 1 , 2 , etc. A number of experiments have reported experimental signatures and should be relatively easy to PC −+ evidence for resonance-like behavior with J = 1 , observe, numerous searches at accelerators and in cos- but their interpretations as true resonances remain a sub- mic rays all reported negative results. The conservation ject of some dispute. The situation is summarized in of electric charge ensures that at least one of the frac- refs. (23) and (24). tionally charged quark types should be stable, in which case there could be a fractionally charged component of On the other hand, the scalar mesons with masses ordinary matter. Searches in minerals, deep sea water, below 1 GeV, f (500), K∗(800), a (980), and f (980), 0 0 0 0 meteorites, moon rocks, etc. all failed to find any sign which have non-exotic J PC = 0++ quantum numbers of this. Reviews of this interesting era of quark search that can be accessed by a spin-singlet (S = 0) qq¯ pair experiments are provided in refs. (28) and (29). in a P-wave, have frequently been cited as candidates Thus, while the usefulness of the quark idea as an for multiquark states (see, for example ref. (25)). In qq¯ effective classifier of the spectrum of hadronic particles systems, the lowest-lying J = 0 P-wave qq¯ states are ex- and for describing the results of deep-inelastic electron- pected to have masses that are above 1.2 GeV, close to nucleon scattering experiments was without question, those of the J P = 1+ and J P = 2+ P-wave mesons, their existence as real physical entities, as opposed to such as the a (1260) and a (1320) resonances. In fact, 1 2 a useful mathematical mnemonic aid, was strongly de- an octet of 0++ states with the expected masses (i.e. the bated. However, this debate was put to rest in 1974– a (1450),K∗(1430), etc.) has been identified, and this 0 0 75 with the discovery of the J/ψ (30; 31), ψ0 (32) and makes the lighter scalar octet supernumerary. An espe- χ (33) mesons6 with masses between 3 and 4 GeV. cially puzzling feature of the low mass scalars is their c0,1,2 These new resonance states, all of which are strikingly mass hierarchy, which is inverted with respect to what narrow, were accurately described by Appelquist and would be expected from the quark model: the strange Politzer as bound states of a c- and ac ¯ quark (34), state, K∗(800) = ds¯ , is lighter than the I = 1 a (980), 0 0 where c denotes the charge= +2/3 “charmed quark” with which is nominally comprised of qq¯ pairs ( q = u or d), charm flavor C = +1. The assortment of possible cc¯ and the f (500), which, in the standard qq¯ meson scheme, 0 mesons are collectively known as charmonium. The large would be an ss¯ state, is the lightest member of the octet. c quark mass (m ' 1.3 GeV) ensures that the c quark This is contrary to the well established quark model fea- c motion in bound cc¯ systems is nearly non-relativistic and ture of other mesons and baryons, where states with more the spectrum of observed states can be reasonably well s quarks are heavier. This peculiar features led to spec- described by the Schrödinger equation with a potential ulation that that the lightest 0++ mesons are comprised that is Coulombic at short distances (in accord with the of some kind of four quark configuration (10; 26; 27). notion of asymptotic freedom) and joined to a linearly in- The isosinglet scalar mesons with masses above 1 GeV, creasing “confining” term at large distances (35; 36). The f (1370), f (1500) and f (1710) are also supernumerary 0 0 0 charmonium spectrum of states, which have a one-to-one since at most two can be attributed to the 13P qq¯ (q = u, 0 correspondence to the allowed atomic levels in the hydro- d, s) states. They fall into the region of the lightest pre- gen atom, is indicated in Fig. 4. All of the states below dicted glueball, i.e. a meson comprised only of gluons, the M = 2m (= 3730 MeV) open-charm threshold7 with no quarks. However, these can mix with conven- D have been experimentally identified and found to have tional qq¯ states, thereby making a clear cut experimental have masses and other properties that are in good agree- identification of a glue-glue bound state component dif- ment with potential model expectations. The simplicity ficult. Detailed discussion of glueballs and other light and dramatic success of the charmonium model resulted exotic hadron candidates can be found, e.g., in ref. (9).5 in a rapid and almost universal acceptance in the particle physics community that quarks are real, physical entities. A systematic theoretical framework for imple-

6 0 The ψ and χcJ are commonly used names for the spin-triplet 5 See review notes on “Quark Model”, “Non-qq¯ Mesons”, “Note on ψ(2S), and χcJ (1P) charmonium states. 7 0 Scalar Mesons Below 2 GeV”, and “Pole Structure of the Λ(1405) Here mD is the mass of the D , the lightest “open-charm” meson Region”. with quark content cu¯ and charm quantum number C = 1. 6 menting corrections to the static potential approach was later developed in form of NRQCD(37; 38). 11200 Υ(6S) 11000 Υ(5S) ψ(4S) 10800

4400 Mass [MeV] ψ (2D) Υ(4S) χ (3P) 1 10600 b1 BB 4200 ψ (3S) Υ(3S)

Mass [MeV] 10400 χ (2P) h (2P)χ (2P) 4000 c2 b b Υ ψ (1D) 2(1D) 1,2 10200 η (2S)Υ(2S) 3800 b ψ(2S) DD 10000 χ (1P) η (2S) hb(1P) b c χ (1P) 3600 c hc(1P) 9800

3400 9600 Υ(1S) η (1S) b 3200 9400 J/ψ(1S) 0 1 1 3 2 1 3 3 4 1 5 3 6 1 7 3 8 1 9 3 10 S0 S1 P1 P0,1,2 D2 D1,2,3 F3 F2,3,4 G4 G3,4,5 η (1S) 3000 c

0 1 1 3 2 1 3 3 4 1 5 3 6 1 7 3 8 1 9 3 10 FIG. 5 The current status of the bottomonium spectrum. The S0 S1 P1 P0,1,2 D2 D1,2,3 F3 F2,3,4 G4 G3,4,5 dashed lines indicate the expected states and their masses based on recent calculations (41) based on the Godfrey-Isgur relativized potential model (40). The solid lines indicates the experimentally es- FIG. 4 The current status of the charmonium spectrum. The tablished bottomonium states, with masses and spin-parity (JPC ) dashed (red) lines indicate the expected states and their masses quantum number assignments taken from ref. (9), and labeled by based on recent calculations (39) based on the Godfrey-Isgur rel- their spectroscopic designations. The open-ﬂavor threshold is also ativized potential model (40). The solid (black) lines indicates indicated (blue line). the experimentally established charmonium states, with masses and spin-parity (JPC ) quantum number assignments taken from ref. (9), and labeled by their spectroscopic designations. The open- ﬂavor threshold is also indicated (blue line). quark are known as “heavy quarks” and often denoted as Q (Q = c or b); likewise charmonium and bottomonium mesons are collectively referred to as “quarkonium” mesons and denoted as QQ¯. 1. The b quark and the spectrum of bottomonium mesons

Three years later, in 1977, a similar family of narrow 2. Non-standard quarkonium-like mesons and quarkonium pentaquarks meson resonances (the Υ, Υ0 &Υ00) was discovered in the 9.4 to 10.4 GeV mass region (42; 43; 44). These states The large heavy-quark masses strongly suppress the were identified as b¯b bound states, where b designates production of QQ¯ pairs from the vacuum during the the charge = −1/3 “bottom,” or “beauty” quark with quark-to-hadron fragmentation process. Thus, if a Q and beauty quantum number B = −1, and are now called a Q¯ quark are found among the decay products of a pre- the bottomonium mesons. It was found that the ap- viously unseen meson resonance, they must have been plication the same potential that was used for charmo- present as constituents of the meson itself. If the Q and nium, with a b quark mass of m ' 4.2 GeV, could pro- b Q¯ quarks are the parent meson’s only constituents, it duce a reasonable description of the bottomonium sys- must be a QQ¯ quarkonium state and, thus, have prop- tem (see Fig. 5). In this case there are more states be- erties that match those of one of the as yet unassigned low the M = 2m (= 10.56 GeV) open-bottom thresh- B allowed quarkonium levels. If it does not fit into one old,8 and most of these have been identified and found to of the available levels, it must have a substructure that have masses and other properties that are in good agree- is more complex than just QQ¯ and, thus, qualify as ment with potential model expectations. The c and b a non-standard hadron. The limited number of unassigned charmonium states with masses below 4.5 GeV and the theoretical expectation that most of the unassigned charmonium states will have relatively low and 8 To conform to the nomenclature of charge = −1/3 s quark system, B mesons contain a ¯b quark and have “beauty flavor” non-overlapping widths, make the identification of non- B = +1 while B¯ mesons contain a b quark and have B = −1; i.e. standard charmonium-like mesons less ambiguous than is B = ¯bq and B¯ = bq¯, where q = u or d the case for light-quark hadrons. For similar reasons, a 7 baryon resonance that decays to a final state containing is their combined spin, L=S, P, D... denotes their rela- a Q and a Q¯ quark must contain a QQ¯ pair among its tive orbital angular momentum and J is the total angular constituents and, thus, have a valence configuration that momentum. Thus, for example, the J/ψ and ψ0 states 3 3 contains at least five quarks. shown in Fig. 4 are the 1 S1 and 2 S1 cc¯ states, respec- 3 In contrast to experiments in the light-quark sector, re- tively, while the χc0, χc1 and χc2 are the 1 P0,1,2 triplet cent searches for non-standard hadrons containing heavy states. quark pairs, i.e. hadrons that contain a cc¯ quark pair, The charmonium (bottomonium) states contain cc¯ (b¯b) have uncovered a number of intriguing states including pairs and, thus, have a zero net charm (beauty) quantum ± the Z(4430) , which is electrically charged and smoking- number; these are sometimes referred to as hidden-charm 9 gun evidence for a four-quark meson that decays to (hidden-beauty) states. Particles with a single charmed 0 ± ψ π (45; 46), and two strong candidates for pentaquark (bottom) quark are referred to as open-charm (open- states, the Pc(4380) and Pc(4450) that both decay to bottom) states. Properties of the lowest-lying open- J/ψp (47). In addition to these, about twenty other can- charm and open-bottom mesons and baryons mentioned didate non-standard hadron states containing cc¯ quarks in this report are listed in Table II. have been found and studied by the BESIII experiment Limits on the electric dipole moment of the neutron at the BEPCII τ-charm factory in Beijing, the Belle and confirm that QCD is matter-antimatter symmetric to a BaBar experiments at the KEKB and PEPII B-factories, high degree of confidence (122). In addition, the exper- the CDF and D0 experiments at the Tevatron, and the imental environments of the measurements discussed in LHCb, ATLAS and CMS experiments at the LHC. In ad- this report are also mostly matter-antimatter symmetric. dition, two non-standard bottomonium-like meson can- Thus, the data samples that are used for these measure- didates were seen by Belle and a candidate for a mixed- ments usually include charge-conjugate reactions. For flavor ¯bsdu¯ was reported by D0 (48). The non-standard example, a measurement of a πDD¯ ∗ system will use a hadron candidates and some of their properties are listed combined set of π+DD¯ ∗, π+D∗D¯, π−DD¯ ∗, and π−D∗D¯ in Table I, where the charmed pentaquark candidates events. In this report, for simplicity and readability we are labeled as P , the charged (I = 1) states as Z, the c abbreviate this to π+DD¯ ∗ with the implicit assump- J PC = 1−− states as Y , and all the rest as X. tion that charge-conjugate combinations are included. In this review, we summarize the results from this For similar reasons, when we discuss meson-antimeson huge amount of experimental activity and discuss how molecule-like possibilities, we abbreviate combinations these findings reflect on theoretical ideas concerning long- √ like (DD¯ ∗ ± DD¯ ∗)/ 2 to simply DD¯ ∗. distance QCD. The emphasis is on the experimental evidence, for recent reviews that have more focus on theoretical issues, see refs. (118; 119; 120; 121).

II. MODELS FOR NON-STANDARD HADRONS 3. Comments on units, terminology and notation In the absence of any rigorous analytical method for In this report we use “natural units” where ~ = c = 1; making first-principle calculations of the spectrum of energy, momentum and mass are expressed in units of non-standard hadrons, simplified models that are moti- either MeV or GeV. In the case of MeV, the units of vated by the color structure and other general features of −1 both length ([L]) and time ([T]) are 1 MeV . These QCD have been developed. The current best hope for a can be related to conventional units by: [L]= ~c/(1 MeV) rigorous, first-principle treatment of at least some of the −22 = 197 fm and [T]=[L]/c=~/(1 MeV) = 6.58 × 10 s. issues discussed here is lattice QCD, which is discussed Also, when an experimental number is quoted, we usually later in this section. list the quadrature sum of the statistical and systematic The color structure of QCD suggests the existence of errors. three types of non-standard hadronic particles. These in- The spectra of cc¯ charmonium and b¯b bottomonium clude: multiquark hadrons (tetraquark mesons and pen- mesons are shown above in Figs. 4 and 5, respectively, taquark baryons) formed from tightly bound colored di- where their J PC quantum numbers and commonly used quarks; hybrid mesons and baryons comprised of color- names are listed. Sometimes it is convenient to describe singlet combinations of quarks and one or more “valence” these states using spectroscopic notation: n2S+1L , r J gluons; and glueball mesons that are comprised only of where n is the QQ¯ radial quantum number, S = 0 or 1 r gluons (with no quarks). Other possible forms of multiquark states are meson-meson and/or meson-baryon molecule-like systems that are bound (or nearly bound) 9 Since the Z(4430)± decays to final state that contains a ψ0, via Yukawa-like nuclear forces, and bound states com- it must have constituent c- andc ¯-quarks plus additional light prised of quarkonium cores surrounded by clouds of light quarks to account for its non-zero electric charge. quarks and gluons. 8

TABLE I Recently discovered non-standard hadron candidates with hidden charm or beauty. The masses M and widths Γ are averages of measurements with uncertainties added in quadrature, except for X(4140), X(4274) (Z+(4200)), where ref. (49; 50) (ref. (51)) values are listed. See sec. V.D (sec. VI.A) for more detailed discussion. The errors on the average values include scale factors in case of tensions between individual measurements (9). We do not quote a mass or width for the Y (4260) structure, since the latest precision data have revealed its double-peak composition (52), with the main component listed under Y (4220) and its high-mass shoulder under Y (4360). The results from single-peak ﬁts to the Y (4260) structure are not included when determining the Y (4220) parameters. For X(3872), only π+π−J/ψ decays are used in the mass average. Ellipses (...) indicate an inclusive reaction. Question marks indicate informed guesses at J PC values or no information. For charged states, C refers to the neutral isospin partner.

State M (MeV) Γ (MeV) JPC Process (decay mode) Experiment X(3872) 3871.69 ± 0.17 < 1.2 1++ B → K + (J/ψ π+π−) Belle (53; 54), BaBar (55), LHCb (56; 57) pp¯ → (J/ψ π+π−) + ... CDF (58; 59; 60), D0 (61) B → K + (J/ψ π+π−π0) Belle (62), BaBar (63) B → K + (D0D¯ 0π0) Belle (64; 65), BaBar (66) B → K + (J/ψ γ) BaBar (63), Belle (67), LHCb (68) B → K + (ψ0 γ) BaBar (69), Belle (67), LHCb (70) pp → (J/ψ π+π−) + ... LHCb (68), CMS (71), ATLAS (72) e+e− → γ + (J/ψ π+π−) + ... BESIII (73) X(3915) 3918.4 ± 1.9 20 ± 5 0++ B → K + (J/ψ ω) Belle (74), BaBar (63; 75) e+e− → e+e− + (J/ψ ω) Belle (76), BaBar (77) +9 +27 −+ + − ∗ ¯ X(3940) 3942−8 37−17 0 (?) e e → J/ψ + (D D) Belle (78) e+e− → J/ψ + (...) Belle (79) +6.4 +27 ++ X(4140) 4146.5−5.3 83−25 1 B → K + (J/ψ φ) CDF (80), CMS (81), D0 (82), LHCb (49; 50) pp¯ → (J/ψφ) + ... D0 (83) +29 +113 −+ + − ∗ ¯ ∗ X(4160) 4156−25 139− 65 0 (?) e e → J/ψ + (D D ) Belle (78) Y (4260) see Y (4220) entry 1−− e+e− → γ + (J/ψ π+π−) BaBar (84; 85), CLEO (86), Belle (87; 88) Y (4220) 4222 ± 3 48 ± 7 1−− e+e− → (J/ψ π+π−) BESIII (52) + − + − e e → (hc π π ) BESIII (89) + − e e → (χc0 ω) BESIII (90) e+e− → (J/ψ η) BESIII (91) e+e− → (γ X(3872)) BESIII (73) + − − + e e → (π Zc (3900)) BESIII (92), Belle (88) + − − + e e → (π Zc (4020)) BESIII (93) +19 +14 ++ X(4274) 4273− 9 56−16 1 B → K + (J/ψ φ) CDF (94), CMS (81), LHCb (49; 50) +4.6 +18.4 ++ + − + − X(4350) 4350.6−5.1 13.3−10.0 (0/2) e e → e e + (J/ψ φ) Belle (95) Y (4360) 4341 ± 8 102 ± 9 1−− e+e− → γ + (ψ0 π+π−) BaBar (96; 97), Belle (98; 99) e+e− → (J/ψ π+π−) BESIII (52) −− + − + − Y (4390) 4392 ± 6 140 ± 16 1 e e → (hc π π ) BESIII (89) +16 +30 ++ X(4500) 4506−19 92−21 0 B → K + (J/ψ φ) LHCb (49; 50) +17 +52 ++ X(4700) 4704−26 120−45 0 B → K + (J/ψ φ) LHCb (49; 50) Y (4660) 4643 ± 9 72 ± 11 1−− e+e− → γ + (ψ0 π+π−) Belle (98; 99), BaBar (96; 97) + − + − e e → γ + (Λc Λc ) Belle (100) +,0 +− + − −,0 +,0 Zc (3900) 3886.6 ± 2.4 28.1 ± 2.6 1 e e → π + (J/ψ π ) BESIII (92; 101), Belle (88) e+e− → π−,0 + (DD¯ ∗)+,0 BESIII (102; 103) +,0 +− + −,0 +,0 Zc (4020) 4024.1 ± 1.9 13 ± 5 1 (?) e e− → π + (hc π ) BESIII (93; 104) e+e− → π−,0 + (D∗D¯ ∗)+,0 BESIII (105; 106) + +24 +51 ?+ + Z (4050) 4051−43 82−55 ? B → K + (χc1 π ) Belle (107), BaBar (108) + +35 + 99 + + Z (4200) 4196−32 370−149 1 B → K + (J/ψ π ) Belle (51) B → K + (ψ0π+) LHCb (46) + +185 +321 ?+ + Z (4250) 4248− 45 177− 72 ? B → K + (χc1 π ) Belle (107), BaBar (108) Z+(4430) 4477 ± 20 181 ± 31 1+ B → K + (ψ0 π+) Belle (45; 109; 110), LHCb (46; 111) B → K + (Jψ π+) Belle (51) + 3 5 ∓ + Pc (4380) 4380 ± 30 205 ± 88 ( 2 / 2 ) Λb → K + (J/ψ p) LHCb (47) + 5 3 ± + Pc (4450) 4450 ± 3 39 ± 20 ( 2 / 2 ) Λb → K + (J/ψ p) LHCb (47) +3.4 +7.2 −− + − + − Yb(10860) 10891.1−3.8 53.7−7.8 1 e e → (Υ(nS) π π ) Belle (112; 113) +,0 +− −,0 +,0 Zb (10610) 10607.2 ± 2.0 18.4 ± 2.4 1 Yb(10860) → π + (Υ(nS) π ) Belle (114; 115; 116) − + Yb(10860) → π + (hb(nP ) π ) Belle (114) − ¯∗ + Yb(10860) → π + (BB ) Belle (117) + +− − + Zb (10650) 10652.2 ± 1.5 11.5 ± 2.2 1 Yb(10860) → π + (Υ(nS) π ) Belle (114; 115) − + Yb(10860) → π + (hb(nP ) π ) Belle (114) − ∗ ¯∗ + Yb(10860) → π + (B B ) Belle (117) 9

Jaﬀe proposed that the puzzles associated with the low- TABLE II Properties of the lowest-lying open-charm and open- mass 0++ mesons, discussed above in Section I.C, could bottom particles. Here I : I3 denote the total and third component of the isospin and S, C and B are the strangeness, charm and beauty be explained by identifying them as four-quark combi- quantum numbers. nations of a diquark and a diantiquark. In this scheme, the a0(980) isotriplet mesons are formed from [qs]-[¯qs¯] P particle quark J I : I3 SCB M cτ (q = u or d) conﬁgurations and their large mass rela- content (MeV) (µm) tive to other octet members is due to the two s quarks D+ cd¯ 0− 1/2 : 1/2 0 1 0 1869.6 312 among its constituents (123; 124; 125). In addition to the 0 − D cu¯ 0 1/2 : −1/2 0 1 0 1864.8 123 light scalar mesons, diquarks and/or diantiquarks could D∗+ cd¯ 1− 1/2 : 1/2 0 1 0 2010.3 ∼ 0 D∗0 cu¯ 1− 1/2 : −1/2 0 1 0 2007.0 ∼ 0 be constituents of other octets of tetraquark mesons, as + − well as pentaquark baryons and six-quark H-dibaryons, Ds cs¯ 0 0 : 0 1 1 0 1968.3 150 + + Λc cud (1/2) 0 : 0 0 1 0 2286.5 60 as illustrated in Fig. 6c. ++ + Σc cuu (1/2) 1 : 1 0 1 0 2454.0 ∼ 0 + + a) Σc cud (1/2) 1 : 0 0 1 0 2452.9 ∼ 0 (du-ud)/√2 (du+ud)/√2 0 + Σc cdd (1/2) 1 : −1 0 1 0 2453.8 ∼ 0 d u d d d u u u d u d u B¯0 bd¯ 0− 1/2 : 1/2 0 0 −1 5279.6 455 _ 3 + 6 B− bu¯ 0− 1/2 : −1/2 0 0 −1 5279.3 491 3 + 3 = dd s u s d s u s B¯∗0 bd¯ 1− 1/2 : 1/2 0 0 −1 5325.2 ∼ 0 s s (ds-sd)/√2 (us-su)/√2 (ds+sd)/√2 (us+su)/√2 B∗− bu¯ 1− 1/2 : −1/2 0 0 −1 5325.2 ∼ 0 B¯0 bs¯ 0− 0 : 0 1 0 −1 5366.8 453 s s s + Λb bud (1/2) 0 : 0 0 0 −1 5619.5 435 b) d u d u d u

_ _ _ 3 3 3 A. QCD-color-motivated models d s u s d s u s d s d u

1. QCD diquarks c) Pentaquark H-dibaryon Tetraquark

It is well known that the combination of a q = u, d, s d u d u d u ¯ _ _ _ light-quark triplet with aq ¯ =u, ¯ d, s¯ antiquark antitriplet s d u u sd s d s gives the familiar meson nonets (an octet plus a singlet) diquark-diquark-antiquark diquark-diquark-diquark diquark-diantiquark of flavor-SU(3). Using similar considerations based on FIG. 6 a) Combining a red and blue quark triplet produces a QCD (10), a red and a blue quark triplet can be com- magenta (antigreen) antitriplet and sextet. The antitriplet is an- bined to form a magenta (antigreen) antitriplet of qq0 tisymmetric in color and flavor while the sextet is symmetric in bothd) quantities.Molecule b) The three anticolored diquarkGlueball antitriplets. c) “diquarks” that is antisymmetric in both color and fla- Hybrid Some of the multiquark,_ color-singlet states that can be formed vor, and a magenta flavor-symmetric sextet, as illustrated from quarks, antiquarks,d diquarks and_ diantiquarks. π,... d u d s in Fig. 6a. The Pauli principle restricts the spin state of _ u antitriplet quarks to S = 0 and that of the sextet quarks These considerations are expanded to include heavy- to S = 1. Since the single-gluon-exchange color force light diquarks (Qq) and diantiquarks (Q¯q¯) in refs. (126) between the quarks in an S = 0 antitriplet diquark is at- and (127). The Qq (Q¯q¯) combinations are color- tractive, Jaffe designated these as “good” diquarks and SU(3) antitriplets (triplets) and flavor-SU(3) triplets those in an S = 1 sextet, where the short-range force is (antitriplets). In this case, since the spin-spin force be- repulsive, as “bad” diquarks (27). From the nucleon and tween the quarks is reduced by a factor of mq/mQ and the 0 ∆ -baryon mass difference he estimated the difference in mass difference between “bad” and “good” diquarks is re- binding between light “bad” and “good” diquarks to be duced. As a result S = 1 Qq diquarks are not so “bad” 2 ∼ 3 (m∆ − mN ) ∼ 200 MeV. and both S = 0 and S = 1 diquarks could be expected to Likewise, green-red and blue-green diquarks form yel- play important roles in hadron spectroscopy (128). More low (anti-blue) and cyan (anti-red) antitriplets as shown detailed discussions of diquark models are provided in in Fig. 6b. Thus, in color space, a “good” diquark an- refs. (119; 129) titriplet looks like an antiquark triplet with baryon number B = +2/3 and spin=0. Since these diquarks are not color-singlets, they cannot 2. QCD hybrids exist as free particles but, instead, they should be able to combine with other colored objects in a manner similar to The linear confining term in the color-force potential antiquark antitriplets, thereby forming multiquark color- produces a force between a meson’s constituent quark singlet states with a more complex substructure than the and antiquark that is constant with increasing separa- qq¯ mesons and qqq baryons of the original quark model. tion. As a result, unlike the electric field lines between 10 opposite charges in QED, which spread out in space, the particles. For the deuteron, single pion exchange is the color field-lines are configured in a tightly confined “flux most important contributor to its binding. Törnqvist tube” that runs between the q and theq ¯ (130). studied the possibility for forming deuteron-like BB¯∗ and In their lowest mass configurations, the flux-tube is in B∗B¯∗ states, which he called “deusons,” using a single a ground state with angular momentum quantum num- pion exchange potential and concluded that such states bers L = 0 and S = 0, and only the relative orbital “certainly must exist” (138); he also predicted that if angular momentum of the quarks and their net spin de- some small additional attraction was provided by shorter termine the quantum numbers of a state; the gluonic range exchanges, bound DD¯ ∗ and D∗D¯ ∗ systems would degrees of freedom do not play any role. As a result, the also exist. J PC quantum numbers of these ground-state or “con- ¯ ¯ ventional” mesons, where J~ = L~ + S~, P = (−1)L+1 Since three-pseudoscalar couplings like DDπ and BBπ and C = (−1)L+S are restricted to values that can be are forbidden by rotation plus parity invariance, single- ¯ ¯ accessed by a quark-antiquark pair: J PC = 0++, 0−+, pion exchange forces do not contribute to DD or BB 1++, 1+−, 1−−, 2++, 2−+, 2−−...; other quantum num- binding and, thus, molecule-like structures in these sys- ber combinations, namely J PC = 0−−, 0+−, 1−+, 2+−..., tems are not expected to occur. are inaccessible and are called “exotic.” However, if the In molecule-like states formed from pairs of open- flux tube is in an excited state, its orbital angular mo- charm or open-beauty mesons that are primarily bound mentum and/or spin can be non-zero, and contribute L by single π-meson exchange, the heavy Q and Q¯ quarks and S values that are consistent with one or more glu- are typically well separated in space with very little over- ons. In this case they contribute to the overall quan- lap. This suggests that “fall-apart” decay modes to pairs tum numbers of the state, producing mesons with exotic of open-flavor mesons would be dominant, while decays quantum number assignments (131). Since gluons have ¯ ¯ to final states in which the Q and Q quarks coalesce to zero isospin, quarkonium hybrids, i.e. QQ-g states, are form a hidden-flavor quarkonium state would be rather necessarily isospin singlets. strongly suppressed. More detailed discussions of molec- Models for the decays of hybrids find that decays to ular models are provided in refs. (118; 120; 139; 140). identical mesons are strongly suppressed, while decays to two different mesons where one is a qq¯ in an S-wave

and the other a qq¯ in a P-wave are enhanced (132; 133).

¯ _ The predicted widths for ππ or KK ﬁnal states for light _ ¯ ¯ a) d c D b) quark hybrids are small, as are the DD and BB decay s d K* widths for quarkonium hybrids. In contrast, light hybrid ¯ decays to a1π, b1π and K1(1400)K decays, where a1, b1 π,σ,ω,… π,σ,ω,…

and K1 are axial-vector mesons, in which the qq¯ pair is in

_ d u a relative P-wave, are expected to be strong. Likewise, c _ quarkonium hybrids are expected to have strong decay u D* u N widths for D∗∗D¯ (∗) and B∗∗B¯(∗) ﬁnal states, where D∗∗ and B∗∗ denote open charm (cq¯) and beauty (bq¯)(q = meson-anmeson meson-baryon u, d) P-wave states, respectively. molecule molecule A recent review of hybrid mesons by Meyer and Swan-

son (24) points out limitations in this naive but useful

30-year old picture and provides references to current _ d)

c) q q _ computations based on the lattice gauge theory. _ c c c c

B. Other models q q

1. Hadronic molecules hadrocharmonium adjoint charmonium

FIG. 7 Illustrations of a a) meson-meson and a b) meson-baryon The idea that Yukawa-type meson exchange forces molecular-like structure bound by Yukawa-type meson exchange could produce deuteron-like bound states of ordinary, forces. c) A sketch of the hadrocharmonium conﬁguration of mul- color-singlet hadrons, as illustrated in Fig. 7a and 7b, tiquark states. Here a color-singlet QQ¯ core state interacts with has been around for a long time (134; 135; 136; 137). a surrounding ‘blob” of gluons and light quarks via QCD versions of Van der Waals type forces. d) In adjoint charmonium states, These “molecular” states are expected to have masses a color-octet QQ¯ pair interacts with surrounding gluons and light that are near the constituent particles’ mass threshold, quarks via color forces. and to have spin-parity (J PC ) quantum numbers that correspond to an S-wave combination of the constituent 11

2. Hadrocharmonium 4. Kinematically induced resonance-like mass peaks

For conventional charmonium states with masses above While the classic signal for the presence of an unstable the open-charm (i.e., DD¯ (∗)) threshold, the branch- hadron resonance is a peak in the invariant mass distribu- ing fractions for fall-apart decays to pairs of open- tion of its decay products, not all mass-spectrum peaks charm mesons are measured to be two or three orders- are genuine hadron states. Some can be produced by of-magnitude higher than decays to hidden-charm final near-threshold kinematic effects. These include thresh- states.10 This is not the case for many of the non- old “cusps,” and anomalous triangle singularities. standard hadrons discussed here, where hidden quarko- Threshold cusps: Figure 8a shows the three lowest- ¯ ∗ nium modes are a common discovery channel with order diagrams for three-body decays Y → πDD . Con- ¯ ∗ branching fractions that are lower that open-flavor fall- sider the one-loop diagram, where the D and D elasti- apart modes, but only by factors of ten or less. The cally rescatter. If the two particles are in an S-wave, the hadrocharmonium model was proposed by Dubynskiy imaginary part of the scattering amplitude is zero for ¯ ∗ and Voloshin (141) in order to account for this property. M(DD ) < (mD + mD¯ ∗ ) and abruptly rises at threshold In this model, a compact color-singlet QQ¯ charmonium as (146; 147; 148):

core state is embedded in a spatially extended “blob” of 2 light hadronic matter. These two components interact ImT (s) ∝ g ρ(s), (1) via QCD versions of the Van der Waals force. They ﬁnd where g is the coupling constant and ρ(s) is the phase- that the mutual forces in this conﬁguration are strong space factor. In order to eventually terminate the growth enough to form bound states if the light hadronic matter of ρ(s) before ImT increases to an unphysically large is a highly excited resonant state. In this model, decays value, it has to be attenuated by a hadronic form factor, to the hidden charmonium core state are enhanced to a F (s), in which case level where they are competitive with those for fall-apart modes (142). Allowing for a sizable branching fraction 2k ρ(s) = √ F (s), (2) into open charm modes requires a careful tuning of the s model parameters. where k is the momentum of one of the particles in the two-particle rest frame. For T (s) to be analytic, it must have a real part of the form

3. Born-Oppenheimer model 1 Z ∞ ds0g2(s0)ρ(s0) ReT (s) = P 0 , (3) π sthresh s − s An “all of the above” approach that incorporates all of the configurations discussed above, plus the adjoint char- where P denotes the principal value integral and sthresh monium configuration illustrated in Fig. 7d, which is like is the mass-squared at threshold. The resulting |T | has a very sharp, cusp-like structure that peaks slightly above hadrocharmonium except with an allowance for the possi- √ bility that the QQ¯ core state has non-zero color, has been the M = sthresh threshold; this peak originates from advocated by Braaten, Langmack and Smith (143; 144). kinematics and has nothing to do with any resonant ¯ ∗ ¯ ∗ This model is modeled on the Born-Oppenheimer approx- structure in the DD two-body system. The M(DD ) imation that is used in atomic and molecular physics behavior of |T | and its real and imaginary parts is shown to treat the binding of atoms into molecules. In this in Fig. 8b. It is argued in ref. (149) that genuine approach, the slow-moving atomic nuclei are replaced cusp effects are small, and that the cusp-based mod- by the heavy quarks and the potential that describes els (146; 147; 148), which described the significant near- the interaction of the positive nuclear charges and the threshold peaks in the experimental data, enhanced the surrounding negative electron clouds are replaced by cusp effect by introduction of ad-hoc, non-analytic form lattice-QCD computed gluon-induced potentials (145). factors in the coupling constant, g → g(s) in Eq. 1, which A first application of this approach was used to predict invalidates the approach. the masses of the lowest lying charmonium hybrid and Anomalous triangle singularity: In three-body decays, tetraquark mesons. diagrams that contain internal triangles, as illustrated in Fig. 8c, may contribute. In 1959, Landau showed that this diagram becomes singular when the three virtual particles that form the triangle are all simultaneously on the mass shell (151). This is called the anomalous triangle singularity (ATS). In kinematic regions where 10 ¯ +8 For example, B(ψ(3770) → DD) = (93−9)% while B(ψ(3770) → the conditions for this singularity are satisfied (152), π+π−J/ψ) = (0.193 ± 0.028)% (9). resonance-like peaking structures that have nothing to 12

ATS-induced mass peaks from genuine resonances are a) discussed in refs. (155; 156; 157).

C. Lattice QCD

tree one-loop In QCD, information about the mass of a hadron H is encoded in the correlation function CH (t) of the hadron creation operator OH evaluated at different † times: CH (t) = hΩ|OH (t)OH (0)|Ωi (see e.g. ref. (158)). Here the state H is created from the vacuum |Ωi at time t = 0 and propagates until time t when it is annihilated. two-loop The operator OH (t) is a suitable composition of quark and gluon field operators, e.g., for a pion, which is a pseu- R 3 b) doscalarud ¯ state, it is Oπ(t) = d r u¯(r, t)γ5d(r, t), Im T where d(r, t) andu ¯(r, t) are the d- andu ¯-quark creation Re T operators. The integration extends over all possible spa- tial configurations of the quark and gluon fields. To avoid |T| the oscillating behavior of the correlator in real time, the integration is performed in the Euclidean space-time where the time coordinate is imaginary. The hadron mass is determined from the correlation function’s asymptotic exponential behavior CH (t) ∝ exp(−mH t). The path integral is impossible to solve analytically. A major conceptual breakthrough occurred in 1974 when -0.2 -0.1 0 0.1 0.2 0.3 0.4 Wilson proposed (159) that long-distance QCD could be M(DD*)-mD-mD* (GeV) digitized by transcribing the relevant integrals to a lattice of discrete space-time points, where quark fields placed at lattice sites interact with each other by interconnected c) gluon links. The resulting equations are solved numeri- cally by using Monte Carlo techniques to generate ran- dom samples of all possible configurations. The difficulty with this approach is that realistic lattice QCD (LQCD) computations require extreme computa- tional resources, much beyond those that were available when Wilson first proposed his ideas. Ideally, the lattice should be several fermi in extent in order to fully contain a hadron while the lattice spacing must be small enough to minimize discretization errors. With a lattice of 32 sites in each of the four dimensions, there are 4 6 FIG. 8 a) Low order diagrams that describe√ a three-body decay 32 ≈ 10 lattice sites. With quark fields restricted to ¯ ∗ process Y → πDD scattering near the s = mD +mD∗ threshold just two quark flavors, u and d, each with a real and (taken from ref. (150)). The dotted curve is ImT ; the dashed curve is ReT and the solid curve is |T |. b) A three-body decay with an imaginary part, with three colors and four spin compo- internal triangle. This diagram is singular when the three virtual nents, plus 32 gluon degrees of freedom (8 color×4 spin), particles that form the triangle are all simultaneously on the mass the dimension of the integral is 324 × (2 × 24 + 32) ≈ 108. shell. Happily, Wilson’s dream is now becoming a reality thanks to the relentless, Moore’s law-like advance in high- performance computing. Systems capable of providing do with true particle resonances can be produced. It has hundreds of teraflop/s-yrs by exploiting large-scale par- been shown that, if the rescattering is purely elastic, the allel programming techniques with calculations running effect of the triangle singularity integrates to zero in the cooperatively across thousands of processors are now Dalitz plot projections (153). However, in case of many available (160).11 This, coupled with major advances in coupled channels, this theorem applies to the sum of in- tensities of all of them, thus the Dalitz plot projections to individual channels can produce mass peaks (154). Properties of the ATS and methods for distinguishing 11 One teraflop/s-yr is defined as the number of floating-point op- 13

LQCD algorithms (see ref. (161) for a recent review), has isospin multiplets with precision that is better, in some resulted in a number important recent results related to cases, than that of the currently available experimental hadron masses. measurements, as shown in Fig. 10. For example, the QCDSF Collaboration (162) reported a lattice calculation of the masses of hadrons composed of u, d, and s quarks, ranging from the η meson to the Ω− baryon using only the charged pion and kaon masses and a combination of the p, Σ, and Ξ masses as inputs; the only tuneable parameters are the quark masses and the coupling constant αs. Recent Results for mesons and baryons are shown in Fig. 9, where there is a good agreement with the established values.

* * * H H B B HH s s c c 2400

2000

1800

1600

1400 FIG. 10 Results of the lattice computations of ∆N = mn − mp, 1200 ∆Σ = mΣ− − mΣ+ , ∆Ξ = mΞ− − mΞ0 , ∆D = mD+ − mD0 and (MeV) 1000 ∆Ξcc = m ++ − m + isospin mass splittings, and a test of the Ξcc Ξcc 800 Coleman-Glashow relation (182) ∆CG ≡ ∆MN −∆MΣ −∆MΞ = 0 600 from ref. (174). The horizontal lines are the experimental values and the grey shaded regions represent the experimental error. The 400 computed precision for the quantities with labels in blue shaded 200 boxes is better than that of current measurements. 0 π ρ ∗ η ω φ Λ ΣΞ ∆ ∗ ∗ Ω K K η′ N Σ Ξ The spectrum of mesons carrying one charmed quark, FIG. 9 The LQCD hadron spectrum from MILC (163; or a charmed-anticharmed pair, has been recently com- 164), PACS-CS (165), BMW (166), QCDSF (162), RBC & puted on the lattice by Cichy et al. (183). To tune the UKQCD (167), Hadron Spectrum (168), UKQCD (169), Fermilab- valence quark masses the authors used experimental val- MILC (170), HPQCD (171), and Mohler & Woloshyn (172). The ues of the masses of electrically neutral and charged π, b-flavored meson masses are offset by −4000 MeV. Horizontal bars (gray boxes) denote experimentally measured masses (widths). K, and D mesons. Using a variety of quark-antiquark (Figure from ref. (173).) meson creation operators the authors were able to determine the masses of the lowest-lying 1S and 1P charmo- To date, because of computing-power constraints, most nium states with levels of precision that are in the range LQCD computations ignore isospin violations and set the 0.2 ∼ 0.8 percent. Cichy et al. (183) also successfuly u- and d−quark masses equal. However, precision lattice verified the masses of several charm mesons with the ex- ∗ results on QCD-generated isospin violations are now be- ception of the Ds0(2317) and Ds1(2460) (see sec. IV.A ing realized. Borsanyi et al. (174) have reported a lattice- below), which have masses close to two-meson thresh- based, ab-initio computation of the (1.293 MeV) neutron- olds and, thus, require more advanced techniques (184), proton mass difference that results from the competi- as discussed in sec. IV.A. tion between electromagnetic and QCD-induced isospin- Determining the highly-excited resonance spectra has breaking effects12 with an accuracy of 300 keV. They recently become possible thanks to a technique pro- 13 posed by Luscher (185). The Hadron Spectrum Col- also determined mass splittings in the Σ, Ξ, D and Ξcc laboration (186) did a comprehensive study of the spectrum of excited charmonium mesons with masses up to 4.5 GeV that included possible cc¯-gluon hybrid states. −+ erations performed in a year by a computer that sustains one They find the lightest cc¯-gluon hybrids are a 0 pseu- trillion operations per second. doscalar with M ' 4195 GeV; a 1−+ “exotic” with 12 The calculation reported in ref. (174) finds a QCD contribution M ' 4215 MeV and a 1−− vector with M ' 4285 MeV. to mn − mp that is 2.52 ± 0.49 times larger than that from the (opposite-sign) electromagnetic effect. The magnitude of this One of the non-standard mesons discussed in this report QCD contribution has huge existential significance; an increase or decrease by as little as ∼ 20% would have dire consequences on Nature’s ability to support life (see ref. (175)). 13 The Ξcc is a candidate for a doubly charmed ccq baryon with ments (178; 179; 180). The LHCb group recently reported a 12σ mass M = 3820 ± 1.0 MeV that was reported by the SELEX signal for a Ξcc candidate at a lower mass of 3621.4 ± 0.8 MeV experiment (176; 177) but was not confirmed by other experi- (181). 14 is the Y (4260) vector state that is considered by some near 10 GeV, and the CDF and D0 experiments at the authors to be a promising candidate for a 1−− hybrid 1.96 TeV Tevatron pp¯ collider. state. (This is discussed below in Sect. V.C). It will be The low energy e+e− experiments have the advantage interesting to see what happens to the LQCD-computed of clean experimental environments and the ability to ex- mass value when calculations extended to three-particle ploit energy-momentum-conservation constraints to help resonances (187; 188; 189) become feasible in the next extract signals from complex final states, including those decades. containing γ-rays and π0-mesons. However, the relevant Recently, first attempts to address questions related to production cross sections are at the few nanobarn level possible quarkonium-like, four-quark mesons have been and, even with the high luminosities achieved by BEPCII reported. For example, in order to get insight into and the B-factories, event rates are low. In contrast, the the structure of the X(3872), a candidate non-standard high energy experiments at hadron colliders enjoy charm meson with mass very near the DD¯ ∗ threshold (i.e., particle production cross sections of a few millibarns and M(X(3872) ' mD + mD∗ ) and discussed in detail in beauty particle cross sections of the order of a hundred Sect. V.A, Padmanath et al. (190) made a LQCD study microbarns, so large event samples can be accumulated. that included standard cc¯ charmonium, DD¯ ∗ meson- The charmed and beauty particles are usually highly meson, and diquark-diantiquark operators, 22 in total, boosted, thereby producing decay vertices that are well that allowed the particle to be a superposition of all three separated from the production point and experimentally configurations. Their result indicated the presence of a cc¯ quite distinct. This makes it possible to isolate very clean and a meson-meson (DD¯ ∗) component, but with no sign samples of events, but only for all-charged-particle final of a diquark-diantiquark component, leading the authors states. Since detected γ-rays and π0-mesons originating to the conclusion that a QCD tetraquark interpretation from a displaced vertex do not have associated trajecto- of the X(3872) was disfavored. Bicudo et al. (191) con- ries, they cannot be distinguished from γ-rays and π0- sidered the possible existence of bound states in the ¯b¯bud mesons that originate from the primary high-energy pp four-quark systems with a net beauty flavor of B = 2. (or pp¯) interaction point and, thus, the reconstruction of Their first exploratory simulations found signs of a state final states containing neutral particles suffer from severe +43 with a binding energy of −90−36 MeV, i.e., about 2σ combinatorial backgrounds. from zero. This was followed up by more precise calcula- A common feature of all the contributing experiments tions - see ref. (192) and references within. For a review is that they were motivated and designed to do some- of the searches of resonances with LQCD see ref. (193). thing other than heavy hadron spectroscopy. The origi- Lattice QCD efforts in the area of non-standard hadron nal goals and highest priorities for BESIII were precision spectroscopy, while still in their infancy, are very encour- measurements of charmed quark decays and studies of aging. With the order-of-magnitude increase in the avail- light mesons and baryons produced in J/ψ decays; the able computing power expected during the next decade B-factory and LHCb experiments were aimed at studies (see, e.g., ref. (160)) and continued advances in the so- of weak interaction processes in the decays of particles phistication of the algorithms that will be used to ex- containing a b-quark; the Tevatron experiment’s main tract physics information from the improved configura- jobs were the discovery of the top-quark and precision tions, LQCD seems to be on the verge of becoming a studies of the Z and W ± weak vector bosons; the CMS very powerful tool for deriving a more profound theoret- and ATLAS experiments discovered the Higgs’ boson and ical understanding of the recently discovered states and have done numerous searches for new physics particles. for providing important guidance for future experiments. The discoveries of heavy non-standard hadrons have, for the most part, been unexpected but, in many cases, have generated levels of interest that rival those of the high III. HEAVY FLAVOR EXPERIMENTS priority topics.

The results reviewed here come from experiments that operate at vastly diﬀerent energies. At the low en- A. Experiments at e+e− colliders ergy extreme is the BESIII experiment at the Insti- tute of High Energy Physics in Beijing that operates Many of the early contributions to this research were at the BEPCII e+e− collider and can access c.m. en- from the BaBar (194) and Belle (195) experiments that ergies between 2 and 4.6 GeV. At the high energy ex- operated at the PEPII (196) and KEKB (197) B- treme are the ATLAS, CMS and LHCb experiments op- factories, respectively, between 1999 and 2010. These erating at the LHC pp collider at CERN, with c.m. en- facilities accumulated data at and near Ecm = 10.58 GeV ergies that are more than three orders of magnitude to study matter-antimatter asymmetries (CP violations) higher, i.e. 7 to 13 TeV. In between are the now defunct in the decays of B mesons and to validate the Kobayashi- BaBar and Belle e+e− B-factory experiments and, ear- Maskawa mechanism for CP violation (198). lier, the CLEO experiment, that all ran at c.m. energies The total cross section for e+e− → hadrons at energies 15

ψ3770 that were accessed by the B-factory colliders is shown ψ4160 ψ ) 4160 in Fig. 11b. There are three narrow peaks, called the - ψ4040 μ + Υ(1S), Υ(2S) and Υ(3S), at c.m. energies of 9.46, 10.02 μ J/ψ

! a) -

and 10.36 GeV, respectively. These are the three low- e

+ Ψ’

est triplet S-wave bottomonium (b¯b) states. Since they (e

are below the Ecm = 2mB = 10.56 GeV open-bottom QED threshold and, thus, not able to decay into a B and a B¯ meson pair, their primary decay channel is via b-quark ¯b- quark annihilation into gluons. Since this is a suppressed hadrons)/σ 14 ! 2m process, the three below-threshold bottomonium states - τ e have natural widths that are less than 100 keV and much + 2mD (e σ smaller than the colliders’ c.m. energy spreads, which are Ecm (GeV) typically ∼ 6 MeV. The fourth peak, the Υ(4S), with a ¯ peak mass of 10.58 GeV, can decay to BB meson pairs b) ϒ(4S) CLEO and has a natural width of Γ(Υ(4S)) ' 20 MeV, and is CUSP distinctly broader than the c.m. energy spread. Most of “ϒ(5S)” the data taking by both B-factory experiments occurred “ϒ(6S)” at a c.m. energy corresponding to the peak mass of the Υ(4S) resonance. The BEPCII e+e− collider (201) in Beijing and its associated BESIII experiment (202) started operation in 2008 and covers the c.m. energy range between E (GeV) 2.0 and 4.6 GeV, which includes the thresholds for pro- cm + − ducing τ τ lepton and cc¯ quark pairs. The cc¯ sys- FIG. 11 a) Total cross section measurements for e+e− annihi- tem has two narrow J PC = 1−− resonances below the lation into hadronic final states in units of the QED cross sec- + − + − 2 tion σQED(e e → µ µ ) = 86.8 nb/s(GeV ) from refs. (203; Ecm = 2mD = 3.73 GeV open-charm threshold: the 0 204; 205; 206; 207). The insert shows the results of a fit to the J/ψ and the ψ (the latter is often denoted as ψ(2S) measurements in the 3.6 to 4.6 GeV energy interval that identi- or ψ(3686)). The first 1−− resonance above that thresh- fies the 1−− charmonium states in this region (208). b) Mea- old is the ψ(3770), which decays almost exclusively into surements of σ(e+e− →hadrons) in the 9.45 to 10.62 GeV energy DD¯ final states. Figure 11a shows σ(e+e− → hadrons) region from CUSP (209). The inset shows measurements between 10.55 and 11.5 GeV from CLEO (210). for energies that are accessible at the BEPCII collider. The BaBar (194), Belle (195) and BESIII (202) detectors are similar in overall structure to the CLEO-II detec- While similar in overall structure and capabilities, tor (211). Each is a nearly 4π solid-angle magnetic spec- these detectors differ in many of their specific details, + − trometer surrounding the e e interaction point that especially in the PID systems, as described in the cited contains an assortment of detection systems. All of these references. As an example, Fig. 12 shows an isometric experiments use a large cylindrical gas-filled drift cham- drawing of the BaBar detector. ber for charged-particle trajectory measurements. Sur- rounding these are particle identification (PID) devices for distinguishing charged pions, kaons and protons fol- 1. The B-factory experiments lowed by an array of CsI(Tl) crystals that serves as an electromagnetic calorimeter for detecting γ-rays and π0- As it is clear from the cross section plot in mesons and identifying electrons. These systems are all Fig. 11b, e+e− annihilations with c.m. energies between situated inside a large superconducting solenoidal mag- 9.4 and 10.8 GeV, the energy range that was accessible to net coil with an external iron magnetic-flux return yoke BaBar and Belle, are good sources of particles containing + − that is instrumented to identify muons and detect KL b-quarks and b¯b quark pairs. In addition, e e collisions mesons. In addition, BaBar and Belle had elaborate, in this energy range also produce relatively large numbers high-precision vertex measuring systems comprised of of particles containing c-quarks and cc¯ quark pairs. The silicon-strip detector arrays that immediately surrounded processes involved are illustrated in Fig. 13 and described the interaction point and were essential for their CP - in the following. violation measurements. Charmed quark production in B-meson decays: B¯ mesons have a bq¯ quark content (¯q =u ¯ or d¯), a mass of 5.28 GeV, and a lifetime of approximately 1.5 ps. In + − 14 The suppression of strong interaction processes in which no quark Ecm = 10.58 GeV e e collisions they are produced in lines connect the initial to the final state is known as the Okubo- BB¯ pairs that are nearly at rest and with no accompa- Zweig-Iizuka (OZI) rule (2; 199; 200). nying particles. The primary decay mechanism is the 16

Ecm/2, which is precisely known from the operating conditions of the collider. This provides two powerful and

Silicon-strip weakly correlated experimental signatures for identifying DIRC PID KL-μ idenﬁer vertex detector events of interest: device magnet coil X ∗ ∆Ecm ≡ Ecm/2 − Ei = 0 (4) + i DIRC e readout - e and s 2 X ∗ 2 Mbc ≡ (Ecm/2) − | ~pi | = mB, (5) i

∗ ∗ where Ei and ~pi are the c.m. energy and three- BaBar Detector momentum of the ith decay product of the B meson candidate. The experimental resolutions for ∆Ecm and Mbc FIG. 12 A schematic view of the BaBar detector. Here the bulk of depend upon the decay mode that is under considera- the charged particle tracking information is provided by a cylindrical gas drift chamber. Particle identification (PID) is provided by tion; typical rms values are 10∼15 MeV for ∆Ecm and the reconstruction of Cerenkov light cones produced in a barrel-like 2.5∼3 MeV for Mbc. For a more detailed discussion of array of quartz bars in a device named the “DIRC.” The electron these variables and an improved definition of Mbc for and positron beams traverse the detector in a vacuum chamber + − that is surrounded by magnetic bending and focusing devices. The asymmetric e e colliders, see sec. 7.1.1.2 of ref. (214). beams collide near the center of the cylindrical vertex detector. The X(3872), the first of the non-standard XYZ meson candidates to be seen, was discovered by Belle as + − Color-suppressed B-meson decays Two-photon fusion processes a narrow peak in the π π J/ψ invariant mass distri-

+ − c _ bution for B → Kπ π J/ψ decays (53). Figure 14 c

+ − PC -+ ++ -- _ shows the Mbc, ∆Ecm and M(π π J/ψ) distributions J =0 ,1 ,1 c − − + − c for B → K X(3872); X(3872) → π π J/ψ event can- JPC=0±+,2±+ didates, where the events in each plot are selected from the signal peak regions of the other two distributions. The background under the signal peaks is mainly com- Double charmonium producon Inial-state radiaon binatorial, i.e. where one of the tracks assigned to the e reconstructed B meson is, in fact, a decay product of JPC=1-- the accompanying B¯. The X(3872) is discussed in detail

c _ below in Section V.A.

_ _

e c c _ e a) b) c) JPC=0±+

FIG. 13 Processes that produce cc¯ pairs in e+e− collisions near Ecm = 10.6 GeV: a) B → K(cc¯) decays; b) two-photon fusion processes; c) e+e− annihilation into ccc¯ c¯; and d) initial state radiation. weak interaction transition b → c with the emission of a virtual W − boson. In about 15% of these decays, the W − materializes as ac ¯- and s-quark. Figure 13a + − illustrates this process for the cases where the s-quark FIG. 14 The a) Mbc, b) ∆Ecm and c) M(π π J/ψ distribu- combines with the spectatorq ¯ to form a K meson. In tions for B− → K−π+π−J/ψ decays (from ref. (54)). The narrow these events the system recoiling against the K meson π+π−J/ψ mass peak in c) is the X(3872) signal. contains a cc¯ quark pair and, to the extent that the originalq ¯ quark is a passive spectator to the decay Two-photon fusion processes: In the two-photon fusion process (the “factorization approximation” (212)), the process, both the incoming e− and e+ radiate photons cc¯ pair has J PC quantum numbers of 0−+, 1−− and 1++, that subsequently interact via the diagram shown in which ﬁnds support in the experimental results (213). Fig. 13b. In this process, the quark-antiquark pair is pro- 4 Sizeable corrections to the factorization approximation duced with a probability that is proportional to eq, where may occur. eq is the quark charge; since ec = 2/3, this favors cc¯ pro- Since the B mesons are produced in pairs with no ac- duction. This process is dominated by events where both companying particles, the c.m. energy of each meson is of the incoming photons are nearly real (q2 ' 0), in which 17

+ − case both the e and e scatter at very small angles and 10.58 GeV and, when an Eγ ' 4.5 GeV γ is radi- are undetectable. For these “untagged” events the net ated, the e+e− annihilation occurs at a c.m. energy of 0 transverse momentum pT of the cc¯ system’s decay prod- Ecm ' 4 GeV, which is in the cc¯ threshold region. As + − ucts is very small, and this provides an important exper- a result, e e collisions at Ecm = 10.58 GeV can di- imental signature. The allowed J PC quantum numbers rectly produce 1−− cc¯ states in association with a sin- for cc¯ systems produced via this process are restricted to gle high-energy γ. Advantages of measurements that ±+ ±+ 0 3 0 and 2 . The conventional χc2 (2 P2) charmonium exploit this initial state radiation process (isr) are that state was first seen by Belle (215) as the distinct peak they can be made parasitically with other measurements near 3930 MeV in the DD¯ invariant mass distribution in and a broad range of reduced energies can be accessed selected, low pT γγ → DD¯ candidate events shown in at the same time. Although isr is a higher-order QED Fig. 15b. process and, thus, suppressed, the very high luminosi- Double charmonium production: Prior to the opera- ties provided by the B-factory colliders have made it tion of the B factories, computations based on a QCD- a valuable research tool. Figure 16b shows the invari- motivated effective field theory, NRQCD, predicted that ant mass distribution from BaBar for π+π−J/ψ events prompt inclusive J/ψ production in continuum e+e− an- produced in association with a high energy γ (84). In nihilation events at Ecm ≈ 10 GeV would be dominated this measurement, the isr γ was not detected and, in- by e+e− → J/ψg and e+e− → J/ψgg processes, where g stead, its existence was established by selecting events + − denotes a gluon, and that e e → J/ψcc¯ processes would with a missing mass, Mmiss, consistent with zero, where p P ∗ 2 P ∗ 2 ∗ ∗ account for no more than 10% of the inclusive J/ψ pro- Mmiss ≡ (Ecm − i Ei ) − | i ~pi | and Ei and ~pi duction rate (216). One of the surprises from the B fac- are the c.m. energy and three-momentum of the ith tories was the Belle observation that the e+e− → J/ψcc¯ detected particle. The π+π−J/ψ mass distribution in process is, in fact, the dominant mechanism for prompt Fig. 16b is dominated by an unexpected distinct peak J/ψ production, accounting for approximately 60% of near 4.26 GeV that BaBar called the Y (4260). Its pro- the total rate for these events (217). Charge conjugation duction from a single virtual photon ensures that the invariance requires that the cc¯ system recoiling against J PC quantum numbers of the Y (4260) must be the same the J/ψ have even charge conjugation parity.15 Fig- as those of the photon, i.e. 1−−. There are no unas- ure 16a shows Belle’s measured distribution of masses signed 1−− charmonium states near 4260 MeV and, so, recoiling from the J/ψ in inclusive e+e− → J/ψ + X the Y (4260) cannot be a conventional cc¯ meson. The q ∗ 2 ∗ 2 Y (4260) is discussed in detail below in Section V.C. production, Mrecoil = (Ecm − EJ/ψ) − |~pJ/ψ| , where ∗ ∗ EJ/ψ and ~pJ/ψ are the c.m. energy and three-momentum of the J/ψ. In the figure, clear peaks corresponding to 0 1 3 2. The BESIII experiment in the τ-charm threshold region the ηc, χc0 and ηc, the well established 1 S0, 1 P0 and 21S charmonium states, respectively, are evident (79). 0 For J PC = 1−− states such as the Y (4260), the BESIII In addition, there is a distinct peak near 3940 MeV that experiment has the advantage that they can be directly cannot be identified with any known charmonium state; produced in e+e− annihilation, e.g., e+e− → Y (4260) → Belle called this peak the X(3940). π+π−J/ψ, with no isr photons and their associated lu- The established charmonium states seen in Fig. 16a minosity penalty. all have even charge conjugation and zero angular mo- By working with exclusive events near threshold, and mentum (J = 0). The absence of signals for the χ c1 exploiting the possibility of applying energy and momen- and χ , which are in the same mass range and have c2 tum kinematic constraints that improve resolution and even C, provides some circumstantial evidence that the signal to noise, the BESIII experiment is uniquely able e+e− → J/ψ + (cc¯) production process favors (cc¯) sys- to isolate events with complex final states. This provides tems with J = 0. opportunities that are not available to B-factory and Initial state radiation: In energy e+e− colliders, the hadron collider experiments that are mostly restricted initial state e+ or e− occasionally radiates a high energy to studies of processes that include a final-state J/ψ or γ and the e+ and e− subsequently annihilate at a cor- √ ψ0 that decays to a pair of leptons. This is because dilep- respondingly reduced c.m. energy: E0 = E 1 − x, cm cm ton events are experimentally distinct, simple to recon- where x = 2E /E is the fraction of the radiating γ cm struct, and have low combinatorial backgrounds. In con- beam particle’s c.m. energy that is carried off by the pho- trast, the BESIII experiment routinely isolates clean sig- ton. B-factory experiments typically operate at E = cm nals of charmonium states that only decay to complex multihadron final states and are plagued by huge combinatorial backgrounds in B-factory and hadron-collider 15 Two charmonium states with the same C-parity can be produced in two-photon annihilation processes, but these are sup- environments. For example, BESIII has made studies of pressed relative to single-photon annihilation by a factor of reactions that have an ηc and/or an hc in the final state, 2 (αQED/αs) (218). by selecting and reconstructing complex, multihadron fi- 18

b) M(DD): 3.91-3.95 GeV/c2 p (DD)≤ 0.05 GeV/c a) b) T a) χc2 ‘ c 2 c c c D

c D _

c) Events/10 MeV/ π+ d) b)

b) c π- a) c _ a) c 2 pT (DD) (GeV/c) M(DD) (GeV2/c ) D c M(DD) (GeV/ c c ) c

c c c D J/ψ J/ψ a) The p distribution for γγ → DD¯ event candidates with 3.91 < M(DD¯) < 3.95 GeV. b) The M(DD¯) distribution for event _

FIG. 15 T c D candidates with p < 0._ 05 GeV (from ref. (215)). Tc D c) c)

2 40 2 d) X(3940) 4 + d) 150 η (2S) 2 10 π

a) c + c π 3 c b) 10 c π- c π- c 30 2 ηc χc0 10 c ! c 10 100 c J/ψ J/ψ c J/ψ J/ψ

N/20 MeV/c 1 20 3.6 3.8 4 4.2 4.4 4.6 4.8 5 Events / 20 MeV/c Evts/20 MeV/

50 10

0 0 2 2.5 3 3.5 4 4.5 3.8 4 4.2 4.4 4.6 4.8 5 2 m(+π+-π-J/ψ) (GeV/c22) Mrecoil(J/ψ) GeV/c M(π π J/ψ) (GeV/c )

FIG. 16 a) The distribution of masses recoiling from the J/ψ in inclusive e+e− → J/ψX events from ref. (79). b) The π+π−J/ψ + − + − invariant mass distribution for e e → γisrπ π J/ψ events from ref. (84)

16 nal states. lent to M(γηc) – where there is a large hc → γηc signal at

This capability is illustrated by a recent BESIII study mhc = 3525 MeV on a relatively small background. With + − + − + − + − of the e e → π π hc process at c.m. energies in the this clean e e → π π hc event sample, the BESIII ex- ± vicinity of the Y (4260) peak, in which they detected the periment discovered a narrow enhancement in the π hc hc via its decay to hc → γηc, which is its dominant decay invariant mass distribution that is a candidate for an elec- mode with a branching fraction of 51 ± 6% (9). To ac- trically charged charmonium-like four-quark state, called + − + − complish this, they selected e e → π π γηc events, the Zc(4020) (93), as discussed below in Section VI.B. where the candidate ηc mesons were reconstructed in Reconstruction of events with an hc in the final state has one of 16 different exclusive hadronic decay channels, never been accomplished in B-factory or hadron-collider and applied conservation of energy and momentum con- experiments. straints. Figure 17a shows a scatter-plot of the mass recoiling against the γπ+π− particle combination (vertical) + − vs. the mass recoiling against the π π pair (horizontal) 3. Future prospects for selected events, where a distinct cluster of events near recoil recoil Mγπ+π− ' mηc and Mπ+π− ' mhc , is evident (89). Fig- The BESIII experiment is scheduled to continue to run recoil ure 17b shows the projection of events with Mγπ+π− in until 2025, with some minor upgrades to the detector and recoil the BEPCII collider. There are serious discussions in the ηc mass region onto the Mπ+π− axis – which is equiva- China (220) and in Russia (221) about the possibility of a new facility in the charm quark threshold energy region with a luminosity of order 1035cm−2s−1, a two-order-of- 16 The ηc is the S = 0 hyperfine partner of the J/ψ and the hc is magnitude increase over that of BEPCII. the S = 0 partner of the (χc0, χc1, χc2) S = 1, P-wave triplet of cc¯ states. Although the existence of the hc was predicted in SuperKEKB is a major upgrade upgrade to the KEKB 1974, it remained undiscovered until thirty years later, when it facility with the ambitious goal of a factor of forty in- 0 0 was found in ψ → π hc decays by the CLEOc experiment (219). crease in instantaneous luminosity (to 8 · 1035 cm−2s−1) 19

+ - + - e e ! π π (γηc) + - + - a) b) e e ! π π (γηc) BESIII

hc!γηc

mηc

m hc

FIG. 17 a) A scatter-plot of M recoil (vertical) vs. M recoil for e+e− → π+π−γη candidate events from ref. (89). The cluster of events γπ+π− π+π− c + − + − + − is the signal for the e e → π π hc; hc → γηc reaction chain. b) The projection of events with γπ π recoil mass near mηc (i.e., between the horizontal dotted lines in panel a) on the M recoil (= M(γη )) axis. The peak near 3525 MeV is the h → γη decay signal. mηc π+π− c c c that will start operation in late 2017 with a targeted to- of varying degree of complexity, and neutrinos. As an ex- tal integrated luminosity of 50,000 fb−1 (50 inverse at- ample, a schematic view of the CDF detector is provided tobarns) by about 2025 (222). BelleII is an upgraded in Fig. 18. version of the Belle detector that is being constructed by a large international collaboration to exploit the physics CDF Detector opportunities provided by SuperKEKB (223). While the main emphasis of the BelleII program is on searches for new, beyond the Standard Model physics processes, ﬂux return iron electromagnec a high-sensitivity program of studies of hadron spec- calorimeter _ troscopy is planned (see, e.g., ref. (224)). hadron p calorimeter

tracker

p B. High-pT detectors at high-energy hadron colliders muon detectors Between 1985 and 2011, the high-energy frontier was centered on the CDF and D0 experiments at the Fermi- lab Tevatron that studied particles produced in proton- magnet coil vertex detector antiproton collisions at a c.m. energy of 1.96 TeV. This frontier moved to CERN in 2010 at the LHC, when the ATLAS and CMS experiments started initial operations FIG. 18 A schematic view of the CDF detector. Here the tracking device is a cylindrical gas drift chamber. The electromagnetic with proton-proton collisions at 7 TeV. These experi- calorimeters (in red) are comprised of alternating layers of plastic ments were designed to study processes at high momen- scintillators and lead sheets; the hadron calorimeters (in blue) are tum transfer using large, multi-story magnetic detectors similar structures with lead replaced by steel. surrounding the regions where the beams were brought into collision. The detector designs, while different in almost all details, follow a common concept. In the in- nermost region, closest to the collision region, vertex de- 1. The Tevatron experiments tection is provided by silicon microstrip and pixel devices that measure trajectory coordinates with about 10 The highest priority of the Tevatron program was the micron precision. The vertex detectors are surrounded discovery of the top quark, the last undiscovered quark of by charged-particle tracking devices to give more com- the Standard Model. Its observation was simultaneously plete trajectory information. Massive calorimeters sur- announced by the CDF (225) and D0 (226) collabora- round the tracking systems and detect γ-rays, identify tions in March 1995. The Tevatron experiments have electrons, and measure the energies of hadronic parti- also contributed to the spectroscopy of heavy hadrons. cles. The only particles that escape the calorimeters are CDF (58) and D0 (61) were the first experiments to con- muons, which are identified in external muon detectors firm Belle’s observation of the X(3872). These experi- 20

ments made the important observations that character- inclusive π+π−Υ(1S) mass distribution at a c.m. en- istics of X(3872) production in hadron collisions were ergy of 8 TeV in search for a bottomonium-like counter- very similar to those of the ψ0, including strong signals parts of the X(3872) or Y (4260). No dramatic signals for prompt production via QCD processes. In addition, were found, but the sensitivity of these searches was not CDF performed the most precise measurement to date of very high. Cross-section times branching-fraction upper the X(3872) mass (60). limits for new state production that are ∼6.5% of the In Fig. 19a, the ∆M = M(π+π−µ+µ−) − M(µ+µ−) Υ(2S) → π+π−Υ(1S) production were established (71); distribution for events in the central part of the D0 de- this is about the same as the CMS measured ratio for tector (with pseudorapidity17 |y| < 1) are shown as solid X(3872) → π+π−J/ψ and ψ0 → π+π−J/ψ production: circles; that for events in the endcap regions (1 < |y| < 2) 6.6 ± 0.7% (71). The inclusive M(π+π−Υ(1S)) distribu- are shown as open circles (61). The ratio of the num- tion measured at ATLAS is shown in Fig. 21b. ber of central events in the X(3872) peak (near ∆M = 775 MeV) to that in the ψ0 peak (near ∆M = 589 MeV) is 0.43±0.08 and in good agreement with the correspond- C. LHCb - forward detector at LHC ing ratio for endcap events, namely 0.45 ± 0.11. The D0 experiment made similar comparisons of X(3872) and ψ0 The LHCb experiment is the first hadron-collider ex- production rates for a number of other quantities and periment that is dedicated to heavy flavor physics. Its found good agreement in all cases, as shown in Fig. 19b. detector (233; 234), shown in Fig. 22, is a single-arm for- This is a strong indication the X(3872) and ψ0 produc- ward spectrometer that captures heavy-quark production tion mechanisms are the same. This is discussed further cross-sections that are comparable to those in the high- below in Section V.A. pT , central detectors at LHC, but concentrated in a com- In the proper time distribution for X(3872) → pact solid angle near the forward direction (0.8o < θ < π+π−J/ψ vertex positions, shown in Fig. 20a, CDF 15.4o). Because of this concentration, a much smaller found that most of the X(3872) production in pp¯ colli- number of electronic channels are required and, thus, sions was due to prompt QCD processes; only 16 ± 5% of there is a smaller data record for each event. As a result, the signal is from displaced vertices that are characteris- the LHCb data acquisition system can record events at a tic of open-bottom-particle decays (227). The displaced- higher frequency than the high-pT detectors; the LHCb vertex fraction for ψ0 production is somewhat larger, recorded data at a 5 kHz rate in Run-I (2011-12) and 28 ± 1%, but comparable. In 2009, with an order-of- 12.5 kHz in Run-II (2015-present), which are about a magnitude larger data set, CDF reported the most pre- factor of five higher than the corresponding rates for the cise single mass measurement to date, M(X(3872)) = ATLAS and CMS detectors. Furthermore, in contrast 3871.61 ± 0.16 (stat) ± 0.19 (syst) MeV, based on a fit with the central detectors, most of the trigger bandwidth to the approximately 6K event X(3872) → π+π−J/ψ is dedicated to heavy flavor physics and includes dimuon invariant mass peak shown in Fig. 20b (60). This events with low transverse-momentum thresholds and mass value is indistinguishable from the D0D¯ ∗0 threshold purely hadronic events that have secondary decay ver- mass, (mD0 +mD∗0 ) = 3871.68±0.10 MeV (9), with high tices that are well separated from the pp collision points. precision, and this is one of the most striking properties The price of these capabilities is a limit on the tolerable of the X(3872). instantaneous luminosity of 4·1032 cm−2s−1, which is almost two orders of magnitude lower than the maximum values that the LHC is capable of delivering. Therefore, 2. The LHC experiments integrated luminosities of LHCb data sets are smaller than that of CMS and ATLAS data sets. This makes The new-generation of high-pT hadron collider ex- CMS and ATLAS experiment competitive in detection periments, ATLAS (228) and CMS (229), are produc- of some B decays to simple final states with muon pairs. ing complementary results on the production of exotic The LHCb detector is equipped with two ring-imaging hadrons. For example, CMS has measured the pT de- Cherenkov (RICH) detectors that provide good suppres- pendence of the prompt X(3872) production cross sec- sion of pion backgrounds for final states that include tion (71) and found it to be about a factor of four be- kaons and protons. The central detectors at LHC and low an NRQCD-based theoretical prediction (230); these Tevatron lack efficient hadron identification and, thus, results are shown in Fig. 21a. CMS (231) and AT- have to cope with high backgrounds in such channels. LAS (232) have also performed measurements of the The Tevatron experiments also had the disadvantage of the lower cross-sections. The production cross-sections for heavy flavors at the LHC are three orders of magnitude larger than those 17 Pseudorapidity is defined as y = − ln[tan(θ/2)], where θ is the at the e+e− B factories. Even after correcting for the polar angle. smaller reconstruction efficiencies and shorter accumu- 21

a) D0 / b) D0 / X(3872)-yield/ψ’-yield

pT |y| θπ δl iso. θμ quanty

FIG. 19 a) ∆M = M(π+π−µ+µ−) − M(µ+µ−) distributions for central events (solid points) and end-cap events (open circles) from the D0 experiment (61). The similarity between the relative signal yields in the X(3872) and ψ0 peaks indicate that the production mechanism + − for the two states has similar dependence on pseudorapidity (|y|). b) Similar comparisons are shown for other quantities: pT (π π J/ψ); cos θπ; proper decay length δ`; jet isolation parameter; and cos θµ (for details, see ref. (61)).

a) X(3872)!π+π-J/ψ CDFII b) CDFII

FIG. 20 a) The proper time distribution of π+π−J/ψ vertices for events in the region of the X(3872) peak from ref. (227). The main source of X(3872) are prompt pp¯ interactions (turquoise peak); production via open-bottom-particle decays (yellow exponential) is only 16 ± 5% of the total. b) The data points in the upper panel show the invariant mass distribution for X(3872) → π+π−J/ψ candidates in the CDF detector (60); the solid curve shows the result of an unbinned likelihood fit and the dashed curve shows the background component. The lower panel shows the fit residuals. lated beam time, the Run-I LHCb data samples of B mination of X(3872)’s J PC quantum numbers (56; 57); decays to J/ψ and light hadrons are an order of magni- confirm the Z(4430)+ structure (46; 111); and demon- tude larger than those accumulated during the ten-year strate its consistency with a Breit-Wigner (BW) reso- operating lifetimes of the B factories. The signal purity is nance hypothesis by means of an Argand diagram (46). even slightly better than in BaBar or Belle, thanks to the Recently, LHCb has performed the first amplitude anal- long visible lifetimes of the lightest open-bottom-flavored ysis of B+ → J/ψφK+ decays that made the first de- hadrons. The identification of tracks produced from a termination of the quantum numbers of X(4140) and es- displaced vertex reduces combinatorial backgrounds as- tablished the existence of three other J/ψφ mass peaks: sociated with additional particles produced in the pri- the X(4274), X(4500) and X(4700) (49; 50). A big ad- mary pp collisions as well as those from the decays of vantage of collecting data at a hadronic collider is the si- 0 the companion bottom-flavored hadron. The large signal multaneous accumulation of large B, Bs, Bc and Λb data sample enabled the LHCb group to make the first deter- sets, as opposed to B factories, where Bs samples require 22

a) b) ϒ(2S)

ϒ(2S)

mB+mB*

FIG. 21 a) The pT dependence of the prompt X(3872) diﬀerential production cross section measured by CMS (71). The red curves show a theoretical prediction that is based on an NRQCD calculation. b) The inclusive M(π+π−Υ(1S)) invariant mass distribution measured by ATLAS (232). Aside from peaks corresponding to Υ(2S) and (Υ(3S)) decays to π+π−Υ(1S), no additional structures are evident. The location of the BB¯∗ mass threshold is indicated.

the most precise measurement to data of the branching fraction ratio (70) LHCb detector B(X(3872) → γψ0) = 2.46 ± 0.70, (6) µ5 B(X(3872) → γJ/ψ) µ4 µ3 µ2 PID µ1 Fe Fe Tracking Fe which is an important quantity for distinguishing

PID HCAL HCAL ECAL ECAL between different theoretical interpretations of the p p X(3872). All of the LHCb results on hadron spectroscopy that have been published to date have been based on analyses of Run-I data; i.e. with integrated luminosities as −1 high as 3 fb at Ecm(pp) = 7 − 8 TeV. The on-going Run-II is expected to conclude in 2018 with an additional 8 fb−1 of integrated luminosity collected mostly at Ecm(pp) = 13 TeV, where the heavy-flavor produc- FIG. 22 The LHCb detector. Vertex detection and tracking is tion cross-sections are about a factor of two higher (235). provided by an array of silicon-strip detectors that surround the pp interaction point, a large-area plane of silicon-strip detectors lo- A major upgrade of the LHCb detector is currently in cated upstream, and three planes of silicon-strips and straw drift preparation (236), which will allow collecting data at tubes located downstream of a 4 Tm bending magnet. Charged 2 · 1033 cm−2s−1 starting around 2021. About 50 fb−1 particles are identified by two ring-imaging Cherenkov (RICH) de- of integrated luminosity is expected by 2030. A second tectors. major upgrade is under consideration, which would allow data taking with an instantaneous luminosity of 2 · 1034 cm−2s−1 with the goal of a final data sample correspond- dedicated data runs, and B mesons and Λ0 baryons are c b ing to 300 fb−1 by the end of LHC operations. not accessible. The large sample of Λb events in LHCb’s Run I data sample led to the discovery of pentaquark- + + like J/ψp mass structures Pc(4450) and Pc(4380) in 0 − IV. HEAVY-LIGHT EXOTIC HADRON CANDIDATES Λb → J/ψpK decays (47). LHCb is equipped with an electromagnetic calorime- A. Charm ter. However, γ-ray and π0 reconstruction efficiencies are much lower than in the e+e− experiments and, because The modern quark model (40; 237) predicts a rich spec- of the lack of vertex information, combinatorial back- trum of heavy-light mesons containing a heavy quark, grounds for photons are large. Nevertheless, exploration Q, and an anti-light quark, q = u, d, s. In contrast to of channels with one γ-ray, or π0 or η is possible. For quarkonium, where the states are best characterized by example, Fig. 23 shows LHCb signals for γJ/ψ and γψ0 the QQ¯ spin S and the relative orbital angular momen- decays of the X(3872). These data were used to provide tum L, the heavy-light Qq¯ mesons are expected to be 23

a) b) LHCb LHCb

MeV MeV events/15 events/10 M(J/ψγK+) M(ψ’γK+)

LHCb LHCb MeV MeV events/10 events/10

M(J/ψγ) M(ψ’γ)

FIG. 23 a) The upper panel shows the M(J/ψγK+) distribution for B → X(3872)K+; X(3872) → J/ψγ candidate events with M(J/ψγ) within ±3σ of 3872 MeV, where σ is the J/ψγ mass resolution. The lower panel shows the M(J/ψγ) distribution for events + + 0 with M(J/ψγK ) within 3σ of mB+ = 5.28 GeV. b) Corresponding plots for the B → X(3872)K ; X(3872) → ψ γ candidate events. The curves are projections of ﬁts described in ref. (70).

best described by ~jq, the orbital angular momentum L~ One of the biggest surprises from the B factories was plus the spin of the light quark ~sq, since the heavy quark the BaBar discovery of a very narrow state decaying 0 spin interactions are suppressed by its large mass. to Dsπ with mass near 2317 MeV produced in inclu- + − + 0 For S-wave Qq¯ systems, jq = 1/2 and there are two sive e e → Ds π + X interactions. CLEO quickly P − ∗ meson states, one with J = 0 and the other with confirmed the BaBar Ds0(2317) discovery and reported P − J = 1 , corresponding to antiparallel and parallel ~jq the observation of a second narrow state decaying to ∗ 0 and ~sQ configurations. For P-wave systems, jq can be Ds π with mass near 2460 MeV that is now called either 1/2 or 3/2, and two doublets of meson states are the Ds1(2460) (241). The Belle experiment established P + ¯ expected: one for jq = 1/2 that contains a J = 0 and the production of both states in exclusive B → DDsJ + P + ∗ 1 meson, and the other for jq = 3/2 with a J = 1 decays, observed the Ds1(2460) → Ds γ decay mode, + and a 2 meson. and established the spin-parity of the Ds1(2460) to be In the charm quark sector (Q = c) the non-strange J P = 1+ (242). (q = u, d) S-wave states are the well established pseudo- The latest world-average results for their masses and scalar D and vector D∗ isospin doublets. The cor- 95% CL upper limits on their natural widths are (9): + responding strange (q = s) mesons are the Ds and ∗+ D∗ (2317) : M = 2317.7 ± 0.6 MeV Γ < 3.8 MeV Ds isospin singlets. The “hyperfine” mass splitting, s0 ∗ ∗ m1− − m0− , for the D -D and Ds -Ds are nearly equal; Ds1(2460) : M = 2459.5 ± 0.6 MeV Γ < 3.5 MeV. for both systems it is about 140 MeV (9). (7) The P-wave D mesons, which are hard to produce and P + tend to be wide and overlapping, are difficult to study Since the J = 1 quantum numbers of the Ds1(2460) + experimentally. For example, in the q = u, d system, the match those expected for the P-wave js = 1/2 1 state, P + ∗ jq = 1/2, J = 0 D0(2400)-meson and the jq = 1/2, and the mass Ds1-Ds0 mass splitting, 141.8 ± 0.8 MeV, P + J = 1 D1(2430) meson have ∼ 300 MeV natural closely matches the hyperfine splitting measured in the S- widths and their properties have only recently been es- wave systems, a natural interpretation of these two states + tablished (238; 239; 240). In the js = 3/2 cs¯ system, is that they are the “missing” P-wave js = 1/2 0 and + ∗ the very narrow (Γ = 0.92±0.05 MeV) Ds1(2536)-meson 1 cs¯ states. Since the Ds0 (Ds1) mass is below the ∗ ∗ and the relatively narrow (Γ = 17 ± 4 MeV) Ds2(2573) DK (D K) mass threshold, it can only decay via isospin- meson were well established in the 1990s but, prior to violating processes, which accounts for its small width.18 + + the operation of B factories, the js = 1/2, 0 and 1 However, their masses, which are much lower than states had still not been identified. According to the quark model, these states were expected to have masses above the mD(∗) + mK threshold and it was suspected ∗ 18 + ∗ that strong decays to DK and D K final states made A 0 assignment for the Ds0 is supported by the absence of any ∗ them wide, and difficult to see. evidence for Ds0 → Dsγ decays. 24

quark-model expectations for P-wave cs¯ states,19 are a et al. (184). The authors examined the J P = 0+ and puzzle. This is illustrated in Table III, where masses of J P = 1+ states that are produced when DK and D∗K cd¯ mesons are compared with those of the corresponding scattering operators are included with the standard cs cs¯ mesons. The cs¯-cd¯ mass differences for the S-wave 0− meson operators. The analysis established the existence and 1− mesons are both very close to 100 MeV, as is of below-threshold poles with binding energies consistent + + ∗ also the case for the 1 and 2 jq = 3/2 P-wave mesons. with Ds0(2317) and Ds1(2460). In the quark model, the corresponding cd¯ and cs¯ mesons have the same configurations, and the ≈ 100 MeV mass difference reflects the s and d quark mass difference. B. Bottom

Recently the D0 collaboration reported evidence for TABLE III Comparison of the masses of the low-lying Ds (cs¯) 0 ± ¯ ∗ a possible four-quark state that decays to Bs π , where and charged D (cd) meson states. Here the Ds0(2317) and the 0 0 + + Ds1(2460) are identified with the P-wave, 0 jq = 1/2 and 1 the Bs decays via Bs → J/ψφ (48). In the analysis, 0 jq = 3/2 mesons, respectively. The masses are taken from ref. (9). 5,500 reconstructed Bs → J/ψφ decay candidates were paired with a charged particle that was assumed to be P ¯ L jq J m(cd) m(cs¯) mcs¯-mcd¯ a pion. Multiple entries for a single event, which occur (MeV) (MeV) (MeV) when more than one pion candidate passes the track se- 0 1/2 0− 1869.6 ± 0.1 1968.3 ± 0.1 98.7 ± 0.1 lection criteria, were suppressed by limiting the angular − 0 20 1 2010.3 ± 0.1 2112.1 ± 0.4 101.7 ± 0.4 separation of the Bs candidate and the charged track. 0 ± 1 1/2 0+ 2318 ± 29 2317.7 ± 0.6 0.3 ± 29 The resultant Bs π invariant mass spectrum, shown in 1+ 2430 ± 36 2449.5 ± 0.1 30 ± 36 Fig. 24a, has a narrow structure that is approximately + 3/2 1 2423.2 ± 2.4 2335.1 ± 0.6 111.9 ± 2.4 60 MeV above the mBs + mπ threshold. 2+ 2464.3 ± 1.6 2571.9 ± 0.8 107.6 ± 1.8 The solid curve in Fig. 24a shows the results of a fit that uses a resolution-broadened BW line shape to represent a signal (dotted curve) plus an incoherent background modeled by an empirical shape that was de- This is not the case for the D∗ (2317) and D (2460) s0 s1 termined from B0-mass sideband events (for non-B0 mesons, if they are taken to be the j = 1/2 and j = 3/2 s s q q background) and MC-simulated inclusive B0 produc- P-wave mesons, in which case the masses of the cs¯ and cd¯ s tion events (for combinatoric backgrounds associated systems are nearly equal, in spite of the s- and d-quark with real B0 mesons). The fitted mass and width of mass difference. This puzzling behavior led to specu- s the peak, which the D0 group called the X(5568), are lation that these states may contain four-quark compo- +0.9 nents, either in a QCD tetraquark arrangement or as M = 5567.8 ± 2.9 (stat)−1.9 (syst) MeV and Γ = 21.9 ± +5.0 molecule-like structure formed from D and K mesons. 6.4 (stat)−2.5 (syst) MeV. The signal significance, includ- In the tetraquark picture (126; 243; 244; 245), the ing look-elsewhere and systematic-uncertainty effects, is ∗ 0 5.1σ. The X(5568) signal is also evident in the B0π± Ds0(2317) could be a [cq][¯sq¯ ] state, in which case a rich s spectrum of similar states is expected to exist. In par- spectrum without the pion direction restriction, shown ticular there should be electrically neutral and doubly in Fig. 24b, albeit with reduced significance. The ratio + ± of the number of B mesons that originate from X(5568) charged partners. A BaBar study of Ds π systems s produced in e+e− annihilations found no states in the decays to all Bs mesons, is determined for the D0 accep- ∗ tance to be ρD0 = (8.1 ± 2.4)%. Ds0(2317) mass region in either channel (246) and Belle X reported upper limits on the production of neutral or In an alternative approach, the authors extracted a ¯ + ± B0π± signal by performing fits of the number of B0 doubly charged partner states in B → DDs π that are s s an order of magnitude below isospin-based predictions, events in the J/ψφ mass distribution in 20-MeV inter- 0 ± making the tetraquark option implausible (247). vals of M(Bs π ). The results of that fit confirm that the ∗ observed signal is due to events with genuine B0 mesons The Ds0 and Ds1 lie about 40 MeV below the DK s ∗ 0 and D K mass thresholds, respectively, suggesting that and eliminates the possibility that some non-Bs process they might be DK(∗) molecules (248), or mixtures of a may mimic the signal. DK(∗) molecule and a conventional cq¯ meson (249). The To confirm the production of the X(5568) with an in- ∗ (∗) dependent sample, D0 studied events in which the B0 idea that the Ds0(2317) and Ds1(2460) may be DK s 0 bound states was studied with lattice QCD by Leskovec meson decayed semileptonically (250). Decays Bs →

19 20 p 2 2 A recent quark calculation of the masses of the jq = 1/2 P-wave The angular separation requirement was ∆R < ∆η + ∆φ , cs¯ mesons ﬁnds 2484 MeV for the 0+ and 2549 MeV for the 1+ where η = ln[tan θ/2] is the “pseudorapidity” and φ is the az- states (237). imuthal angle. 25

90 120 D0 Run II, 10.4 fb-1 D0 Run II, 10.4 fb-1 80 2 a) 2 b) DATA 100 70 Fit with background shape fixed Background 60 Signal 80

50 60 40

N events / 8 MeV/c 30 N events / 8 MeV/c 40 DATA 20 Fit with background shape fixed 20 Background 10 Signal

0 0 155.5 5.55 5.6 5.65 5.7 5.75 5.8 5.85 5.9 205.5 5.55 5.6 5.65 5.7 5.75 5.8 5.85 5.9 15 10 10 5 5 0 0 -5 -10 -5 -15 Residuals (Data-Fit) -10 Residuals (Data-Fit) -20 -25 5.5 5.55 5.6 5.65 5.7 5.75 5.8 5.85 5.9 5.5 5.55 5.6 5.65 5.7 5.75 5.8 5.85 5.9 0 ± 2 0 ± 2 m (B S π ) [GeV/c ] m (B S π ) [GeV/c ]

0 ± FIG. 24 The M(Bs π ) distribution together with the background distribution (dashed curve) and ﬁt results (solid curve) for events a) 0 ± with and b) without the application of the Bs -π opening angle requirement (from ref. (48)).

of ref. (48). The combined signiﬁcance of the signal in 250 the two channels is 5.7 standard deviations. 2 200

150 The LHCb group searched for X(5568) production -1 D0 preliminary, 10.4 fb in pp collisions at Ecm = 7 − 8 TeV (251). With DATA 0 0 − + 100 44,000 Bs → J/ψφ and 65,000 Bs → Ds π recon- Fit with background shape fixed N events / 8 MeV/c structed events and a superior signal-to-background ra- Background 0 ± 50 Signal tio, no peaking structure in the Bs π invariant mass distribution is observed in the X(5568) mass region (see 0 the left panel of Fig. 26). Upper limits on ρLHCb of 5.55 5.6 5.65 5.7 5.75 5.8 5.85 5.9 X 0 ± 2 < 1.2% (< 2.4%) for p (X) > 5 GeV (> 10 GeV) are m (B S π ) [GeV/c ] T established at the 95% C.L. In addition, the CMS group found no sign of an X(5568) peak in a preliminary analy- 0 ± 0 FIG. 25 The invariant mass distribution M(Bs π ) for the Bs → 0 sis of a 48,000 event sample of reconstructed Bs → J/ψφ DsµX event sample with the results of the ﬁt superimposed (from CMS ref. (250)). decays, and reported an upper limit of ρX < 3.9% at the 95% C.L. (252) (see the right panel of Fig. 26).

∓ ± µ Ds X, where X denotes a neutrino possibly accom- No satisfactory theoretical description of the X(5568) panied by mesons, are much more abundant than the structure has yet been proposed (253; 254; 255; 256). If 0 exclusive decay Bs → J/ψφ. The mass resolution is confirmed, this state would be comprised of two quarks worse due to the presence of the undetected neutrino, and two antiquarks of four different flavors: b, s, u, d. 0 ± but it is possible to select events where this effect is min- Such a state might be a tightly bound Bd-K molecule imized by requiring that the Ds meson and the muon or a [bd]-[¯su¯] tetraquark. However, the low mass of the 0 0 ± account for a large fraction of the Bs momentum. The X(5568), about 200 MeV below both the BdK thresh- data show an excess over the simulated background at old and the three-quark (bsu)Ξb baryon, disfavors both the mass expected from events produced by the de- of these interpretations. A Lattice QCD study of the 0 ± 0 cay X(5568) → Bs π with Bs → J/ψφ, as seen in Bsπ scattering (257) does not support the existence a Fig. 25, thereby providing a confirmation of the results J P = 0+ state with the X(5568) parameters. 26

CMS Preliminary 19.7 fb-1 (8 TeV) 900 LHCb p (B0) > 5 GeV Claimed X(5568) state 1400 800 T s Combinatorial 700 1200 600 500 1000 400 800 300 200 600 Candidates / 8 MeV 100 Candidates / (5 MeV) 0 400 4 2 0 200 Pull −2 −4 0 5550 5600 5650 5700 5750 5800 5850 5900 5950 6000 5.5 5.6 5.7 5.8 5.9 0π ± 0 ± 0 m(Bs ) (MeV) ∆M(B π )+M(B ) [GeV] s s PDG

0 ± FIG. 26 The Bs π distributions (points with error bars) observed by the LHCb (251) (left) and by the CMS (252) (right). The LHCb plot shows the result of a ﬁt an X(5568) signal (not visible) included on top of the combinatorial background. 0 The continuous blue band in the CMS plot is the distribution observed for the Bs -mass sideband data. The vertical red band illustrates the MX ± ΓX region of the X(5568) state claimed by D0.

V. NEUTRAL EXOTIC HADRON CANDIDATES shown in Fig. 27b. In their 3 fb−1 Run-I data sample, the LHCb exper- A. X(3872) iment detected a 1011 ± 38 signal events for the decay chain: B+ → K+X(3872); X(3872) → π+π−J/ψ; J/ψ → µ+µ− on a small background as shown in The first quarkonium-like candidate for a non-standard Fig. 28a. In an amplitude analysis based on the an- hadron to be seen was the X(3872), which was found by gular correlations among the five final-state particles in Belle (53) as an unexpected narrow peak in the π+π−J/ψ these events, the LHCb group found that the J PC = 1++ invariant mass distribution in B → Kπ+π−J/ψ decays quantum number hypothesis had the highest likelihood shown in Fig. 27a. It is experimentally well established, value (56; 57). They evaluated the significance of the 1++ having been seen and studied by a number of experi- assignment using the likelihood ratio t ≡ −2 ln[Lalt/L++] ments (55; 58; 61; 68; 71; 72; 73). Its most intriguing as a test variable, where L++ is the likelihood for the 1++ feature is its mass: the 2016 PDG world-average value hypothesis and Lalt is that for an alternative. (With this is M(X(3872)) = 3871.69 ± 0.17 MeV, which, at current definition, positive values of t favor 1++.) The solid-blue levels of precision, is indistinguishable from the D0D¯ ∗0 (dashed-red) histograms in Fig. 28b show t value distri- mass threshold m 0 + m ∗0 = 3871.68 ± 0.10 MeV (9); D D butions for ensembles of Monte Carlo (MC) experiments the difference is δm ≡ (m 0 + m ∗0 ) − M(X(3872)) = 00 D D generated with alternative and 1++ J PC values,21 with −0.01 ± 0.20 MeV. Whether this close proximity of the the t value determined for the real data indicated by ver- X(3872) to the D0D¯ ∗0 mass threshold is a coincidence tical black lines. The experimental results favor the 1++ or a feature of hadron dynamics is an issue that has at- hypotheses over all alternative even-CJ PC assignments tracted considerable interest. The X(3872) is also quite with J ≤ 4 by a wide margin; in all comparisons the sta- narrow; Belle has reported a 90% C.L. upper limit on tistical significance of the 1++ assignment, determined its total width of Γ < 1.2 MeV (54). In addition to the from the distributions for the ensembles of MC experi- production in B → X(3872)K decays, the X(3872) state ments, is more than 16σ. was also observed in B → X(3872)Kπ decays (258). The only available 1++ standard charmonium level The radiative decay process X(3872) → γJ/ψ has that is expected to have a mass near 3872 MeV is the been measured by BaBar (259) and Belle (67) to have 3 0 2 P1 cc¯ state, commonly known as the χc1(2P) or χc1. a branching fraction that is 0.24 ± 0.05 that for the However, for a number of reasons, the assignment of the π+π−J/ψ mode. This, plus BaBar (69) and LHCb (70) 0 X(3872) as the χc1 charmonium state has been deemed reports of strong evidence for X(3872) → γψ0 decays (see to be “improbable” (260). Among these are the X(3872) Fig. 23b), establish the charge conjugation parity of the X(3872) as even (C = +), in which case the π+π− system in the X → π+π−J/ψ decay process must be from 0 + − + − ρ → π π decay. This is consistent with π π line- 21 The experiments are generated with numbers of signal and back- shape measurements done by CDF (59), Belle (54), and ground events that fluctuate around those in the experimental CMS (71). The π+π− line shape measured by Belle is data according to the observed statistical errors. 27

40 a) Belle b) 35 Belle Ψ’ 30

X(3872) 10 Events/ 0.02 GeV 5

0 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 M(π+π-l+l-)-M(l+l-) (GeV) M() (GeV)

+ − + − + − + − + − + − FIG. 27 a) The M(π π ` ` ) − M(` ` ) distribution for B → Kπ π ` ` events with |M(` ` ) − mJ/ψ| < 20 MeV (53). b) The π+π− invariant mass distribution for X(3872) → π+π−J/ψ events in Belle. The curves shows results of ﬁts to a ρ → π+π− line shape including ρ-ω interference (54). The dashed (solid) curve is for even (odd) X(3872) parity a) b) B + → K +π +π − J /ψ

MeV Candidates/1

-1000 -500 0 500 1000 -1000 -500 0 500 1000 ΔM=M(π+π- J/ψ)-M(J/ψ) (MeV) t

+ − + + + − FIG. 28 a) The M(π π J/ψ) − mJ/ψ distribution for B → K π π J/ψ events from LHCb (57). b) Distributions of t ≡ −2 ln[Lalt/L++] for simulated experiments for alternative JPC hypotheses (blue histograms) and 1−− (red dashed histograms). The vertical lines show the values of t determined from the data. Similar results for JPC = 3±+ and 4±+ are not shown.

mass and width values, and the apparent isospin viola- splitting for the 1P states: δM2−1(1P) = 46.5±0.1 MeV. tion in its discovery decay channel X(3872) → ρJ/ψ. This conflicts with cc¯ potential model expectations that 0 δM2−1(nrP) decreases with increasing radial quantum Mass: The χc2, the J = 2 spin-multiplet partner of the χ0 , was identified by Belle in 2006 as a distinct peak nr (39; 40). For cc¯ states above the threshold for de- c1 ¯ ¯ ∗ in the γγ → DD¯ cross section at 3927 ± 3 MeV (see cays into open-charmed DD and DD mesons, potential Fig. 15b), with an angular distribution that is character- model calculations should be modified to include the ef- istic of a D-wave DD¯ meson system and a production fects of intermediate on-mass-shell open-charmed-meson rate that is consistent with charmonium model expecta- loops. These effects have been estimated by three group 3 using three different approaches (263; 264; 265); all three tions for the 2 P2 cc¯ state (215). BaBar confirmed this observation in 2010 (261) and found properties that are of these analyses predict that δM2−1(2P) decreases to consistent with those reported by Belle. There is general values that are even lower than potential model expecta- agreement in the quarkonium community that the iden- tions. 0 tification of the Belle peak as the χc2 is reliable (262). Width: The Belle group’s upper limit Γ(X(3872)) < 0 If, with this assignment for the χc2, the X(3872) is iden- 1.2 MeV is only slightly higher than the measured width 0 0 0 tified as the χc1, the χc2-χc1 mass splitting would be of the the 1P χc1 state, Γ(χc1) = 0.84 ± 0.04 MeV (9). δM2−1(2P) = 56 ± 3 MeV and larger than the measured However, since the X(3872) has a number of additional 28 allowed decay channels that are not accessible to the χc1, gin, the X(3872) should exist for a significant frac- including, for example, the X(3872) → ρJ/ψ discovery tion of the time as a D0D¯ ∗0 molecule-like state (either mode and the order of magnitude stronger D0D¯ ∗0 mode bound or virtual) with a size comparable to its scat- p that is discussed below, these are expected to be reflected tering length: a00 = ~/ µ|δm00|, where µ00 is the in a substantially larger total width if the X(3872) were, D0D¯ ∗0 reduced mass. The limited experimentally al- 0 in fact, the χc1 (263). lowed range for non-zero δm00 values given above im- Isospin Violation: Since standard charmonium states plies that the mean D0-D¯ ∗0 separation has to be huge: contain no constituent u- or d-quarks, they necessarily a00 ≥ 7 fm. Although the X(3872) mass is well below have zero isospin. On the other hand, since the ρ-meson the D+D∗− mass threshold, it is expected to exist for is an isovector, the ρJ/ψ decay final state has isospin I = a smaller fraction of the time as a D+D∗− molecule-like 0 + ∗− 1, and the χc1 → ρJ/ψ decay process violates isospin and state. The extent of the D D configuration, for which should be strongly suppressed, and an unlikely discovery δm+− = (mD+ − mD∗− ) − M(X(3872)) = 8.2 MeV and mode for a charmonium state (260). a+− ' 2 fm, is much different. The very different proper- These reasons, plus the close correspondence between ties of the D0D¯ ∗0 and D+D∗− configurations ensure that 22 its mass and the mD0 + mD∗0 threshold, led to consid- the X(3872) isospin is not precisely defined as was first erable speculation that the substructure of the X(3872) pointed out in ref. (273). is more complex than that of a simple cc¯ charmonium One diagnostic of the nature of X(3872) is the relative state (266). strength of the γψ0 and γJ/ψ decay modes (274). The An interesting question about the X(3872) is the value preference for γψ0 over γJ/ψ, as indicated in Eq. 6, is in of its isospin. Explicit evidence for strong isospin viola- accord with expectations for a 1++ charmonium, where 0 0 tion in X(3872) decays came from observations by both the χc1 and the ψ have the same radial wave-function 0 0 Belle (62) and BaBar (63) of the X(3872) → ωJ/ψ de- and the χ1 → γψ E1 transition is favored over that for cay mode with a branching fraction that is nearly equal γJ/ψ, which are “hindered” (39) by the mis-match be- to that for ρJ/ψ; the PDG average is B(X(3872) → tween the orthogonal initial- and final-state radial wave ωJ/ψ)/B(X(3872) → π+π−J/ψ) = 0.8 ± 0.3 (9). Since functions.23 In contrast, in models in which the X(3872) 0 MX(3872) − mJ/ψ ' 775 MeV, the upper kinematic is a pure molecular state, the γψ decay channel is boundary for the mass of the π+π− system is right at strongly suppressed relative to that for γJ/ψ (275; 276). the peak mass of the ρ resonance and ∼ 7 MeV below Another diagnostic that has been proposed is the na- mω. Thus, while the decay X(3872) → ρJ/ψ is kinemat- ture of its prompt production in high-energy hadron ically allowed to proceed through nearly the entire low- collisions (277). As discussed in Section III.B above, mass side of the ρ resonance, X(3872) → ωJ/ψ can only the hadron collider experiments see strong signals for proceed via a small fraction of the low-mass tail of the ω prompt X(3872) production in Ecm = 1.96 TeV pp¯ col- peak. These considerations imply a kinematic suppres- lisions at the Tevatron (61; 278), and in pp collisions at sion of the amplitude for X(3872) → ωJ/ψ decays rela- Ecm = 7 TeV (71) and 8 TeV (72) collisions at the LHC. tive to the ρJ/ψ channel by a factor of about ∼4, in which In each of these experiments, the measured properties case the near equality of the ρJ/ψ and ωJ/ψ decay rates of X(3872) production are quite similar to those for the implies that an I = 0 assignment is favored (267), but a ψ0 aside from an overall scale factor of about one-tenth, sizable isovector component in the X(3872) wavefunction as illustrated in Fig. 30, where ATLAS measurements of 0 is still allowed. If the X(3872) had I = 1, it would have the transverse momentum (pT ) dependence of prompt ψ charged partners. Searches for narrow, charged partners and X(3872) production are shown as solid black and red of the X(3872) decaying into ρ±J/ψ by BaBar (268) and circles, respectively (72). Belle (54) set branching ratio limits that are well below If the X(3872) is a composite DD¯ ∗ molecule-like ob- expectations based on isospin conservation. These results ject, as suggested by the closeness of its mass to the suggest that the X(3872) is mostly an isospin singlet and mD0 + mD∗0 threshold, one would expect that its pro- that the ρJ/ψ decay mode violates isospin symmetry. duction properties in prompt, high-energy hadron colli- The X(3872) → D0D¯ ∗0 decay mode has been ob- sions would be less like those of the ψ0 and more like served by both Belle (269) and BaBar (66) with a mea- those of known composite objects, like light nuclei or hy- sured branching fraction that is 9.9 ± 2.3 times that pernuclei. In the absence of any direct measurements of for the π+π−J/ψ channel (see Figs. 29a and b). The J PC = 1++ quantum number assignment implies that 0 ¯ ∗0 the X(3872) couples to a D D pair in an S- and/or D- √ 22 0 ¯ ∗0 + ∗− wave and, because the D0D¯ ∗0 system is right at thresh- Since |I = 1; I3 = 0i = [|D D i +√ |D D i]/ 2 and |I = 0 ¯ ∗0 + ∗− old, the S-wave can be expected to be dominant. In 0; I3 = 0i = [|D D i − |D D i]/ 2, a well defined I = 1 or I = 0 state implies equal D0D¯ ∗0 and D+D∗−content. this case some very general and universal theorems ap- 23 In this case the 2P-1S overlap integral is only non-zero because ply (140; 270; 271; 272). One consequence of these the final-state 1S radial wave-function is boosted relative to that theorems is that, independently of its dynamical ori- for the initial-state 1P state. 29

a) Belle b) BaBar

FIG. 29 M(D0D¯ ∗0) distributions from B → KD0D¯ ∗0 from a) Belle (269) and b) BaBar (66). The peaks near threshold are the signals X(3872) → D0D¯ ∗0 decays. light nuclei and hypernuclei production in 7∼8 TeV pp collisions, the authors of ref. (279) extrapolated measurements from the ALICE experiment (280; 281) of inclusive 3 3 deuteron, He and hypertriton ΛH production cross sections in Pb-Pb collisions (with nucleon-nucleon c.m. en- ! ergies of E (NN) = 2.76 TeV), to pp collisions at 7 TeV ) cm ! by means of a Glauber-model calculation. These are in- Ψ’ @ATLAS !| ! Ψ’ @ATLAS ! cluded in Fig. 30 where the associated curves are results nb/GeV !| !

( | of ﬁts to the commonly used blast-wave-model function T ! X(3872) !| for particle production in high energy heavy ion colli- @ATLAS X(3872)

/dp @ATLAS

sions (282). pp dσ In the Glauber model, the nucleons inside heavy ions interact independently, and multi-nucleon, collective effects are ignored. The blue dash-dot curve shows the ref. (279) estimate for how the hypertriton extrapolation and fit would change if large collective effects were included. The extrapolations from Pb-Pb measurements to pp collisions and the blast-wave model are very ap- pT (GeV) proximate and likely to be wrong by large factors. How- ever, the differences between these extrapolations and FIG. 30 Differential cross sections for particle production vs. p the measured X(3872) pT -dependence are many orders- T at the LHC. The solid red (black) circles are ATLAS measure- of-magnitude too large to be accounted for by refinements 0 ments of prompt X(3872) (ψ ) production in Ecm = 8 TeV pp in the models. collisions (72). Results for deuteron (green) 3He (orange), and 3 ΛH (blue) are extrapolations of ALICE Pb-Pb measurements at Ecm(NN) = 2.76 TeV to Ecm(pp) = 7 TeV using a Glauber The BESIII experiment recently reported X(3872) model (279). The associated curves are the results of fits of blast- production in the process e+e− → γπ+π−J/ψ at c.m. en- wave model (282) expectations in the absence of any corrections for ergies in the region of the Y (4260) charmonium-like res- multi-nucleon collective effects. The blue dash-dot curve are the extrapolated results for 3 H when collective effects are included. onance peak (73). The X(3872) was detected via its Λ π+π−J/ψ decay channel; a π+π−J/ψ invariant mass distribution summed over the data at four energy points is shown in Fig. 31a, where a 6.3σ peak at the mass of the termines X(3872) is evident. Figure 31b shows the energy depen- B(Y (4260) → γX(3872)) dence of the X(3872) production rate where there is some > 0.05, (8) indication that the observed signal is associated with the B(Y (4260) → π+π−J/ψ) Y (4260). Assuming that Y (4260) → γX(3872) decays are the source of this signal, and using the PDG lower which is substantial and suggests that there is some com- limit B(X(3872) → π+π−J/ψ) > 0.026 (9), BESIII de- monality in the nature of the Y (4260), X(3872) and 30

24 Zc(3900). tum number assignment. Based on this result, they iden- 3 tified the X(3915) as a candidate for the 2 P0 char- 0 monium state, commonly known as the χc0, and the B. X(3915) 0 PDG classified the X(3915) as the χc0 in the 2014 Me- son Summary Tables (283). However, although BaBar’s After finding the X(3872) in B → KρJ/ψ decays, preferred J PC = 0++ values match expectations for the Belle studied B → KωJ/ψ decay, where, in a data sam- 0 χc0, other properties of the X(3915) make it a poor can- ple containing 275M BB¯ meson pairs, they observed a 3 didate for the 2 P0 charmonium state (265; 284; 285). prominent, near-threshold enhancement in the ωJ/ψ in- The mass is too high; the χ0 -X(3915) mass splitting, variant mass distribution shown in Fig. 32a (74). Belle c2 δM2−0(2P ) = 8.8 ± 3.2 MeV is only 6% of the 1P split- fitted this enhancement with an S-wave BW resonance ting: δM2−0(1P ) = 141.5±0.3 MeV, in strong contradic- shape and found a mass and width for this peak, which tion with theoretical expectations (263; 264; 265). An- they originally dubbed the Y (3940), of M = 3943 ± 0 other peculiarity of the X(3915) = χc0 assignment is the 17 MeV and Γ = 87 ± 24 MeV. The Belle result was con- lack of any experimental evidence for X(3915) → DD¯ de- firmed by BaBar with a data sample containing 383M cays and the apparent strength of the X(3915) → ωJ/ψ ¯ BB meson pairs (75) and, later, with BaBar’s final, discovery mode, which conflicts with expectations that 467M BB¯-meson-pair data sample (63). BaBar’s fits χc0 → DD¯ would be a strongly favored fall-apart mode to the data yielded lower mass and width values: M = 0 and χc0 → ωJ/ψ an OZI-rule-violating process that is 3919±4 MeV and Γ = 31±11 MeV. With their full data expected to be strongly suppressed (2; 199; 200). sample, BaBar was able to resolve an X(3872) → ωJ/ψ The authors of ref. (286) added to the controversy contribution to the enhancement (see the inset in the by pointing out that the BaBar spin-parity analysis upper panel of Fig. 32b). The weighted average of the that ruled out the J PC = 2++ hypothesis assumed Belle and BaBar results are M = 3920 ± 4 MeV and the dominance of the helicity-2 amplitude over that for Γ = 41 ± 10 MeV. helicity-0. Their reanalysis of the BaBar angular distri- An ωJ/ψ mass peak with similar mass and width butions showed that when a helicity-0 amplitude is in- PC ++ on a very small background was reported by Belle in cluded, a J = 2 assignment cannot be ruled out, the two-photon process γγ → ωJ/ψ, and shown in and make an argument that identifies the X(3915) as 0 Fig. 33a (76). The BaBar group subsequently observed the χc2 charmonium state. However, their argument 0 a very similar peak (77) in the same process with mass for the X(3915) = χc2 assignment ignores the conse- and width values that were in good agreement with those quences of X(3915) production in B → KωJ/ψ de- reported by Belle. The weighted average of the Belle cays. For example, since the total branching fraction + + −5 and BaBar measurements are M = 3917.4 ± 2.4 MeV B(B → K χc2(1P)) = (1.1 ± 0.4) × 10 is smaller and Γ = 14 ± 6 MeV. The close agreement between the than the product of branching fractions masses determined for the Y (3940) → ωJ/ψ peak in + + +0.9 −5 B → KωJ/ψ decays and the X(3915) → ωJ/ψ signal B(B → K X(3915))×B(X → ωJ/ψ) = 3.0−0.7 ×10 , seen in γγ → ωJ/ψ production, and the similar values of (10) 0 + the widths suggest that these are two different produc- the X(3915) = χc2 assignment would imply a B → + 0 tion mechanisms for the same state. In the following we K χc2 partial decay width that is substantially larger + + assume this to be the case and refer to this state as the than that for B → K χc2, which is contrary to models X(3915). The PDG tables (9) list the results from both for B-meson decays to charmonium states, where these channels as a single entry with average mass and width widths are expected to be proportional to the square of values of the cc¯ wave function at the origin, which decreases with increasing radial quantum number (287). M(X(3915)) = 3918.4 ± 1.9 MeV On the other hand, the X(3915) → ωJ/ψ signals Γ(X(3915)) = 20.0 ± 5.0 MeV. (9) seen in B decays and in γγ production may be unrelated. More data and separate spin-parity determinations for the ωJ/ψ systems produced in B → KωJ/ψ and γγ → ωJ/ψ processes and with fewer assumptions are 1. Is the X(3915) the χc0 charmonium state? needed. At present, the situation remains confused, as evidenced by the 2016 edition of the PDG report, which BaBar performed a spin-parity analysis with their no longer identifies this as the χ0 and has reverted to PC ++ c0 γγ → ωJ/ψ events that favored a J = 0 quan- calling this state the X(3915) (9). Recently Belle re- 0 ported the observation of an alternative χc0 candidate, the X∗(3860), with none of the problems associated with 24 0 The Y (4260) meson is discussed below in Sect. V.C and the the X(3915) = χc0 assignment (288). This is discussed Zc(3900) is discussed in Sect. VI below in Section V.E. 31

a) BESIII b) BESIII

FIG. 31 a) The data points show the BESIII experiment’s M(π+π−J/ψ) distribution for e+e− → γπ+π−J/ψ events at energies near +1.7 the Y (4260) resonance (73). The ﬁtted peak has a mass and width of M = 3871.9 ± 0.7 MeV and Γ = 0.0−0.0 MeV (< 2.4 MeV), which are in good agreement with the PDG world average values for the X(3872). b) The energy dependence of the BESIII σ(e+e− → γX(3872)) × B(X(3872) → π+π−J/ψ) measurement. The solid curve is the Y (4260) line shape ﬁtted to the data; the dashed curves show phase-space and linear production model expectations.

2. Is the X(3915) a ccs¯ s¯ four-quark state? the ηηc partial width should be large is only qualitative and our limited level of understanding of these processes The above-mentioned provisos notwithstanding, the precludes the ability of making a reliable quantitative es- most parsimonious interpretation of existing data is to timate of just how large it should be. Because of this, assume that the ωJ/ψ peaks seen in B decays and γγ the absence of an ηηc mode would probably only be fa- production are due to the same state. In that case, tal to the ccs¯ s¯ quark assignment if its partial width was the most likely J PC assignment is 0++, and the mass, shown to be definitely much smaller than that for ωJ/ψ strength of the ωJ/ψ decay channel, and absence of any decays.25 evidence for a significant DD¯ decay mode rule against its identification as a cc¯ charmonium state. The mass 3. Discussion is 18.2 MeV below the 2mDs threshold, and this suggests that it may contain a significant ccs¯ s¯ component, + − Since it is relatively narrow and is seen as clear sig- either in a Ds Ds molecule-like configuration (289), a [¯cs¯][cs] tetraquark (290) or a mixture of the two. In any nals in both B-meson decays and γγ fusion reactions, of these pictures, the DD¯ decay mode would strictly vi- the X(3915) is one of the most intriguing of the XYZ olate the OZI-rule, while the ω meson’s small, but non- exotic meson candidates. However, significant progress in negligible ss¯ content (291) would partially mitigate the our understanding of its underlying nature will probably ωJ/ψ mode’s violation of the rule and an ωJ/ψ decay not be forthcoming until larger data samples are avail- width that is comparable or greater than that for DD¯ able in future experiments such as BelleII (293). With would not be a priori ruled out. For a ccs¯ s¯ combina- the order-of-magnitude larger event samples that are ex- PC tion configured either as a molecule-like or a tetraquark pected for BelleII, we can expect definitive J deter- arrangement, the decay mode least effected by OZI sup- minations and measurements of, or more stringent limits on, the strengths of the DD¯ and ηη decay channels pression would be X(3915) → ηηc and this could be ex- c pected to be a dominant decay mode. However, Belle for both the B-meson-decay and γγ-fusion production searched for this mode, saw no significant signal, and es- modes. The LHCb experiment has demonstrated ability tablished a (90% CL) product branching fraction upper to detect ω mesons in B decays (294) and should also be limit (292): able to probe the X(3915) quantum numbers.

+ + −5 B(B → K X(3915))×B(X → ηηc) < 4.7×10 . (11) C. Y (4260) and other J PC = 1−− states Since this limit is not very stringent, it is diﬃcult to draw a deﬁnite conclusion from it. A comparison of it with After the discovery of the X(3872) in π+π−J/ψ decays the ωJ/ψ measurement given in Eq. 10 indicates that, and before its J PC = 1++ quantum number assignment in spite of Belle’s null result, the partial decay width for X(3915) → ηηc could still be larger than that for ωJ/ψ by as much as a factor of ' 2. The expectation that 25 This issue is discussed in ref. (289). 32

mass peak, using their full data set, are shown in Fig. 34a. This peak was quickly confirmed by CLEO (296) and 30 a) Belle Belle (87). The most recent Belle measurements (88) of σ(e+e− → π+π−J/ψ) in the Y (4260) region, based on their full data set, are shown in Fig. 34b, where the sim- 20 ilarity with the BaBar measurements is apparent. The weighted average of the mass and width values determined by BaBar, CLEO and Belle from fits of a single BW resonance line shape to the Y (4260) peak in their 10 data are (9): M(Y (4260)) = 4251 ± 9 MeV Γ(Y (4260)) = 120 ± 12 MeV. (12) 0 + − 3880 4080 4280 The excess of events near 4 GeV in their π π J/ψ cross M(J/) (MeV) section measurements was attributed by Belle to an additional possible resonance that they called the Y (4008) b) (9; 87), but a similar excess was not observed by BaBar (85) and was not confirmed by recent BESIII results (52). The production mode of the Y (4260) ensures that its J PC quantum numbers are the same as those of the photon, i.e. 1−−. Its discovery decay mode, Y (4260) → π+π−J/ψ, provides strong evidence that its constituents contain a cc¯ quark pair. However, all of the 1−− cc¯ char- BaBar monium levels with mass below 4500 MeV have already been assigned to well established 1−− resonances that are seen in the total cross section for e+e− → hadrons between 2.6 and 4.6 GeV (206; 207) (see the inset in Fig. 11a). In addition, even though its mass is well above (∗) (∗) all of the D D¯ open-charmed-meson mass thresh-

olds, there is no evidence for its decay to pairs of open- charmed mesons in the inclusive e+e− → hadrons to- FIG. 32 X(3915) → ωJ/ψ signals in B → KωJ/ψ decays from a) + − tal cross section. BESII measurements of σtot(e e → Belle (Fig. 2a from ref. (74)) and b) BaBar (Fig. 2 from ref. (63)). In the latter, the upper panel shows results for B+ → K+ωJ/ψ hadrons) at c.m. energies between 3.7 and 4.6 GeV, 0 and the lower panel shows those for B → KS ωJ/ψ. The inset in shown in Fig. 35, exhibit considerable structure that is the upper panel shows an expanded view of the low end of the ωJ/ψ primarily due to the production and decay to pairs of mass scale, where the smaller, low-mass peak is due the X(3872) → open-charmed mesons of the established 1−− ψ(3770), ωJ/ψ and the larger, higher mass peak is the X(3915) → ωJ/ψ signal. ψ(4040), ψ(4160) and ψ(4415) charmonium states. The + − strong signals for these states in σtot(e e → hadrons) plus their absence in the M(π+π−J/ψ) invariant mass was established, The BaBar group considered the possi- distributions shown in Figs. 34a and 34b reﬂect the ex- bility that it might be a 1−− vector state and searched pected strong dominance of fall-apart decays to open- its direct production in the initial-state-radiation pro- charmed-meson pairs over OZI-rule-suppressed decays to + − + − cess e e → γisrπ π J/ψ (295). They did not see hidden-charm ﬁnal states that is characteristic of above- an X(3872) signal and were able to conclude that the open-charm-threshold charmonium states. In contrast, X(3872)’s J PC quantum numbers were not 1−−. They the absence of any sign of Y (4260) decays to charmed + − did see, however, an unexpected strong accumulation mesons in σtot(e e → hadrons) plus its strong signal in of events with π+π−J/ψ invariant masses that peaked the π+π−J/ψ decay channel is opposite to expectations near 4.26 GeV, shown in Fig. 16b of Section III.A, for charmonium. As a result, there has been consider- that they called the Y (4260) (84). Subsequent BaBar able theoretical speculation that the Y (4260) might be measurements (85) of the “Born” cross sections26 for some kind of a multi-quark meson or a cc¯-gluon hybrid e+e− → π+π−J/ψ at c.m. energies near the Y (4260) state (262; 297; 298).

26 “Born” cross sections are cross sections that correspond to the tively correcting” observed cross sections for higher-order QED lowest-order Feynman diagram and are determined by “radia- eﬀects such as initial-state-radiation and vacuum polarization. 33

a) b) Belle BaBar

W(ωJ/ψ) (GeV) W(ωJ/ψ) (GeV) FIG. 33 X(3915) → ωJ/ψ signals in γγ → ωJ/ψ fusion reactions from a) Belle (76)and b) BaBar (77). The bold solid curves in each figure are results of fits with a BW resonance shape to represent the signal and a smooth function of p∗ to represent the background, where p∗ is the J/ψ momentum in the γγ c.m. system. The dash-dot curve in a) is the result of a fit with no BW resonance term; the dashed vertical line in b) indicates the location of W = 3872 MeV. The shaded histograms in both plots show the non-J/ψ background estimated from events in the J/ψ mass sidebands.

e+e-!hadrons (mostly D(*)D_ (*)) + -! + - + - + - a) e e γisrπ π J/ψ BaBar b) e e !γisrπ π J/ψ Belle BESII Ψ(4040) Ψ(4160) Ψ(3770) Ψ(4415)

Ecm(GeV) 4251 MeV FIG. 34 a) The data points show the Born cross sections for e+e− → π+π−J/ψ, measured via the initial-state radiation pro- + − + − cess e e → γisrπ π J/ψ by BaBar (85). The curve show results of a fit that used a single BW resonance to represent the Y (4260) resonance plus a linear background term. b) Belle measurements + − FIG. 35 Measurements of the ratio R = σtot(e e → of the same cross sections (88). + − + − + − + − hadrons)/σQED(e e → µ µ ), where σQED(e e → µ µ ) = 86.85 nb/s (s in GeV2), from ref. (207). The structures above R ' 2 are attributed to the indicated 1−− charmonium mesons A BaBar search for Y (4260) → π+π−ψ0 decays in decaying to DD¯, DD¯ ∗ open-charmed or D∗D¯ ∗ final states. The + − + − 0 + − 0 expected position for a Y (4260) signal, indicated by an arrow, is e e → π π ψ events resulted in the π π ψ invari- located at a local minimum in the measured cross section. ant mass distribution shown in Fig. 36a, where there is a strong peaking of events near 4320 MeV on a nearly negligible background (96). This peak is not compati- Belle and BaBar mass and width measurements of this ble with the measured mass and width of the Y (4260), second peak, called the Y (4660), are (9): as indicated by the dashed curve in the figure. A subsequent study of the same reaction with a larger data M(Y (4660)) = 4643 ± 9 MeV sample by Belle confirmed the BaBar observation, albeit Γ(Y (4660)) = 72 ± 11 MeV. (14) at a somewhat higher mass near 4360 MeV as shown in Fig. 36b (98). The current PDG values for the mass and width of this peak, called the Y (4360), are (9): 1. BESIII as a “Y (4260)-Factory” M(Y (4360)) = 4346 ± 6 MeV The BaBar and Belle results on the Y (4260), Y (4360) Γ(Y (4360)) = 102 ± 12 MeV. (13) and Y (4660) all relied on production of these states via the isr process illustrated in Fig. 13d and discussed in In addition, Belle observed a second distinct π+π−ψ0 Section III.A. This process has the advantage of sam- invariant mass peak near 4660 MeV that is evident pling many e+e− c.m. energies at once, but is limited by in Fig. 36b, an observation that was confirmed by a severe, order αQED, luminosity penalty associated with BaBar (97). In addition, Belle also reported a peak with the radiation of a hard photon. For detailed studies of + − similar mass and width in the Λc Λc invariant mass in these states, the BESIII experiment has the advantage + − + − e e → γisrΛc Λc events (100). The PDG average of the of operating at and near c.m. energies corresponding to 34

+ - + - e+e-!γ π+π-ψ’ a) e e !γisrπ π ψ’ b) isr σ BaBar Belle a) 4260 = 0.33±0.04 σ 4230

+ − e e →η J /ψ

M(π+π-/ψ’) (GeV/c2) M(π+π-/ψ’) (GeV/c2)

FIG. 36 a) The data points show the π+π−ψ0 invariant mass dis- 4230 + − + − 0 tribution for e e → γisrπ π ψ events in BaBar (96). The solid curve shows results of a fit that used a single BW resonance to represent the signal plus a linear background term. The dashed 4260 curve shows the results of a fit with mass and width constrained to the Y (4260) values. b) The blue histogram shows the corresponding results from Belle (98). The solid curve shows the results of a fit that uses two interfering BW amplitudes, one with mass near 4360 MeV and the other near 4660 MeV. The dashed curves show σ b) 4230 4260 the individual resonance contributions from two equally good fits = 0.43±0.13 + − σ 4230 e e →ωχ that have different interference phases. c0 4260 the Y (4260) and Y (4360) peaks, thereby functioning as a “Y -factory.” In this mode of operation, large event samples can be accumulated near the peaks of these resonances. On the other hand, lineshape measurements of the resonance parameters and the separation of resonance signals from underlying non-resonant backgrounds require time-consuming energy-by-energy scans. BESIII’s first data-taking run in this energy range accumulated a 525 pb−1 data sample at 4260 MeV in which they found 1477 ± 43 π+π−J/ψ events that in- + − ∓ ± cluded 307±48 events of the type e e → π Zc(3900) ; + − ± ± ± FIG. 37 a) Cross section measurements for e e → ηJ/ψ from Zc(3900) → π J/ψ, where the Zc(3900) is a rel- BESIII are shown as black points (91). For comparison, Belle isr atively narrow, resonance-like structure with non-zero measurements of the e+e− → π+π−J/ψ cross section over the electric charge that is discussed in some detail below in same energy range are shown as blue crosses (88). The red star Section VI. BESIII subsequently did a scan of measure- indicates a previous BESIII ηJ/ψ cross section measurement near the peak of the ψ(4040) charmonium state (299). b) The data ments around the Y (4260) and Y (4360) peaks, includ- points show BESIII measurements of the cross section for e+e− → ing relatively high statistics points at Ecm = 4230 MeV, ωχc0 (90). The solid curve shows the result of a fit of a threshold- 4260 MeV and 4360 MeV.27 With these data, BESIII constrained BW resonance shape to the data. The dash-dot curve measured the cross sections for e+e− → ηJ/ψ shown in indicates what a phase-space-only distribution would be like. + − Fig. 37a (91) and e e → ωχc0 shown in Fig. 37b (90). Figure 37a includes a comparison of BESIII’s e+e− → are a poor match to the PDG values for the Y (4260) ηJ/ψ cross sections with Belle isr results for σ(e+e− → given in Eq.12. The absence of any constraining ηJ/ψ π+π−J/ψ) (88), where it is evident that the peak seen data points on the lower side of the peak, i.e., be- in the ηJ/ψ channel is much narrower than Belle’s tween M(ηJ/ψ) = 4100 and 4200 MeV, precluded BE- + − Y (4260) → π π J/ψ peak. The ωχc0 cross section SIII from doing a meaningful fit for a ηJ/ψ line shape. (Fig. 37b) shows a behavior that is similar as that for Instead they characterized the shapes of the ηJ/ψ and ηJ/ψ. The red curve in this figure is the result of ωχc0 peaks by the ratio of their cross sections at the a fit of a threshold-constrained BW resonance to the high-statistics Ecm = 4230 and 4260 MeV data points: 4260 + − 4260 σ (e e →f) ωχc0 data points, which returns mass and width values, R4230(f) = σ4230(e+e−→f) , where they find good agree- Mωχ = 4230 ± 10 MeV and Γωχ = 38 ± 12 MeV that 4260 4260 c0 c0 ment: R4230(ηJ/ψ) = 0.33 ± 0.04 and R4230(ωχc0) = 0.43 ± 0.13. The evident incompatibility of the narrow structures in the e+e− → ηJ/ψ and e+e− → ωχ cross sections 27 The three “high luminosity” data samples have integrated lumi- c0 + − nosities of 1047 pb−1 at 4230 MeV, 827 pb=−1 at 4260 MeV; with the broad Y (4260) → π π J/ψ peak prompted −1 and 540 pb at 4360 MeV. The other points have luminosities BESIII to map out the Ecm energy region in the vicinity of about 50 pb−1. of the Y (4260) with two additional, independent data 35 sets (52). One consists of 19 “high luminosity” data runs BESIII measurements of the energy dependence of the −1 + − + − with at least 40 pb /point between Ecm = 3773 MeV cross section for e e → π π hc with the same two data and 4599 MeV. The other consists of 60 “low luminosity” sets (89) are shown in Fig. 39. The solid red curve in the energy-scan data runs with 7 − 9 pb−1/point between figure shows the results of a fit to the measurements with Ecm = 3882 MeV and 4567 MeV. Figures 38a and b show a coherent sum of two BW amplitudes. The parameters e+e− → π+π−J/ψ cross section measurements from the determined from the fit are: high- and low-luminosity data scans, respectively, where it is evident that the line shape of the “Y (4260)” peak M1 = 4218 ± 4 MeV Γ1 = 66 ± 9 MeV is not well described by a single BW resonance function. M2 = 4392 ± 6 MeV Γ2 = 140 ± 16 MeV, (16) The curves in the figures show the results from fits to the data in both plots with two interfering BW resonance where the statistical and (smaller) systematic errors are amplitudes that provides mass and width values of added in quadrature. The lower mass BW term, shown in the figure as a dashed green line, has a fitted mass and M1 = 4222 ± 4 MeV Γ1 = 44 ± 5 MeV width that is consistent with the M ' 4220 MeV peak +27 + − M2 = 4320 ± 13 MeV Γ2 = 101−22 MeV, (15) seen in ηJ/ψ, ωχc0 and π π J/ψ. No evidence for the + − higher mass π π hc peak is seen in the ηJ/ψ or ωχc0 where the statistical and (smaller) systematic errors are channels and its measured parameters are inconsistent added in quadrature. The simplest interpretation of with those of the Y (4360), for both the π+π−J/ψ and these results is that the first peak is the Y (4260), which π+π−ψ0 channels. has a significantly lower mass and narrower width than the B-factory-measured values that are given above in + − e+e− → π +π −h low-lum. scan data Eq. 12, and that the second peak is the due to a π π J/ψ c BESIII

+ − + −

) e e → π π h high-lum. data decay mode of the Y (4360) resonance, with slightly lower c mass and narrower width values than those determined nb ) ( + − 0 c h from the π π ψ decay mode listed in Eq. 13. - π + π

- e + σ(e

FIG. 39 The data points show BESIII measurements of the cross + − + − section for e e → π π hc, where the hc was detected via its hc → γηc decay mode with the ηc reconstructed in one of 16 exclusive multihadron decay channels (89). The solid black dots are from the low-luminosity-scan and the solid red points are the high- luminosity-scan points. The solid red curve shows the results of a ﬁt to the data with a coherent sum of two interfering BW amplitudes discussed in the text.

2. Discussion

The Y (4260) and the other, higher-mass 1−− states have attracted considerable attention; the BaBar (84; 96) and Belle (98) papers reporting their discoveries rank among these experiments most highly cited papers. Most of the theoretical discussions to date have been focused on Y (4260) mass and width parameters that were de- FIG. 38 BESIII measurements (52) of the cross section for termined from single BW ﬁts to isr line shapes shown e+e− → π+π−J/ψ for a) the “high luminosity” scan data and b) the “low luminosity” scan data. Dashed arrows in both plots in Fig. 34. However, the recent measurements of the + − + − indicate the “Y(4260)” mass value from the PDG-2016 average e e → ηJ/ψ, ωχc0 and π π hc cross sections, shown of results based on single-BW resonance ﬁts to pre-2016 measure- in Figs. 37 and 39, respectively, and precise results for ments given in Eq. 12. e+e− → π+π−J/ψ shown in Fig. 38, demonstrate that 36

the single-resonance assumption that was used to deter- A conventional cc¯ charmonium state with this mass mine the mass and width values given in Eq. 12 was too would be able to decay to a variety of open-charmed- na¨ıve and the values that were derived are not reliable. meson pair final states via allowed fall-apart decays and The older results based on single-peak fits to π+π−J/ψ have an expected width that is much higher than CDF’s mass distribution ought to be ignored and the Y (4260) measured value for the X(4140). Moreover, the observed label retired. Averaging the mass and width determina- J/ψφ decay mode would be OZI-suppressed for charmo- + − + − tions in π π J/ψ, π π hc and ωχc0 channels, we ob- nium state decays and expected to have an undetectably tain: small branching fraction. Because of these conflicts with charmonium-model-based expectations, the CDF obser- M(Y (4220)) = 4222 ± 3 MeV vation triggered considerable interest. It was suggested Γ(Y (4220)) = 48 ± 7 MeV, (17) that the X(4140) structure could be a molecular state (305; 306; 307; 308; 309; 310; 311; 312; 313; 314), a where the error on the width was scaled up to account tetraquark state (290; 315; 316; 317; 318), a hybrid state for mild disagreements between the different channels. (319; 320) or a rescattering effect (150; 321). Some theoretical papers interpreted the Y (4260) as a bound state of a D meson and a D¯ (2420), a J P = 1+ 1 A analysis of B+ → J/ψφK+ decays by the LHCb P-wave excitation of the D meson with mass 2421 MeV collaboration, based on a fraction of their Run-I data and width Γ = 27.4 MeV (300; 301). For the Eq. 12 sample (322), found no evidence for a narrow X(4140)- mass value for the Y (4260), this implied a DD¯ bind- 1 like peak, and set an upper limit on its production ing energy of ' 35 MeV, which is somewhat larger than that was in 2.4σ tension with the CDF results (94). typical values for nuclear systems that are bound by Belle (323; 324) (unpublished) and BaBar (325) searches Yukawa meson-exchange forces. With the lower, Eq. 17 for a narrow X(4140) state did not confirm its presence, value for the Y (4220) mass, the implied DD¯ binding 1 but the limits that they set were not in serious conflict energy nearly doubles to 66 MeV, which suggests that with the CDF measurements. In 2014, an X(4140) → the DD¯ molecule interpretation should be reevaluated. 1 J/ψφ-like signal with mass and width values consistent Other authors have suggested that the Y (4260) might be with the CDF results and a statistical significance of 5σ, a cc¯-gluon hybrid meson (302; 303; 304). A lattice QCD shown in Fig. 40b, was reported in B+ → J/ψφK+ de- calculation (with pion mass ∼ 400MeV) finds a candi- cays by the CMS collaboration (81). Also in 2014, D0 date for a 1−− hybrid state at a mass of 4285 ± 14 MeV reported the M(J/ψφ) distribution shown in Fig. 41a, that the authors suggested as a possible interpretation where there is 3σ evidence for an narrow X(4140)-like for the Y (4260) (186). A large radiative width of the structure, but with a mass, 4159 ± 8 MeV, that was Y (4260) would be at odds with the hybrid interpreta- about two standard deviations higher than the CDF tion, and this calls for improved measurements of the value (82). In addition, D0 reported a 4.7σ signal for e+e− → γX(3872) (73) cross-section in the relevant mass prompt X(4140) production in E = 1.96 TeV pp¯ col- range, to correlate it better with the observed Y struc- cm lisions as shown in Fig. 41b (83). The BESIII collab- tures and to extract their absolute radiative branching oration did not find evidence for X(4140) → J/ψφ in ratios. e+e− → γX(4140) and set upper limits on its production cross-sections at c.m. energies of 4.23, 4.26 and 4.36 D. X(4140) and other J/ψφ structures GeV ] (326).

Studies of mass structures in J/ψφ have a vivid and In an unpublished update to their B+ → J/ψφK+ controversial history that involves a number of experi- analysis (94), the CDF collaboration presented 3.1σ evi- ments, as summarized in Tables IV and V. The relative dence for a second relatively narrow J/ψφ mass peak near ease of triggering on J/ψ → µ+µ− decays, supplemented 4274 ± 8 MeV, an observation that has also received con- with the distictively narrow φ → K+K− mass peak, pro- siderable attention in the literature (327; 328). There are vides a relatively clean signature, even in hadron collider signs of a second J/ψφ mass peak in the CMS distribu- experiments with no hadron identification capabilities. tion shown in Fig. 40b, but at a mass of 4314 ± 5 MeV, The history started in 2008, when the CDF collaboration which is 3.2 standard deviations higher than the CDF presented 3.8σ evidence for a near-threshold J/ψφ mass value; no statistical significance of this structure is re- peak in B+ → J/ψφK+ decays, shown in Fig. 40a, with ported (81). There is some hint of a second peak near +9.1 mass M = 4143 ± 3 MeV and width Γ = 11.7 −6.2 MeV, 4330 MeV in the D0 J/ψφ mass distribution shown in that is called the X(4140) (80).28 Fig. 41a, but with a small, ∼ 1.7σ significance. The Belle collaboration saw 3.2σ evidence for a narrow J/ψφ peak at 4351 ± 5 MeV in two-photon collisions, which implies J PC = 0++ or 2++, and found no evidence for 28 In the literature, this is sometimes referred to as the Y (4140). X(4140) in the same analysis (95). 37

CMS, s = 7 TeV, L=5.2 fb-1 + + 300 a) B → K J /ψ φ + + b) Data B → K J /ψ φ Global fit 250 Three-body PS (global fit) ±1σ uncertainty band +

) / 20 MeV 200 Event-mixing (J/ψ, φ, K ) + Event-mixing (J/ψ, φ K+ ) 1D fit N(B 150

100

0 1.1 1.2 1.3 1.4 1.5 ΔM = M(J /ψ φ)− M(J /ψ ) (GeV) ΔM = M(J /ψ φ)− M(J /ψ ) (G∆emV )[GeV]

FIG. 40 a) The ∆M = M(J/ψφ) − M(J/ψ) distribution for a 58 event sample of candidate B+ → J/ψφK+ decays from the CDF experiment (80). The histogram shows the data and the red curve shows the result of a ﬁt with a BW signal shape and a three-body phase-space term to represent the non-resonant background. b) The corresponding plot for a 2.5K event sample of candidate B+ decays from the CMS experiment (81). Here the ﬁt includes two BW signal shapes, one for the X(4140) and the other for the enhancement near ∆M ' 1.22 GeV.

a) + + 3500 B → K J /ψ φ b) 3000 Events

2500 -1 D0 Run pp →II, 10.4J /ψ fb φ X (1.96 TeV) 2000 Data 0

FIG. 41 a) The M(J/ψφ) distribution for a 215 event sample of candidate B+ → J/ψφK+ decays from the D0 experiment (82). The solid blue curve is the result of a ﬁt with two BW signal shapes and a three-body phase-space term to represent the non-resonant background. b) The distribution of invariant masses for prompt J/ψφ combinations produced in inclusive pp¯ → J/ψφX reactions from the D0 experiment (83).

1. The 6-dimensional LHCb Amplitude Analysis invariant masses and decay angles spanned by the five final-state particles could not be described by a model All the analyses mentioned above had limited data sets that contains only excited kaon states that decay into and were based on simple J/ψφ mass fits, with a Breit- φK; an acceptable description of the data was only ob- Wigner shape to represent the signal and an incoher- tained when four coherent X → J/ψφ peaking structures ent background described by an ad-hoc functional shape were included. The K∗+ amplitude model determined (usually a three-body B+ → J/ψφK+ phase-space dis- from the analysis that included the four J/ψφ resonant tribution). While the M(φK) distribution in this decay structures is consistent with expectations based on the process has been observed to be featureless, several res- quark model and previous experimental K∗+ → φK+ onant contributions from K∗ → Kφ excitations are ex- resonance results. pected. The first amplitude analysis of B+ → J/ψφK+ Figure 42 shows the J/ψφ invariant mass distribu- decays that was capable of separately resolving possible tion from the 4.3K reconstructed B+ → J/ψφK+ de- K∗+ → φK+ and X → J/ψφ resonances was recently cays in the LHCb Run-II data sample with the pro- reported by the LHCb collaboration. This was based on jected results from the 6D fit superimposed as a red a nearly background-free sample of B+ → J/ψφK+ de- histogram with error bars. There is no narrow J/ψφ cays that was larger than that for any of the previous mass peak just above the kinematic threshold as first analyses (49; 50). In this analysis, it was found that the reported by CDF. Instead, a broad enhancement with +4.6 data across the full, 6-dimensional (6D) phase-space of a mass, M = 4146.5 ± 4.5−2.8 MeV, that is consis- 38

tent with the X(4140) values from CDF and CMS, but +21 140 with a width, Γ = 83 ± 21 −14 MeV, that is substan- X(4274) 29 LHCb tially broader than the CDF value , is observed with X(4500) high (8.4σ) significance. The J PC quantum numbers 120 of this structure are determined from the LHCb fit to ++ be 1 ; other hypotheses are ruled out with a signifi- 100 cance of 5.7σ or more. The 1++ quantum number as- X(4700) signment has an important impact on possible interpretations for the X(4140), in particular, it rules out 80 X(4140) ++ ++ ∗+ ∗− the 0 or 2 Ds Ds molecular models proposed in refs. (305; 306; 307; 308; 309; 312; 313). It was 60 ± ∗∓ suggested that below-J/ψφ-threshold Ds Ds kinematically induced cusp (150; 314) may be responsible for the 40 observed X(4140) structure (Appendix D in ref. (50)), Number of events / (10 MeV) though the cusp model used in this analysis is theoreti- 20 cally controversial as discussed in sec. II.B.4. The PDG’s 2017 update to ref. (9) lists an average 0 of all published measurements (80; 81; 82; 83) of the 4100 4200 4300 4400 4500 4600 4700 4800 X(4140) parameters as its mass, 4146.8 ± 2.5 MeV, and +8 + Mass of J/ψφ system [MeV] width, 19−7 MeV. The evolution of the Z(4430) mass and width determination (45; 109; 110), discussed below in sec. VI.A.4, provides the valuable lesson that a FIG. 42 The points with error bars show the distribution one-dimensional fit to a mass distribution of a resonance of J/ψφ invariant masses in the LHCb experiment’s 4.3K + + peak, together with an ad hoc assumption about the event sample of candidate B → J/ψφK decays (49; 50). background shape and its incoherence, is prone to yield The non-B-decay background estimate is shown by the lower red histogram. Projections of the 6-dimensional amplitude biased mass and width results and underestimated sys- fit, with the four X → J/ψφ resonance terms shown as tematic errors. Therefore, in Table I we list mass and hatched histograms plus contributions from a X → J/ψφ width values that are based only on the results from non-resonant amplitude (blue circles) and K∗∗ → φK exci- the full amplitude analysis (49), since this is the only tations, are shown by the solid-line red histogram with error one that resolved various background contributions and bars. added them coherently to the signal amplitude. The analysis also established the existence of the +17.2 0++ nonresonant term plus two, previously unseen 0++ X(4274) structure with M = 4273.3 ± 8.3−3.6 MeV at the 6σ significance level and with quantum numbers that resonances, the X(4500) (with 6.1σ significance) and the ++ were determined to be 1++ at the 5.8σ level. No proposed X(4700) (with 5.6σ significance). The 0 quantum molecular bound-state or cusp model can account for numbers of these states are established with significances these X(4274) J PC values. A hybrid charmonium state of more than 4σ. Wang et al. (311) predicted a virtual ∗+ ∗− in this mass region would have J PC = 1−+ (319; 320). Ds Ds state at 4.48 ± 0.17 GeV. Most models that interpret the X(4140) as a tetraquark None of the J/ψφ structures observed in B decays are state predicted that the J PC values of the next higher- consistent with the state seen in two-photon collisions by mass state to be different from 1++ (290; 316; 317; 318; the Belle collaboration (95). 329). An exception is a tetraquark model implemented by Stancu (315) that not only correctly assigned 1++ to the X(4140), but also predicted a second 1++ state at a 2. Charmonium Assignments for the J/ψφ states? mass that is not much higher than that of the X(4274). A lattice QCD calculation with diquark operators found The main reason that the X(4140) attracted a lot no evidence for a 1++ tetraquark below 4.2 GeV (190). of interest was the narrow width reported by the However, given than not all dynamical effects were sim- early measurements. However, the widths determined ulated, this calculation probably does not rule them out. from the LHCb analysis are larger, ranging between In addition, the LHCb analysis, which was the first 56 and 120 MeV, depending on the J/ψφ peak, and high-sensitivity investigation of the high J/ψφ mass re- these cannot a priori be considered to be too narrow to gion, uncovered three significant 0++ contributions: a be charmonium states. The X(4140) and X(4274) both have quantum numbers that match the χc1(3P) state, and their masses are in the range of potential model pre- 29 This should be considered “tension”, rather than disagreement dictions for this state (39; 40; 330; 331; 332; 333). since the CDF and LHCb results differ by 2.7σ. The dominant decay modes are expected to be to DD¯ ∗, 39

TABLE IV Results related to the X(4140) → J/ψφ mass peak, first observed in B+ → J/ψφK+ decays. The first (second) significance quoted for ref. (83) is for the non-prompt (prompt) production components (the mass and width were determined from the non-prompt sample). The last column gives a fraction of B+ → J/ψφK+ rate attributed to the X(4140) structure, however, the CDF and D0 results were normalized to a B+ → J/ψφK+ rate that excluded the high J/ψφ mass range. Year Experiment B → J/ψφK X(4140) peak luminosity yield Mass [MeV] Width [MeV] Significance Fraction % −1 +8.3 2008 CDF 2.7 fb (80) 58 ± 10 4143.0 ± 2.9 ± 1.2 11.7 −5.0 ± 3.7 3.8σ 2009 Belle (323) 325 ± 21 4143 .0 fixed 11 .7 fixed 1 .9 σ −1 +2 .9 +10 .4 2011 CDF 6.0 fb (94) 115 ± 12 4143 .4 −3 .0 ± 0 .6 15 .3− 6 .1 ±2 .5 5 .0 σ 14 .9 ± 3 .9 ± 2 .4 2011 LHCb 0.37 fb−1 (322) 346 ± 20 4143.4 fixed 15.3 fixed 1.4σ < 7 @ 90%CL −1 +15 2013 CMS 5.2 fb (81) 2480 ± 160 4148.0 ± 2.4 ± 6.3 28 −11 ± 19 5.0σ 10 ± 3 (stat.) −1 +1.0 2013 D0 10.4 fb (82) 215 ± 37 4159.0 ± 4.3 ± 6.6 19.9 ± 12.6 −8.0 3.0σ 21 ± 8 ± 4 2014 BaBar (325) 189 ± 14 4143.4 fixed 15.3 fixed 1.6σ < 13.3 @ 90%CL −1 +4.6 +21 +4.8 2016 LHCb 3.0 fb (49) 4289 ± 151 4146.5 ± 4.5 −2.8 83 ± 21 −14 8.4σ 13.0 ± 3.2 −2.0 −1 +6.2 2015 D0 10.4 fb (83) pp¯ → J/ψφ... 4152.5 ± 1.7 −5.4 16.3 ± 5.6 ± 11.4 5.7σ (4.7σ)

TABLE V Results related to J/ψφ mass structures heavier than the X(4140) peak. The unpublished results are shown in italics. The last column gives a fraction of the total B+ → J/ψφK+ rate attributed to the given structure. Year Experiment B → J/ψφK X(4274 − 4351) peaks(s) luminosity yield Mass [MeV] Width [MeV] Significance Fraction [%] −1 +8 .4 +21 .9 2011 CDF 6.0 fb (94) 115 ± 12 4274 .4 −6 .7 ± 1 .9 32 .3 −15 .3 ± 7 .6 3 .1 σ 2011 LHCb 0.37 fb−1 (322) 346 ± 20 4274.4 fixed 32.3 fixed < 8 @ 90%CL −1 +30 2013 CMS 5.2 fb (81) 2480 ± 160 4313.8 ± 5.3 ± 7.3 38 −15 ± 16 2013 D0 10.4 fb−1 (82) 215 ± 37 4328.5 ± 12.0 30 fixed 2014 BaBar (325) 189 ± 14 4274.4 fixed 32.3 fixed 1.2σ < 18.1 @ 90%CL −1 +17.2 + 8 +3.5 2016 LHCb 3.0 fb (49) 4289 ± 151 4273.3 ± 8.3 − 3.6 56 ± 11 −11 6.0σ 7.1 ± 2.5 −2.4 +12 +21 +3.5 4506 ± 11 −15 92 ± 21 −20 6.1σ 6.6 ± 2.4 −2.3 +14 +42 +9 4704 ± 10 −24 120 ± 31 −33 5.6σ 12 ± 5 −5 +4.6 +18 2010 Belle (95) γγ → J/ψφ 4350.6 −5.1 ± 0.7 13 − 9 ± 4 3.2σ

∗ ¯ ∗ ¯ ∗ D D and DsDs , final states with total width predictions resembling the J/ψφ mass peaks, as illustrated in Fig. 43, that range from low values near 30 MeV (39; 333) to val- which argues against a charmonium interpretation for ues of 58 MeV (330). Given the considerable theoreti- any state among the X(4140), X(4274), X(4500) and cal uncertainties of these predictions, either the X(4140) X(4700). or the X(4274) can be considered as a candidate for the χc1(3P) state. The X(4500) and the X(4700) have been suggested as candidates for the χ (4P) and χ (5P) c0 c0 E. X∗(3860), X(3940) and X(4160) states, since they lie in the predicted mass and width ranges for these states (332; 333). These higher charmo- As discussed above in Section III.A, the X(3940) was nium states would have a large number of allowed decay first seen by Belle (79) as an unexpected peak in the modes to open charm mesons but, unfortunately, there distribution of masses (Mrecoil(J/ψ)) recoiling against a are no published measurements of mass spectra in the + − J/ψ in inclusive e e → J/ψX annihilation at Ecm ' relevant mass ranges for B → D(∗)D¯ ∗ K decays. (s) (s) 10.6 GeV shown in Fig. 16a. In this figure, there are Na¨ıvely, one expects the couplings of the χcJ (nP ) four distinct peaks: the lower three are due to the ex- + − + − states to J/ψφ and to J/ψω to be very similar, with the clusive processes e e → J/ψηc, e e → J/ψχc0 and + − 0 rate for the latter being enhanced by the larger phase- e e → J/ψηc. The fourth peak, near 3940 MeV, can- space that is available for the lighter states and the rel- not be associated with any known or expected charmo- ative ease of producing light uu¯ or dd¯ quark pairs that nium state and has been named the X(3940). The curve comprise the ω from the vacuum compared to that for shows results of a fit that includes four BW line shapes, more massive ss¯ pairs that comprise the φ. The J/ψω three for the established ηc, χc0 and ηc(2S) charmonium mass spectrum in B → J/ψωK decays measured by the states plus a fourth one to accommodate the unexpected BaBar collaboration (325) does not show any structures peak near 3940 MeV. From the fit, the mass of the fourth 40

600 space spanned by the final state particles. For each choice of nonresonant amplitude, an additional, coher- ± ± 500 B → J/ψωK BaBar ent BW amplitude was needed. The mass and width of B±→ J/ψφK± LHCb the BW resonance determined from the best fit to the / (20 MeV) 400 data (shown in Fig. 44b as a solid blue histogram) are ψ J/ M = 3862+26 +40 MeV and Γ = 201+154 +88 MeV. The p −32 −13 −67 −82 300 J PC = 0++ quantum number hypothesis gives the best fit to the data and was favored over the 2++ hypothesis 200 by 2.5σ. The mass, 0++ quantum numbers and strong DD¯ decay mode of the X∗(3860) all match well to ex- 100

Signal yield / pectations for the χc0(2P) charmonium state, making it a superior candidate for this assignment than the X(3915). 0 4100 4200 4300 4400 4500 4600 4700 4800 mJ/ψφ or mJ/ψω [MeV] 2. X(3940) → DD¯ ∗ FIG. 43 The efficiency-corrected and background-subtracted ∗ J/ψφ invariant mass spectrum for B+ → J/ψφK+ decays Figure 45a shows the the DD¯ invariant mass dis- (red points) from LHCb (49; 50) and the J/ψω mass spectrum tribution for e+e− → J/ψDX annihilation events where + + ∗ for B → J/ψφK decays (blue points) from BaBar (325), Mrecoil(J/ψD) is in the D¯ peak (78). Here the hatched where the signal yields (in arbitrary units) have been divided histogram is the non-J/ψ and/or non-D-meson back- by the J/ψ momentum in the X rest frame to account for ground determined from J/ψ and D-meson mass side- phase-space differences. The two distributions are normalized band events. The inset shows the background-subtracted to have equal areas for masses above the J/ψφ threshold. M(DD¯ ∗) distribution, which is dominated by a near- threshold peak. A fit of a BW resonance to these data, shown as a solid curve in the figure, returns a mass and state was found to be M = 3943 ± 6 MeV, and a limit on +27 the total width of Γ ≤ 52 MeV was established. width of M = 3942 ± 9 MeV and Γ = 37−17 MeV, values that are consistent with results for the X(3940) deter- Belle did subsequent studies of the exclusive processes + − e+e− → J/ψD(∗)D¯ (∗) decays in the same energy region, mined from the inclusive e e → J/ψX missing mass where, to compensate for the low detection efficiency for distribution (79). D and D∗ mesons, a partial reconstruction technique was used that required the reconstruction of the J/ψ and 3. X(4160) → D∗D¯ ∗ only one D or D∗ meson, and the presence of the un- ¯ ¯ ∗ detected D or D was inferred from energy-momentum Figure 45b shows the the D∗D¯ ∗ invariant mass conservation. With this technique, Belle found a strong distribution for e+e− → J/ψD∗X annihilation events ¯ ∗ signal for X(3940) → DD (78) plus two other states: where M (J/ψD∗) is in the D¯ ∗ mass region. Here the ∗ ¯ ∗ ¯ ∗ recoil the X (3860) → DD (288) and Y (4160) → D D (78). mass-sideband-estimated non-J/ψ and/or non-D∗-meson Although these three states have not been confirmed by backgrounds are very small. The curve shows the result any other experiment, the significance of the Belle ob- of a fit to a single BW resonance term plus a phase-space- servations in all three cases is above the 5σ level and we like background. The fitted mass and width for this peak, briefly discuss them here. which is called the X(4160), is M = 4156 ± 27 MeV and +113 Γ = 139− 65 MeV (78).

∗ 1. X (3860) → DD¯; an alternative χc0(2P) candidate? 4. Discussion Figure 44a shows the distribution of masses recoiling against a detected J/ψ and D meson in e+e− → J/ψD+ Neither the X(3940) nor the X(4160) show up in the X annihilation events collected in Belle at c.m. energies DD¯ invariant mass distribution for exclusive e+e− → at and near 10.58 GeV. There two peaks are apparent, J/ψDD¯ at the same energies. Also, as mentioned above, one centered at Mrecoil(J/ψD) = mD, corresponding to the absence of signals for any of the known non-zero exclusive e+e− → J/ψDD¯ events and the other centered spin charmonium states in the inclusive spectrum of + − ∗ at mD∗ , corresponding to exclusive e e → J/ψDD¯ Fig. 16a provides circumstantial evidence for J = 0 as- events (288). Figure 44b shows the distribution of DD¯ signments for the X(3940) and X(4160). If the X(3940) pairs in the exclusive J/ψDD¯ event sample, where there has J = 0, its DD¯ ∗ decay mode ensures that its J PC is a strong peaking at small masses. Fits to the data with quantum numbers are 0−+. If the X(4160) has J = 0 a variety of nonresonant-model amplitudes were unable the absence of any sign of X(4160) → DD¯ decay sup- to describe the data over the four-dimensional phase- ports a 0−+ assignment for this state as well. In both 41

a) e+e− J / D X b) + − → ψ e e → J /ψ D(D) * Belle J /ψ DD J /ψ DD

* X (3860)→ DD

Mrecoil(J/ψD) (GeV) M(DD) (_ GeV)

FIG. 44 a) The distribution of masses recoiling from a reconstructed J/ψ and D-meson in e+e− → J/ψDX annihilation at and near + − ∗ Ecm = 10.58 GeV. The two peaks correspond to exclusive e e → J/ψDD¯ and J/ψDD¯ events. The shaded histogram indicates the background level determined from the J/ψ and D mass sidebands. b) The DD¯ invariant mass distribution for the exclusive e+e− → J/ψDD¯ events. The solid blue histogram is the result of a ﬁt with a BW resonant amplitude plus a coherent non-resonant background. The red dash histogram is the ﬁt result when only a non-resonant amplitude is included (288).

+ − * This pattern conﬂicts with expectations from potential a) e e → J /ψ D(D ) Belle models, where hyperﬁne splittings are proportional to * X(3940)→ DD the square of the cc¯ radial wave-function at r = 0 and decrease with increasing nr (40), and is the main reason that the X(3940) and X(4160) are considered candidates for non-standard charmonium-like hadrons.

0 + − * * b) e e → J /ψ D (D )

* * X(4160)→ D D VI. CHARGED NON-STANDARD HADRON CANDIDATES

Distinguishing neutral candidates for non-standard mesons that decay into quarkonia states, from excitations of conventional QQ¯ states is a complex task that can be fraught with ambiguities. In contrast, charged quarkonium-like candidates are explicitly non- FIG. 45 a) The M(DD¯ ∗) distribution for e+e− → J/ψDD¯ ∗ events where the J/ψ and D-meson are reconstructed and the four- standard and the only outstanding issues concern the momentum of the undetected D¯ ∗-meson is inferred from energy- nature of their internal dynamics. Candidates for both momentum conservation. The hatched histogram is the non-J/ψ charmonium-like and bottomonium-like charged states and/or non-D meson background determined from the J/ψ and D-meson mass sidebands. The curve shows the results of the ﬁt are discussed in the section. to the X(3940) resonance described in the text. b)The M(D∗D¯ ∗ distribution for exclusive e+e− → J/ψD∗D¯ ∗ events. The curve is the result of the ﬁt for the X(4160). A. Z(4430)+ and similar structures in B decays

1. The Z(4430)+ → ψ0π+ in B → ψ0π+K decays cases, the measured masses are far below expectations for the only available unassigned 0−+ charmonium lev- The first established candidate for a charged els: the ηc(3S) and ηc(4S). Since there are no strong charmonium-like state dates back to 2007, when the reasons to doubt the generally accepted identifications Z(4430)+ was observed by the Belle collaboration as a of the ψ(4040) peak seen in the inclusive cross section peak in the the invariant mass of the ψ0π+ system in B¯ → + − 0 + 0 − for e e →hadrons as the ψ(3S) and the ψ(4415) peak ψ π K decays (45) (K = Ks or K ). The BaBar exper- as the ψ(4S) (207), these assignments would imply hy- iment, with a data sample containing a similar number of 3 1 0 + perfine nrS − nrS mass splittings that increase from the B → ψ π K decay events, did not find strong evidence + measured value of 47.2 ± 1.2 MeV for nr = 2 (9), to for a Z(4430) signal that could not be attributed to re- + ∼ 100 MeV for nr = 3 and ∼ 250 MeV for nr = 4 (334). flections from various kaon excitations decaying to Kπ 42 that were analyzed in a model-independent way (335). 1.0 < M2(K-,π+) < 1.8 GeV2/c4 However, the BaBar results were not sensitive enough to 4

directly contradict the Belle observation. Subsequently, /c the Belle collaboration reanalyzed their data with an am- 2 plitude model that combined coherent Kπ+ and ψ0π+ LHCb resonant contributions to fit to the data distribution 200 across a two-dimensional (M 2(Kπ) vs. M 2(ψ0π)) Dalitz plane (109). This was later refined to include two additional kinematic variables that were angles that describe ψ0 → `+`− decays (110). Both analyses reaffirmed Belle’s Events / 0.2 GeV original claim for a significant Z(4430)+ signal, albeit 100 + with a substantially larger mass and total width than the Zc(4430) values given in the initial Belle report, which was based 0 + on a na¨ıve fit to the ψ π mass distribution. The latter, + Zc(4240) four-dimensional amplitude analyses favored a J P = 1+ spin-parity of the Z(4430)+ over other possible J P as- 0 signments at the 3.4σ level. 15 16 17 18 19 20 21 22 23 + The existence of the Z(4430)+ structure was indepen- M2(ψ(2S),π ) GeV2/c4 dently confirmed in 2014 (with 13.9σ significance) by the LHCb experiment (46), which was based on a four- dimensional analysis of a B¯0 → ψ0π+K− event sample that was an order of magnitude larger than those used in the Belle and BaBar experiments (see Fig. 46(upper)). The LHCb amplitude analysis yielded results that were consistent with the Belle determination, including the confirmation of the J P = 1+ assignment, but in this case at the 9.7σ level. The average of the Belle and LHCb mass and width values are (9) +15 M(Z(4430)) = 4478−81 MeV Γ(Z(4430)) = 181 ± 31 MeV. (18) The large event sample enabled the LHCb group to measure the 1+ Z(4430)+ amplitude’s dependence on ψ0π+ mass independently of any assumptions about the resonance line shape. The resulting “Argand diagram” of the real vs. imaginary parts of the 1+ amplitude, shown in Fig. 47(left), shows a nearly circular, counter- FIG. 46 The points with errors show distributions of (up- 2 0 + ¯0 0 + − clockwise motion with an abrupt change in the amplitude per) M (ψ π ) in B → ψ π K decays from LHCb (46) and (lower) M 2(J/ψπ+) in B¯0 → J/ψπ+K− from Belle (51). phase at the peak of its magnitude that is characteristic Here only events with K−π+ invariant masses that are be- of a BW resonance amplitude. This diagram rules out ∗ 0 ∗ 0 tween the K (892) and K2 (1430) resonances are included in an interpretation of the Z(4430) peak as being due to order to suppress contributions from the Kπ channel. Projec- the effects of a rescattering process proposed by Pakhlov tions of four-dimensional amplitude fits that include coherent and Uglov (336) that predicted a clock-wise phase mo- contributions from kaon excitations and two Z+ terms are su- + tion. Since other rescattering mechanisms or coupled- perimposed as solid-line histograms. The individual Z terms channel cusps could produce a counter-clockwise phase are shown as blue and green points; the dashed red curve in the Belle plot shows the projection of all the K−π+ terms motion similar to that of a BW resonance, higher statis- combined. tics studies of the Argand diagram are needed to probe the amplitude-dependence on mass at a level of detail that is fine enough to distinguish a resonance pole from other types of meson-meson interactions. The LHCb collaboration also performed an analysis decays at the 8σ level, as shown in Fig. 48. While this of their B¯0 → ψ0π+K− events using a K−π+ model- approach demonstrates the need for contributions from a independent approach (111) similar to the one that was non-Kπ source in the Z(4430)+ mass region, it does not earlier performed by the BaBar collaboration (335). This provide any independent way to extract any of the char- approach yielded conclusive results that demonstrate the acteristics of these contributions; for this, an amplitude requirement for non-Kπ contributions to B¯0 → ψ0π+K− analysis approach is necessary. 43

+ 70 +31 +17

+ Γ = 370±70−132 MeV, mass 4196 −29 −13 MeV, and a sig- Z 4.277 0.2 niﬁcance of 6.2σ, and the second corresponding to J/ψπ Im A Im 4.344 LHCb decay mode of the Z(4430). The analysis showed that the + 0 4.411 Z(4200) interferes destructively with the Z(4430) → + 2 + + J/ψπ amplitude, producing a dip in the M (J/ψπ ) Zc(4430) -0.2 distribution near the Z(4430) peak mass, as shown in

4.475 Fig. 46(lower). In the analysis, the mass and width of -0.4 + 4.605 the Z(4430) → J/ψπ BW amplitude were fixed at the 0 + 4.541 values determined from the ψ π analysis. The statisti- -0.6 -0.6 -0.4 -0.2 0 0.2 cal significance (not including systematic errors) of the + Re AZ Z(4430) → J/ψπ+ amplitude was determined to be 5.1σ, and the magnitude of the Z(4430) → J/ψπ term was FIG. 47 Fitted values of the real and imaginary parts of the 0 + 0 + found to be much smaller than that for Z(4430) → ψ π in amplitude for (left) LHCb’s Z(4430) → ψ π signal (46) + and (right) Belle’s Z(4200)+ → J/ψπ+ signal (51), for six spite of the larger available phase-space. The Z(4200) M 2(ψ, π+) bins of equal width that span the resonance. The state awaits independent confirmation, although some in- solid red curve in the LHCb plot shows the pattern expected dication for it in ψ(2S)π+ decays may have been seen in for a Breit-Wigner resonance amplitude. Units are arbitrary. the LHCb B → ψ0πK analysis (46), where they reported evidence for a state in this mass region with either 0− or 1+ quantum numbers that is shown by the green points in Fig. 46(left).30 )

2 The Belle collaboration presented Argand diagrams for P + + 14000 the J = 1 J/ψπ amplitude for two helicity ampli- LHCb tudes. One of them, shown in Fig. 47(right), displays a 12000 nearly circular phase motion that is consistent with ex- 10000 pectations for a BW resonance amplitude.

8000 Yield / (25 MeV/c

6000

4000

2000

0 3800 4000 4200 4400 4600 4800 M(ψ(2S),π+) MeV/c2

FIG. 48 The dots with error bars show background- subtracted and eﬃciency-corrected M(ψ0π+) distribution for B¯0 → ψ0π+K− events in LHCb (111). The solid (dashed) blue lines correspond to contributions from the K−π+ channel for a maximum-allowed angular momentum of Jmax = 2 (Jmax = 3). Since the lightest known J = 3 resonance, the ∗ K3 (1780), is already beyond the kinematically allowed Kπ mass limit for B¯ → ψ0πK decay, no plausible contribution from the Kπ channel can account for the shape of the M(ψ0π) distribution in the Z(4430)+ mass region.

2. The Z(4200)+ → J/ψπ+ in B¯0 → J/ψπ+K− decays

The Belle collaboration performed an amplitude analysis of B¯0 → J/ψπ+K− decays (51) and found that in this channel too, the data could not be well de- 30 Using a 0− hypothesis, the LHCb obtained a mass of 4239 ± 18+45 MeV and a width of 220 ± 47+108 MeV, which are con- scribed solely with contributions from the Kπ channel. −10 − 74 sistent with the Belle results but cannot be averaged with them A satisfactory ﬁt was obtained only after contributions since they are obtained using diﬀerent JP assignments. For the from two J/ψπ+ resonances were included: one corre- 1+ hypothesis, LHCb only reported a width, 660±150 MeV, and sponding to a very broad 1+ Z(4200)+ state with width that without a systematic uncertainty. 44

2 + FIG. 49 The points with error bars show the M (χc1π ) 0 + − distribution for in B¯ → χc1π K decays detected in Belle (107). The projection of a two-dimensional amplitude ﬁt that included kaon excitations and two Z+ terms are superimposed as a solid-line histogram. The dotted line corresponds to all − + K π terms combined and the non-B and/or non-χc1 background contribution is shown by the dashed line. Z+ removed

K*(890)

Z+(4430) + 0 + − Kπ S-wave 3. Charged χc1π resonances in B¯ → χc1π K decays

The Belle collaboration also reported evidence M2(ψ’π) (GeV2) + for charged χc1π resonances in a two-dimensional 2 2 0 2 0 + (M (Kπ) vs. M (χc1π)) Dalitz plot analysis of B¯ → FIG. 50 The black points show the M (ψ π ) distribution + − for all of the LHCb B¯0 → ψ0π+K− events (46). The solid- χc1π K decays. The data could not be fitted with red histogram is the projection of the four-dimensional fit resonances in the Kπ channel only, and was best de- + + + that includes the Z(4430) amplitude and the dashed-brown scribed when two χc1π resonances, the Z(4050) and histogram shows the best fit that was found with no ψ0π+ + Z(4250) , were included, as shown in Fig. 49 (107). resonances. Contributions from individual fit components BaBar saw an enhancement in the same mass region, but are shown, with the dominant ones labeled. The upper blue could account for it with reflections from Kπ+ resonances points show the final fit results with the Z+ terms removed. analyzed with the model-independent method described The vertical dashed-blue line indicates the fitted Z+ reso- above (108); their results neither confirmed nor contra- nance mass value. + dicted the Belle results. These two candidate χc1π resonant states still await independent confirmation and a with amplitudes in the Kπ channel. The shape of the complete amplitude analysis that spans all 6 dimensions total Z+ contribution is much different than that of the of the decay phase-space and determines their quantum Z+ term alone, shown as the lower blue points, because numbers. of strong interference effects that are constructive on the low mass side of the Z+ resonance and switch to destructive at higher masses, reflecting the abrupt phase change 4. Discussion that occurs at the peak of a BW resonance amplitude. The Belle group’s original Z(4430)+ results were based The neutral X(3872), X(3915) and Y (4260) on a na¨ıve BW line-shape fit to the visible peak, which charmonium-like states discussed in Section V showed only corresponds to the lower lobe of the actual pattern. up as distinct, relatively narrow peaks on a small As a result, they reported low values for the mass and background. In these cases, fitting the peaks with simple width (45). BW line shapes and ignoring the effects of possible While the presence of coherent non-resonant processes signal interference with a coherent components of the complicates the extraction of resonance signals, it pro- non-resonant backgrounds were reasonable approxima- vides the possibility of measuring the signal amplitude’s tions. However, for the charged charmonium states phase motion across the resonance (see Fig. 47), thereby discussed in this subsection, this approximation is no providing valuable information that would otherwise be longer valid. Here, since the states are broad and inaccessible. contributions from coherent non-resonant processes are substantial, interference effects distort the signal line shapes to such an extent that they no longer resemble + + + − B. Charged Zb and Zc states produced in e e processes that of a standard BW resonance peak.

This is illustrated for the case of the LHCb group’s 1. The Zb charged bottomonium-like mesons Z(4430)+ → ψ0π+ analysis (46) in Fig. 50, where the black data points show the M 2(ψ0π+) distribution for The large Y (4260) → π+π−J/ψ signal discovered all of their selected B¯0 → ψ0π+K− events (with no in the charmonium mass region by BaBar motivated Kπ mass selection). The solid red histogram shows the a Belle search for similar behavior in the bottomo- results of the final LHCb four-dimensional fit that in- nium system (337). This uncovered anomalously large + + − cluded a Z(4430) amplitude and the upper blue points π π Υ(nrS) (nr = 1, 2, 3) production rates that peak + − show that fit’s results with the all terms involving the around Ecm(e e ) = 10.89 GeV as shown in the up- Z(4430)+ → ψ0π+ removed. The difference between the per three panels of Fig. 51 (113). This peak energy is red histogram and the upper blue points is the total Z+ close to a peak in the e+e− → b¯b cross section near contribution to the fit, including effects of interference Ecm ' 10.87 GeV, shown in the lower panel of Fig. 51, 45

-3 x10 2 + − ϒ(1S)π π Belle a) Belle R1S ϒ ϒ ϒ

x10-3 Events/1 MeV/c + − ϒ(2S)π π R2S

ππ x10-3

2 ϒ(2S) + − b) Belle ϒ(3S)π π R3S ϒ(1S) hb(2P)

hb(1P) ϒ(3S)

Events/5 MeV/c Y2(1D) e+e− → bb R b MM(π+π-) GeV

FIG. 52 a) Distribution of masses recoiling against π+π− pairs at c.m. energies near 10.87 GeV and (b) residuals from piece-wise ﬁts to the data with smooth polynomials (from ref. (340)). The hb(1P) and hb(2P) peaks, shaded in yellow, were the ﬁrst observations of Ecm (GeV) these two states.

+ − + − FIG. 51 Cross sections for e e → π π Υ(nrS) (nr = 1, 2, 3) (upper) and e+e− → b¯b (lower) in units of the Born QED cross sec- + − + − + − + − 2 2 10.866 GeV) in order to investigate the source of this tion for e e → µ µ (σQED(e e → µ µ ) = (4πα )/(3Ecm)) in the vicinity of the Υ(5S) resonance (from ref. (113)). anomaly, 121.4 fb−1 in total. Figure 52a shows the distribution of masses recoiling against all of the π+π− pairs in these events (340). The combinatoric background is huge that is usually associated with the conventional Υ(5S) – there are typically 106 entries in each 1 MeV bin – and bottomonium meson. + − the statistical errors are tiny (∼ 0.1%). The data were fit If the peaks in the π π Υ(nrS) cross sections piece-wise with sixth-order polynomials and the residu- are attributed to Υ(5S) decays, it implies Υ(5S) → + − als from the fits are shown in the lower panel of Fig. 52b, π π Υ(nrS) (nr = 1, 2, 3) partial widths that are where, in addition to peaks at the Υ(1S), Υ(2S), Υ(3S) two orders of magnitude larger than theoretical predic- masses and some expected reflections, there are unam- tions (112), and the measured value of the Υ(4S) width 1 31 + − biguous signals for the hb(1P) and hb(2P), the 1 P1 and (9). This suggests that either the peak in the e e 1 2 P1 bottomonium states. This was the first observation annihilation cross section near Ecm = 10.87 GeV that of these two elusive levels (340). One puzzle is that the has long been identified as the Υ(5S) b¯b bottomonium + − π π hb(mrP), (mr = 1, 2) final states are produced at state (210) is not a standard b¯b meson but, instead, a + − rates that are nearly the same as those for π π Υ(nrS) b-quark-sector equivalent of the Y (4260) (339), or there + − (nr = 1, 2, 3), even though the Υ(5S) → π π hb transi- is an overlap of the conventional Υ(5S) with a nearby tion requires a heavy-quark spin flip that is expected to b-quark-sector equivalent of the Y (4260), or the Υ(5S) result in a strong suppression (341). experiences some dynamical effects that have little or no + − Figure 53a show the π π hb yields vs. the maxi- influence on the Υ(4S). We follow the PDG and refer to ± this peak as the Υ(10860). mum hbπ invariant mass for hb = hb(1P) (upper) and hb = hb(2P) (lower), where it can be seen that essentially Belle accumulated a large sample of data at and near + − + − all of the π π hb events are associated with the produc- the energy of the Υ(10860) mass peak (Ecm(e e ) = tion of an hbπ system with an M(hbπ) value near either 10 610 MeV or 10 650 MeV (114). Studies of fully reconstructed π+π−Υ(n S), (n = 1, 2, 3) Υ(n S) → `+`− 31 r r r For example, the PDG average value of Υ(4S) branching frac- events in the same data sample found Υ(n S)π mass tion to π+π−Υ(1S) measurements is B(Υ(4S) → π+π−Υ(1S) = r (8.1 ± 0.6) × 10−5 (9). In contrast, the Belle measurement peaks at the same masses in the Mmax(Υ(nrS)π) dis- for the peak near 10.86 GeV is more than 50 times larger, tributions for all three narrow Υ(nrS) states; these are B(Υ(10860) → π+π−Υ(1S)) = (5.3 ± 0.6) × 10−3 (338). shown in the three panels of Fig. 53b. Here the frac- 46

+ − ∗ ∗ ∗ ∗ tions of π π Υ(nrS) events in the two peaks are sub- fit and a Zb(10650) → B B¯ amplitude for the B B¯ stantial – ∼ 6% for the Υ(1S), ∼ 22% for the Υ(2S) (Fig. 54b) fit and gives an adequate description of the and ∼ 43% for the Υ(3S) – but, unlike the case for the data. Other variations: phase-space only (dotted); sin- + − π π hb(mrP) channels, they only account for a frac- gle BW amplitudes plus phase-space (dashed-dot) and + − tion of the anomalous π π Υ(nrS) event yield (115). two BW amplitudes plus phase-space (long dashed) do Thus, the production and decays of the two Zb states not make any significant improvements. can explain some, but not all of the anomalously large From the default fit, the branching fraction values + − + ∗0 0 ∗+ Υ(5S) → π π Υ(1, 2, 3S) decay rates. The fitted values B(Zb(10610) → B B¯ + B¯ B ) = (86 ± 3)% and ∗+ ∗0 of the peak masses (indicated by the vertical dashed lines B(Zb(10610) → B B¯ ) = (74 ± 6)% are inferred. The in each panel of Fig. 53) and widths in all five channels B(∗)B¯∗ fall-apart modes are stronger than the sum to- + + are consistent with each other; the weighted average mass tal of the π Υ(nrS) and π h(mrP) modes, but only and width values of the two peaks, dubbed the Zb(10610) by factors of ∼ 6 for the Zb(10610) and ∼ 3 for and Zb(10650), are the Zb(10650). The measured branching fraction for ∗ Zb(10650) → BB¯ is consistent with zero. This pat- Zb(10610) : M1 = 10 607 ± 2 MeV ∗ tern, where BB¯ decays dominate for the Zb(10610) and ∗ ∗ Γ1 = 18.4 ± 2.4 MeV B B¯ decays are dominant for the Zb(10650) are consis- Zb(10650) : M2 = 10 652 ± 2 MeV tent with expectations for molecule-like structures (342), Γ = 11.5 ± 2.2 MeV, (19) which were proposed even before these states were ob- 2 served (343; 344). A tetraquark interpretation of these 0 0 respectively. A Belle study of π π Υ(nrS), (nr = 1, 2, 3) states (345) was also made before their discovery (346). 0 found a 6.5σ signal for the neutral Zb(10610) isospin 0 partner state with a mass M(Zb(10610) ) = 10 609 ± 6 MeV and a production rate that is consistent with 2. The Zc charged charmonium-like mesons isospin-based expectations (116). The Zb(10610) mass is only 2.6 ± 2.2 MeV above the As discussed in the previous Section, the discovery mB + mB∗ mass threshold and the Zb(10650) mass is in the c-quark sector of the unexpected Y (4260) → + − only 2.0 ± 1.6 MeV above 2mB∗ . Dalitz-plot analyses π π J/ψ signal in the initial-state-radiation process + − P + + − + − of the π π Υ(nrS) final states establish J = 1 quan- e e → γisrπ π J/ψ at Ecm ' 10.6 GeV moti- tum number assignments for both states (115). The close vated Belle to look for possible related anomalies in ∗ + − + − proximity of the Zb(10610) and Zb(10650) to the BB¯ e e → π π Υ(nrS) (nr = 1, 2, 3) reactions near and B∗B¯∗ thresholds, respectively, and the J P = 1+ Ecm = 10.86 GeV. This resulted in the discovery of quantum number assignment suggests that they may be anomalously high rates transitions of what was thought virtual S-wave molecule-like states (341). to be the Υ(5S) charmonium state to π+π−Υ(1, 2, 3S), as The B(∗)B¯∗ molecule picture is supported by a Belle shown in the top three panels of Fig. 51 (338). Further study of Υ(10860) → πB(∗)B¯∗ final states in the same investigations of these anomalies led to the discovery of data sample (117), where the the pion and one B-meson the Zb(10610) and Zb(10650) charged bottomonium-like is reconstructed and the presence of the accompanying states. These discoveries in the b-quark sector prompted B¯ and the distinction between πBB¯∗ and πB∗B¯∗ are the BESIII group to take data with the BEPCII collider inferred from energy-momentum conservation; the BB¯∗ operating at Ecm = 4.26 GeV, to see if there were c-quark and B∗B¯∗ invariant masses are inferred from the pion sector equivalents of the Zb states produced in the decays momentum. The data points in Figures 54a and 54b of the Y (4260). show the BB¯∗ and B∗B¯∗ invariant mass distributions, The Zc(3900) : Figure 55 shows the distribution of respectively, where the background, mostly from contin- the largest of the π+J/ψ and π−J/ψ/ invariant mass uum e+e− → cc¯ events and estimated from events where combinations in Y (4260) → π+π−J/ψ events in a −1 the pion charge and the flavor of the detected B meson 525 pb BESIII data sample accumulated at Ecm = do not match, is shown as hatched histograms. 4.260 GeV (92). Here a distinct peak, called the ∗ The M(BB¯ ) distribution (Fig. 54a) has a distinct Zc(3900), is evident near 3900 MeV. A fit using a ∗ ∗ ± peak near the mass of the Zb(10610) and the M(B B¯ ) BW amplitude to represent the π J/ψ mass peak and distribution (Fig. 54b) peaks at the Zb(10650) mass. Fits an incoherent phase-space-like function to represent the to the data with various combinations of Zb BW ampli- non-resonant background gives a mass and width of tudes, both with and without a coherent non-resonant M(Zc(3900)) = 3899.0 ± 6.1 MeV and Γ(Zc(3900)) = phase-space term, are shown as curves in the figures. 46±22 MeV, which is ∼ 24 MeV above the mD∗+ +mD¯ 0 In these fits, the masses and widths of the BW am- (or mD+ + mD¯ ∗0 ) threshold. The Zc(3900) was observed plitudes are fixed at the values given in Eq. 19. The by Belle in isr data at about the same time (88). default fit, shown as short-dashed curves, uses only a A subsequent BESIII study of the D0D∗− systems pro- ∗ ∗ + − + 0 ∗− Zb(10610) → BB¯ amplitude for the BB¯ (Fig. 54a) duced in e e → π D D final states in the same data 47

+ − ϒ(10860)→ π π h (1P) + − a) b Belle b) ϒ(10860)→ π π ϒ(1S) Belle

M(ϒ(1S)π±) (GeV/c2)

+ − ϒ(10860)→ π π ϒ(2S)

π ± 2 M(hb(1P)π) (GeV/c )

ϒ(10860)→ π +π −h (2P) b

M(ϒ(2S)π±) (GeV/c2)

+ − ϒ(10860)→ π π ϒ(3S)

± 2 ± 2 M( (3S)π ) (GeV/c ) M(hb(2P)ππ) (GeV/c ) ϒ

+ + + − + − FIG. 53 a) Invariant mass distributions for hb(1P)π (upper) and hb(2P)π (lower) from e e → π π hb(nrP) events. b) Invariant + + + + − + − mass distributions for Υ(1S)π (upper), Υ(2S)π (center) and Υ(3S)π (lower) in e e → π π Υ(nrS) events. The vertical dashed lines in each panel indicate the mass values given in Eq. 19. The figures are from ref. (114). sample (102) found the very strong near-threshold peak background are ignored, an approximation that can bias in the D0D∗− and invariant mass distribution shown in mass measurements by amounts comparable to the res- Fig. 56a. The solid curve in the figure shows the results onance widths, and this effect could account for the dif- of a fit to the data with a threshold-modified BW am- ferent mass values. Thus, we consider it highly likely plitude to represent the peak and an incoherent phase- that the Zc(3885) is the Zc(3900) in a different de- space-like function to represent the background. The cay channel. If this is the case, the partial width for − ∗0 ∗ same analysis found a similar peak in the D D invari- Zc(3900) → DD¯ decays is 6.2 ± 2.9 times larger than ant mass distribution in e+e− → π+D−D∗0 events. The that for J/ψπ+, which is small compared to open-charm masses and widths from the two channels are consistent vs. hidden-charm decay-width ratios for established char- and their average values are M = 3883.9 ± 4.5 MeV and monium states above the open-charm threshold, such as Γ = 24.8 ± 12 MeV, the ψ(3770) and ψ(4040), where corresponding ratios are measured to be more than an order-of-magnitude Since the mass is ' 2σ lower than the Z (3900) mass c larger (9). On the other hand, this ratio is similar to reported in ref. (92), BESIII cautiously named this DD¯ ∗ the properties of the X(3872) and Zb states. state the Zc(3885). In the mass determinations of both ∗ the Zc(3885) and Zc(3900), effects of possible interfer- The strong Zc(3885) → DD¯ signal enabled the BE- ence with a coherent component of the non-resonant SIII group to determine its J P quantum numbers from 48

yield as a function of | cos θπ|, together with expecta- + * − ϒ(10860)→ π (BB ) Belle tions for J P = 0+ (dashed red), 1− (dotted blue) and Belle J P = 1+. The J P = 1+ assignment is clearly preferred default model and the 0− and 1− assignments are ruled out with high conﬁdence. BESIII also reported neutral counterparts of the 0 + − 0 0 Zc(3900) in the π J/ψ channel in e e → π π J/ψ events (101), and the D+D∗− and D0D¯ ∗0 channels in e+e− → π0(DD¯ ∗)0 events (103), with mass and width values that are in good agreement with the charged

+ * * − Z (3900) state measurements. The relative signal yields ϒ(10860)→ π (B B ) c in the charged and neutral channels are consistent with default model expectations based on isospin conservation. The Zc(4020) : With data accumulated at the peaks of the Y (4260), Y (4360) and nearby energies, BESIII + − made a study of π π hc(1P) ﬁnal states (93). Exclu- sive hc(1P) decays were detected via the hc → γηc transition, where the ηc was reconstructed in 16 exclusive hadronic decay modes. With these data, BESIII ob- ± served a distinct peak near 4020 MeV in the Mmax(π hc)

M(B(*)B*) (GeV/c_ 2) distribution that is shown in Fig. 57a. A fit to this + peak, which the BESIII group called the Zc(4020) , FIG. 54 a) The M(BB¯∗) distribution for π+BB¯∗ events and b) with a signal BW amplitude (assuming J P = 1+) plus the M(B∗B¯∗) distribution for π+B∗B¯∗ events. The short-dashed ¯∗ a smooth background, returns a ∼ 9σ significance sig- curves show results of fits with only a Zb(10610) → BB contri- ∗ ¯∗ bution to a) and a Zb(10650) → B B contribution the b). The nal with a mass of M(Zc(4020)) = 4022.9 ± 2.8 MeV other curves and the hatched (background) histogram are described – about 5 MeV above mD∗+ + mD¯ ∗0 – and a width of in the text. The figures are from ref. (117). Γ(Zc(4020)) = 7.9 ± 3.7 MeV. The inset in Fig. 57a shows the result of includ- + + + − ing a Zc(3900) → π hc term in the fit. In this Y(4260)→ π π J /ψ + + a) case, a marginal ∼ 2σ signal for Zc(3900) → π hc is seen to the left of the Zc(4020) peak. This trans- BESIII lates into an upper limit on the branching fraction for + + Zc(3900) → π hc decay that is less than that for + + Zc(3900) → π J/ψ by a factor of five. BESIII also observed the neutral isospin partner of 0 the Zc(4020) (104). The Mmax(π hc) distribution for + − 0 0 e e → π π hc events in the same data set used for the ± Zc(4020) , shown in Fig. 57b, looks qualitatively like + the Mmax(π hc) distribution with a distinct peak near 4020 MeV. A fit to the data that includes a BW term with + a width fixed at the value measured for the Zc(4020) and floating mass returns a mass of 4023.9 ± 4.4 MeV; this and the signal yield are in good agreement with expectations based on isospin symmetry. ± FIG. 55 Distribution of the larger of the two π J/ψ masses in A study of e+e− → D∗+D¯ ∗0π− events in the E = e+e− → π+π−J/ψ events collected in the BESIII detector at cm 4.260 GeV data sample using a partial reconstruction Ecm = 4.260 GeV. The histogram shows the level of the non-J/ψ background, which is determined from J/ψ mass sideband events. technique that only required the detection of the bach- The figure is from ref. (92). elor π−, the D+ from the D∗+ → π0D+ decay and one π0, either from the D∗+ or the D¯ ∗0 decay, to isolate the process and measure the D∗+D¯ ∗0 invariant mass (105). ∗+ ∗0 − the dependence of its production on θπ, the bachelor pion The signal for real D D¯ π final states is the dis- production angle relative to the beam direction in the tinct peak near 2.15 GeV in the distribution of masses + − P − + − e e cm system. For J = 0 , dN/d| cos θπ| should go recoiling from the reconstructed D and π , shown in 2 − 2 ∗ ∗ as sin θπ; for 1 it should follow 1 + cos θπ and for Fig. 58a. The measured D D¯ invariant mass distri- 1+ it should be flat (0+ is forbidden by Parity). Fig- bution for events in the 2.15 GeV peak and inferred − ure 56b shows the efficiency-corrected Zc(3885) signal from the π momentum is shown as the data points in 49

0.5 a) Y(4260)→ π +D0D*− d)# Y(4260)→ π +D0D*− BESIII 0.45 b) BESIII# BESIII 0.4 P ,# 0.35 J =1 0.3 JP=1+# 0.25 0.2 0.15 JP=0,# 0.1

Fractional yield 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

|cos | 0 ∗− + − + 0 ∗− FIG. 56 a) The D D invariant mass distribution in e e → π D D events collected in the BESIII detector at Ecm = 4.260 GeV (102). The solid curve shows the result of a fit to the data points with a threshold-modified BW amplitude plus an incoherent phase-space-like background (dashed curve). b) The efficiency corrected Zc(3885) production angle distribution compared to expectations for different JP quantum number assignments. The figures are from ref. (102).

+ − Y(4260)→ π π h 0 0 c Y(4260)→ π π h a) b) c BESIII BESIII

± 2 Mmax(π hc) (GeV/c )

± 2 0 2 Mmax(π hc) (GeV/c ) Mmax(π hc) (GeV/c )

± + − + − FIG. 57 a) The distribution of the larger of the two π hc masses in e e → π π hc events collected in the BESIII detector at 0 Ecm = 4.260 and 4.360 GeV. The inset shows a larger M(πhc) that includes the Zc(3900) mass region. b) The Mmax(π hc) distribution + − 0 0 for e e → π π hc events. The histograms show the level of the non-hc background determined from hc mass sideband events. The curves are described in the text. The ﬁgures are from refs. (93) and (104), respectively.

Fig. 58b, where a strong near-threshold peaking behavior ues that agree within errors to those measured for the + + that cannot be described by a phase-space-like distribu- Zc(4020) → π hc channel. Although BESIII cautiously ∗ ∗ + tion, shown as a dash-dot blue curve, or by combina- calls this (D D¯ ) signal the Zc(4025), we consider this toric background, which is determined from wrong-sign to likely be another decay mode of the Zc(4020). (WS) events in the data (i.e. events where the pion and A neutral D∗D¯ ∗ state with a mass and width that charged D meson have the same sign) that are shown are consistent with the Z (4025)+ was seen by BESIII in as the shaded histogram. The solid black curve shows c e+e− → π0(D∗D¯ ∗)0 events (106). the results of a fit to the data points that includes an ∗ ∗ − efficiency weighted S-wave BW function (long dashes), The Zc(4020) → D D¯ and π hc signal yields re- the combinatoric background shape (short dashes) scaled ported in refs. (105) and (93), respectively, imply a par- ∗+ ∗0 − ∗ ∗ to measured non-D D¯ π background level under the tial width for Zc(4020) → D D¯ that is larger than signal peak in Fig. 58a, and a phase-space term (dash- that for Zc(4020) → πhc, but only by a factor of dot). The fit returns a 13σ signal with mass and width 12 ± 5, not by the large factors that are characteris- M = 4026.3 ± 4.5 MeV and Γ = 24.8 ± 9.5 MeV, val- tic of conventional charmonium. In addition, there is ∗ no sign of Zc(4020) → DD¯ in Fig. 56a, where there 50

a) b) BESIII

+ - 2 _ Mrecoil(D π ) (GeV/c ) M(D*+D*) (GeV/c2)

FIG. 58 a) Distribution of masses recoiling against the reconstructed π− and D+ in e+e− → π−(D∗D¯ ∗)+ events collected in the BESIII + − − ∗+ ∗0 + ∗+ ∗0 detector at Ecm = 4.260 GeV. The peak near 2.15 GeV corresponds to e e → π (D D¯ ) signal events. b) The M(D D¯ ) distribution inferred from the π− momentum for signal events. The histograms show the level of the combinatoric background determined from events where the reconstructed pion and D meson have the same electric charge. The curves are described in the text. The ﬁgures are from ref. (105).

0 ∗− is a ∼ 500 event Zc(3885) → D D signal. A re- pentaquark baryons qqqqq¯. Experimental searches for ∗ cent BESIII study of Zc(3900) → DD¯ decays (347) pentaquarks comprised of light flavors have a long and set a 90% confidence level upper limit B(Zc(4020) → often controversial history that is briefly summarized in ∗ ∗ DD¯ ) < 0.13 × B(Zc(3885) → DD¯ ). This absence of sec. I.C. No undisputed candidates have been found in ∗ any evident signal for Zc(4020) → DD¯ suggests that the over fifty years of searches, although unusual properties ∗ Zc(4020) → DD¯ partial width is considerably smaller of some ordinary baryons, such as, e.g. the Λ(1405), are ∗ ∗ than that for Zc(4020) → D D¯ , which mirrors the be- often attributed to mixing of qqq and qqqqq¯ systems. havior of the two Z states and is suggestive of some b In 2015, convincing evidence for pentaquark-like struc- relation to the Z (4020)’s proximity to the 2m ∗ thresh- c D tures with a minimal quark content of uudcc¯ was reported old. 0 − + − by LHCb in a study of Λb → J/ψpK (J/ψ → µ µ ) Many similarities between the Zc and Zb states discov- + − decays (47). In addition to contributions from many con- ered in e e annihilations to ππ plus a heavy quarko- ventional Λ∗ → K−p baryon resonances (with a quark nium states can be taken as a reflection of Heavy Quark content of uds), the data contain a narrow peak in the Symmetry. However, there are also differences between J/ψp mass distribution that is evident as a distinct hor- them that await an explanation. While the Zb(10610) izontal band in the M 2(J/ψp) vs. M 2(K−p) Dalitz plot and Zb(10650) both decay to πΥ(nrS) and πhb, the shown in Fig. 59), and the distribution of J/ψp invariant Zc(4020) is not observed in πJ/ψ and the Zc(3900) is 32 masses shown in Fig. 60b. not observed in πhc. The latter is particularly difficult to accommodate in a purely molecular interpretation, in In order to clarify the nature of this band, an am- which both Zc states should copiously decay to πhc (349). plitude analysis was performed that was modeled after the four-dimensional analysis of B¯0 → ψ0π+K− (ψ0 → µ+µ−) that the LHCb group used to study the VII. PENTAQUARK CANDIDATES Z(4430)+ → ψ0π+ charmonium-like state as described in Section VI.A. Although the properties of the initial state At the birth of the quark model, Gell-Mann (1) and particles are quite different – the spin 1/2 Λb vs. the Zweig (2) both suggested the possibility of particles built spin 0 B-meson – the final states for the two processes from more than the minimal quark content, including are very similar, with π+ being replaced by p. The signal statistics, 26 000 ± 170, and the background level, 5.4%, are also very comparable. A quasi-two-body amplitude model was used that was based on an isobar approxima- 32 There is also possibly a different resonant πψ0 substructure in tion (i.e. summing up Breit-Wigner amplitudes) with the e+e− → π+π−ψ0 (348). dynamics of the contributing decay processes parameter- 51

] the ﬁgure. In contrast, in the M(J/ψp) projection at the 2 26 other extreme of the Dalitz plane, at low Kp mass val- LHCb ues (1.55 ≤ M(Kp) ≤ 1.70 GeV) shown in Fig. 61a, the + [GeV interference between the two Pc states is constructive. p 24

ψ High M(Kp) values correspond to cos θPc values near +1, 2 J/ while low M(Kp) values correspond to cos θP ≈ −1. The m 22 c observed pattern, with interference that is constructive

20 near cos θPc ≈ −1 and destructive near cos θPc ≈ +1, can only occur between odd and even partial waves, thereby + 18 indicating that the two Pc states must have opposite parities. A similar interference pattern is observed in the 16 cos θΛ∗ distribution (Fig. 7 in ref. (47)) that reflects the ∗ 2 3 4 5 6 presence of parity-doublets in the Λ spectrum. Unfortu- 2 + m2 [GeV ] nately, the spins of the two Pc states were not uniquely Kp determined. Within the statistical and systematic am- 0 − FIG. 59 Dalitz plot distribution for Λb → J/ψpK decays as biguities, (3/2, 5/2) and (5/2, 3/2) combinations with ei- observed by LHCb (47). ther (−, +) or (+, −) parities, are not well resolved. All other combinations are disfavored. There is a strong + dependence of the data preference for the Pc spins on ized by a helicity formalism. The amplitude fit spanned the Λ∗ model used in the amplitude fit (see sec. 13.1 in a kinematically complete, six-dimensional space of inde- ref. (350)), and this calls for some caution in the inter- pendent kinematic variables, including invariant masses + pretation of the observed Pc states until their quantum M(Kp) and M(J/ψp), decay helicity angles (θ) of Λb, numbers are more firmly determined. ∗ + J/ψ,Λ or pentaquark candidate Pc → J/ψp, and an- Argand diagrams for the two P + states are shown in 33 − c gles between the decay planes. For the K p channel, Fig. 62. These were obtained by replacing the Breit- ∗ fourteen reasonably well established Λ resonances were + Wigner amplitude for one of the Pc states at a time by included with masses and widths set to their values given a combination of independent complex amplitudes at six in the 2014 PDG tables (283), and varied within their un- equidistant points in the ±Γ0 range (interpolated in mass certainties when evaluating systematic errors. Their he- for continuity) that were fit to the data simultaneously licity couplings (between 1 and 6 complex numbers per with the other parameters of the full matrix element resonance) were determined from the fit to the data. It model. While the narrower P (4450)+ state shows the ex- ∗ c was found that these Λ contributions taken by them- + pected resonant behavior, the diagram for the Pc(4380) selves fail to describe the data. It was necessary to add deviates somewhat from BW expectations. However, + two non-standard Pc → J/ψp pentaquark contributions the statistical errors are large, especially for the broader to the matrix element (10 free parameters per resonance) + Pc(4380) state. before the narrow structure seen in M(J/ψp) could be The inclusion of additional Λ∗ states beyond the well reasonably well reproduced, as illustrated in Fig. 60. ∗ + established ones, of Σ excitations (expected to be sup- The lower mass state, Pc(4380) , has a fitted mass pressed) and of non-resonant contributions with a con- of 4380 ± 8 ± 29 MeV, width of 205 ± 18 ± 86 MeV, stant amplitude, did not remove the need for two pen- a fit fraction of 8.4 ± 0.7 ± 4.2 % and a significance of + taquark states in the model to describe the data. On 9σ. The higher mass state, Pc(4450) , has a fitted mass the other hand, Λ∗ spectroscopy is a complex subject, of 4449.8 ± 1.7 ± 2.5 MeV, a much narrower width of from both experimental and theoretical points of view. 39 ± 5 ± 19 MeV, a fit fraction of 4.1 ± 0.5 ± 1.1 % and This was demonstrated by a recent reanalysis of KN¯ a significance of 12σ. + scattering data (351) in which the Λ(1800) state, which The need for a second Pc state is visually more ap- was previously considered to be “well established,” is not parent in Fig. 61b that shows the M(J/ψp) projections seen, and where evidence for a few previously unidenti- for large Kp invariant masses (M(Kp) ≥ 2.0 GeV), ∗ fied states is included. In fact, all theoretical models where contributions from Λ resonances are the small- ∗ + for Λ baryons (352; 353; 354; 355; 356; 357) predict est. Even though contributions from the two Pc states a much larger number of higher mass excitations than are most visible in this region, they interfere destruc- is established experimentally. The high density of pre- tively in this part of the Dalitz plane, as is evident in dicted states, which are generally expected to have large widths, makes it difficult to identify individual states experimentally. Non-resonant contributions with a non- − 33 The decay helicity angle is the angle between one of the decay trivial K p mass dependence may also occur. There- products and the boost direction in the rest frame of the parent fore, LHCb also inspected their data with an approach particle. that is nearly independent of way the K−p contributions 52

250 2200 b) data 1000 m all m >2 GeV a) data Kp 200 Kp 2000 total fit background total fit LHCb 150 1800 Pc(4450) background P (4380) c 800 100 1600 Λ(1405) Pc(4450) Events/(20 MeV) Events/(15 MeV) Λ(1520) 1400 Pc(4380) 50 Λ(1600) (1405) 600 Λ 0 1200 Λ(1670) 4 4.2 4.4 4.6 4.8 5 Λ(1690) Λ(1520) 1000 (1800) Λ Λ(1600) Λ(1810) 400 800 Λ(1820) Events / ( 15 MeV ) and other 600 Λ(1830) Λ*s LHCb Λ(1890) 400 Λ(2100) 200 Λ(2110) 200

0 0 1.4 1.6 1.8 2 2.2 2.4 2.6 4 4.2 4.4 4.6 4.8 5 m [GeV] m [GeV] M(K p) (GeV) Kp M(J/ψ p) (GeV) J/ψp + + FIG. 60 Projections of the amplitude fit with Pc(4380) and Pc(4450) states included (red histogram) onto the a) M(Kp) and 0 − b) M(J/ψp) distributions (black squares with error bars) in the LHCb group’s Λb → J/ψpK event sample (47). Contributions from individual components of the fit are indicated as different color/line-style histograms as labeled.

+ c 0.15 0.15 P 1.55< M(Kp)<1.70 GeV M(Kp)> 2.00 GeV Im a) b) 0.1 a) 0.1 b) LHCb A Im cosθ ≈-1 cosθ ≈+1 ) Pc Pc 0.05 0.05 p p 0 0 MeV θP θ K c K Pc -0.05 + -0.05 Pc(4450) P (4380)+ 200 J/ψ J/ψ -0.1 -0.1 c -0.15 -0.15

events/ (15 Λ(1600) -0.2 -0.2

-0.25 -0.25 -0.3 LHCb-0.3 -0.35 -0.35 0 - -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 -0.150.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 P+ P+ Re A c Re A c M(J/ψ p) (GeV) M(J/ψ p) (GeV) FIG. 62 Fitted values of the real and imaginary parts of the am- + + + FIG. 61 Projections of the amplitude fit with Pc(4380) and plitudes of the Pc(4450) (left) and Pc(4380) (right) states for + 0 − Pc(4450) states included (red histogram) onto the M(J/ψp) in- Λb → J/ψpK shown in the Argand diagrams as connected points 0 − with the error bars (masses increase counterclockwise) (47). The variant mass distributions from the LHCb group’s Λb → J/ψpK events (black squares with error bars) with a) 1.55 ≤ M(Kp) ≤ solid red curves are the predictions from the Breit-Wigner formula, 1.70 GeV and b) M(Kp) > 2.0 GeV (47). The individual fit com- with resonance masses and widths set to the nominal fit results and ponents are shown with the same color/line-style designations that scaled to the displayed points. are used in Fig. 60.

tified to be at least at the 9σ level, and demonstrates − are modeled (358). A representation of the Dalitz plane that the hypothesis that K p contributions alone can distribution was constructed using the measured M(Kp) generate the observed mJ/ψp mass structure can be re- distribution and Legendre polynomial moments of the jected with very high confidence without any assump- − cosine of the Λ∗ helicity angle determined from the data tions about the number of K p contributions, their res- as a function of M(Kp). The maximal rank of the mo- onant or non-resonant character, or their mass shapes or ments generated by the K−p contributions alone cannot interference phases. This establishes the presence of con- be higher than twice their largest total angular momen- tributions from either non-standard hadron channels or tum. Since high-spin Λ∗ states cannot significantly con- from rescattering effects of conventional ones. However, tribute at low M(Kp) values, high rank moments were this approach says nothing about their characterization. excluded from the representation (see Figs. 1 and 3 in The LHCb collaboration also inspected Cabibbo- 0 − ref. (358)). When projected onto the M(J/ψp) axis of suppressed decays Λb → J/ψpπ for signs of the + + the Dalitz plane, this representation cannot describe the Pc(4380) and Pc(4450) states (359). The recon- 0 data as shown in Fig. 63. The disagreement was quan- structed Λb signal yield in this channel is more than an 53

these results failed to conﬁrm any of these states, and 1000 more data are needed for more conclusive results.

800 LHCb VIII. SUMMARY AND FUTURE PROSPECTS

Yield / (20 MeV) Yield Here we do not attempt to provide a detailed review of 600 the successes and failures of the large variety of theoretical models that have been proposed as explanations of 400 the non-standard hadrons discussed in this report. For this we refer the reader to three recent and comprehensive discussions of these issues by experts who have somewhat 200 different viewpoints (118; 119; 360). Instead we provide our experimentally oriented sense of where this field is at, and where it is heading. 0 4 4.2 4.4 4.6 4.8 5 Experimentally, it is remarkable that the number of m [GeV] J/ ψ p charmonium-like states above the DD¯ threshold that have unexpected properties, like narrow total widths FIG. 63 The efficiency-corrected and background-subtracted dis- and/or relatively large decay rates to hidden-charm tribution of M(J/ψp) for the LHCb data, shown as black points with error bars, is compared with the best fit obtained using re- states in spite of the existence of easily accessible de- flections based on the observed K−p mass distribution and mo- cay channels with open charm, is about double the num- ments of the K−p helicity angle patterns, shown as the solid blue ber of known charmonium states in this mass range that curve (358). The possibility that the M(J/ψp) distribution can be − conform to expected behavioral patterns (see Fig. 65). accommodated by any plausible reflections from the K p system ¯ is ruled out at the > 9σ level. Clearly, the simple QQ model of charmonium, which works so well for states below the open-flavor threshold, fails at higher masses, and some new degrees of freedom order of magnitude smaller and has a background frac- have become relevant. tion that is worse by a factor of three than the Cabibbo- The high-mass bottomonium system is not as ex- favored mode, thereby precluding the ability to perform perimentally well explored as that for charmonium an unconstrained search for J/ψp states. Instead, the (Fig. 66). However, when explored with the same tech- + + − Pc parameters were fixed to the values measured in the nique, i.e. e e energy scans, it revealed anomalous 0 − Λb → J/ψpK channel, and varied within their uncer- states with apparently similar characteristics as those P tainties (including J ambiguities) in systematic studies. observed in the charmonium system, as expected from Only the production helicity couplings were allowed to heavy-quark symmetry. be different (4 free parameters per state). The possible Finding and understanding these new degrees of free- − − presence of the Zc(4200) → J/ψπ resonance, observed dom presents a great challenge to current theoretical 0 − + by Belle in B → J/ψπ K decays, further complicates models of hadronic structures. the amplitude analysis, adding 10 free parameters even after its mass and width had been fixed to the measured ∗ − values. Up to 14 known N → pπ resonances were in- A. Theory cluded in the fit. As a result, even after neglecting contributions from higher orbital angular momenta in the 1. Molecules N ∗ decays, there were as many as 106 free parameters in the six-dimensional fit to the relevant masses and helicity We, as sentient beings, owe our existence to residual angles. strong forces between nucleons, i.e. between individually The analysis yielded 3.1σ evidence for the summed confined, color-singlet groups of three quarks in baryons. − + presence of non-standard (Zc(4200) , Pc(4380) and The resulting nuclei support the rich diversity of atoms + Pc(4450) ) hadron contributions. The M(pπ) and in nature. In the context of QCD, this binding resem- M(J/ψp) projections of the fit are compared with the ex- bles the binding of atoms into molecules by residual elec- perimental data in Figs. 64a and 64b, respectively. The tromagnetic forces and, thus, nuclei can be pictured as inset in Fig. 64b shows the M(J/ψp) projection for events baryon-baryon molecules. Nuclear physics provides good with M(pπ) > 1.8 GeV, where there is some, but not models for the “molecular” forces between nucleons, and + very significant, indication of a Pc(4450) → J/ψp sig- it is natural to expect that meson-meson and meson- + − nal. However, ambiguities between Pc and Zc terms baryon combinations may also experience similar forces. eliminate any ability to establish the presence of any in- But, since nuclear models are not based on direct deriva- dividual non-standard hadron contribution. As a result, tions from the fundamental theory of strong interactions 54

Data a) LHCbLHCb 250 40 2 RM N*+Zc+2Pc b) LHCb 35 10 30 mpπ>1.8 GeV EM N* 200 25 Pc(4450) 20 LHCb 15 P (4380) c 10 Zc(4200) 5 150 0 4.5 5

Yields/ (25 MeV) Yields/ 10 Yields/ (50 MeV) Yields/ 100

1 0 1 1.5 2 2.5 4.5 5 5.5 M(p π) (GeV) mpπ [GeV] M(J/ψ p) (GeV) mJ/ψ p [GeV] FIG. 64 Comparisons of projections of the amplitude fits (red histogram) onto a) M(pπ) and b) M(J/ψp) data distributions for 0 − Λb → J/ψpπ decays in LHCb (359). The dashed green histogram shows the results of a fit with no non-standard hadrons in the pπ and J/ψp channels. The inset in b) shows the M(J/ψp) fit-data comparison for events with M(pπ) > 1.8 GeV, where there is some hint of a + Pc(4450) signal.

(QCD), it is not a priori known how strong the forces Ecm = 1.96 TeV pp¯ annihilations with production cross in these other, non-nucleon-nucleon, systems are, or if sections and other characteristics that are similar to those bound molecule-like meson-meson or meson-baryon com- for prompt ψ0 production (61; 278), while detailed combinations actually exist. putations for a loosely bound DD¯ ∗ composite showed The 2003 Belle paper (53) that reported the discovery that such similarities were highly unlikely (277). Also, in of the X(3872) → π+π−J/ψ emphasized two intrigu- the deuson picture, the X(3872) is primarily a D0D¯ ∗0 ing experimental features. One was the close proxim- bound state. Searches for other near-threshold DD¯ ∗ ity of the X(3872) mass and the D0D¯ ∗0 mass threshold; combinations, such as mostly D+D∗−, or D0D∗− states, at that time, the measurement precision of the X(3872) with the same J PC = 1++ quantum numbers, came up mass was ±0.8 MeV and that of the PDG-2002 value empty (54; 268). Another problem with the deuson idea world average for mD0 + mD∗0 was ±1 MeV (361) and is the large rate for X(3872) → γψ(2S) reported by δm00 = (mD0 +mD∗0 )−M(X(3872)) = −0.9±1.3 MeV. BaBar (69) and LHCb (70) (see Eq. 6), which is expected 3 The second intriguing feature was the concentration of for the 2 P1 charmonium state but counter to predictions π+π− invariant masses near the ρ meson mass, that was for molecules (275; 276). a strong indication that the decay violated isospin sym- At present, and as pointed out in ref. (270), it seems metry in a substantial way (53). likely that the X(3872) is a quantum mechanical mix- 3 Within a few weeks after the Belle results were made ture of a tightly bound cc¯ core in 2 P1 configuration and public, papers were posted by Törnqvist (266), and a molecule-like DD¯ ∗ combination. This idea was veri- Close and Page (362) that pointed out that these mass fied by detailed computations in refs. (272) and (363); and isospin-breaking properties were characteristic of the latter found that the bulk of the DD¯ ∗ binding comes expectations for a DD¯ ∗ molecular state. In fact, a from the coupling between the cc¯ core and the DD¯ ∗ com- J PC = 1++, DD¯ ∗ bound state with mass near 3870 ponents, and not much comes from the mutual attrac- MeV had been predicted (and named!) in a 1994 pa- tion between the D and the D¯ ∗, which is the key feature per by Törnqvist(138); inspired by its similarity to the of deuson models. In this picture for the X(3872), its deuteron, Törnqvist called the state a “deuson.” As prompt production in high energy hadron collisions and a result, at that time, experimenters and theorists ex- radiative decays to the ψ0 proceed via the cc¯ core compo- pected that a thorough understanding of the underlying nent of the X(3872) and, thus, have characteristics that 0 nature of the X(3872) would be a straightforward exer- are similar to those of the χc1. cise and that they could look forward to exploring a rich The bulk of the huge theoretical literature on non- spectroscopy of related deuson states, both in the charm standard hadrons is on molecular models (140; 301; quark and bottom quark sectors. 312; 314; 364; 365; 366; 367; 368; 369; 370; 371). In However, this optimism turned out to be short-lived. these, binding is provided by pion- and other light- As discussed above, in Section V.A, the CDF and D0 meson-exchange forces. Since the binding provided by groups found the X(3872) was produced promptly in these forces is not expected to be very large, molecu- 55

4800 X(4700) Y(4660) φ 4600 ππ ψ + X(4500) (4S) Z (4430) + Pc(4450) Y(4390) + Mass [MeV] 4400 p Y(4360) Pc(4380) ψ(2D) Y(4220) X(4274) Z+(4250) + 4200 X(4160) Z (4200) X(4140) ψ(3S) + +,0 Z (4050) D*D* 4000 Zc (4020) χ (2P) X(3940) c2 +,0 X(3915) Z (3900) ψ (1D) DD* ψ c X(3872) 2 3800 (1D) ρ0,ω π ψ(2S) η (2S) DD c χ (1P) c2 3600 hc(1P) χ (1P) c1 χ (1P) η c0 3400 γ 3200 J/ψ(1S) η (1S) 3000 c

0 2 -- 4 +(-) 6 8 10 12 -- 14 0-+ 1 1 0++ 1++ 2++ 2 & other

FIG. 65 The current status of the charmonium-like spectrum. The dashed (red) horizontal lines indicate the expected states and their masses based on recent calculations (39) based on the Godfrey-Isgur relativized potential model (40), supplemented by the calculations in ref. (332) for high radial excitations of the P-wave states. The solid (black) horizontal lines indicate the experimentally established charmonium states, with masses and spin-parity (JPC ) quantum number assignments taken from ref. (9), and labeled by their spectroscopic assignment. The open-flavor decay channel thresholds are shown with longer solid (brown) horizontal lines. The candidates for exotic charmonium-like states are also shown with shorter solid (blue or magenta) horizontal lines with labels reflecting their most commonly used names. All states are organized according to their quantum numbers given on horizontal axis. The last column includes states with unknown quantum numbers, the two pentaquark candidates and the lightest charmonium 2−− state. The lines connecting the known states indicate known photon or hadron transitions between them: dashed-green are γ transitions; (thick E1, thin M1), solid-magenta are π; thin (thick) dashed-blue are η (φ); dashed-red are p; dotted-blue are ρ0 or ω; and solid-blue other ππ transitions, respectively. lar states are expected to be near the masses of their threshold peaks that are not related to a physical res- constituent hadrons and have appropriate S-wave J PC onance (372). Moreover, unlike the X(3872), no evi- quantum numbers. This is the case for the Zb(10610) dence for these states have been found in lattice QCD and the Zb(10650), which are within a few MeV of the calculations (373; 374; 375; 376). On the other hand, ∗ ∗ ∗ BB¯ and B B¯ thresholds, respectively, and applies rea- detailed studies of the BESIII’s Zc(3900) → J/ψπ and ∗ sonably well to the Zc(3900) and Zc(4020), which are DD¯ signals (149) and Belle’s corresponding Zb sig- ' 10 MeV above the DD¯ ∗ and D∗D¯ ∗ thresholds, re- nals (157; 377; 378) show that the observed peaks can spectively. However, the interpretation of these states be identified as virtual states with associated poles in as molecules is controversial. Peaks at masses that are the complex scattering t-matrices. slightly above threshold are dangerously similar to expec- The J P = 1+ Z(4430) (now with a mass near tations for kinematically induced cusps (146; 147; 148) 4478 MeV) has been proposed as a radial excitation of the (see Fig. 8b and related text). Anomalous triangle singu- ∗ Zc(3900), comprised of a molecule-like DD¯ (2S) configu- larities are another mechanism that can produce above- ration (379; 380), where the D∗(2S) is the radial excita- 56

11200

Υ 11000 (6S) Υ(5S) Yb (10860) 10800 ππ Mass [MeV] + Zb (10650) B*B* Υ(4S) +,0 BB* 10600 Zb (10610) χ (3P) b1 BB

10400 Υ(3S) χ (2P) χ (2P) hb (2P) χ (2P) b1 b2 b0 Υ (1D) 10200 2

η (2S) Υ(2S) ω b 10000 χ χ (1P) h (1P) (1P) b2 b χ (1P) b1 b0 η π 9800 γ 9600 Υ(1S) η (1S) b 9400 0 2 -- 4 6 8 10 12 -- 14 0-+ 1 1+- 0++ 1++ 2++ 2

FIG. 66 The current status of the bottomonium-like spectrum. The current status of the bottomonium-like spectrum. The dashed (red) lines indicate the expected states and their masses based on recent calculations (41) based on the Godfrey-Isgur relativized potential model (40). The solid (black) horizontal lines indicate the experimentally established charmonium states, with masses and spin-parity (JPC ) quantum number assignments taken from ref. (9), and labeled by their spectroscopic assignment. The open-flavor decay channel thresholds are shown with longer solid (brown) horizontal lines. The candidates for exotic bottomonium-like states are also shown with shorter solid (blue or magenta) horizontal lines with labels reflecting their most commonly used names. The known photon and hadron transitions are also indicated (see the caption of Fig. 65). tion of the D∗. Although the existence of the D∗(2S) ence for the Z(4430) to decay to ψ(2S)π over J/ψπ (re- 0 ∗ has not been firmly established, the BaBar group re- call that ψ =ψ(2S)). The large DJ (2600) width could ported a strong candidate for this state in the D+π− and also explain the large Z(4430) width, although for such a D∗+π− invariant mass distributions in inclusive e+e− → broad constituent, it is not clear whether the molecular (∗)+ − D π X reactions at Ecm = 10.58 GeV (381); LHCb formalism still applies. Also, unlike the Z(4430) state, (∗) subsequently reported observations of D π invariant the Zc(3900) state is not produced in B → ZK decays mass structures with peak and width values similar to (51), which casts doubt on any model in which these two BaBar’s that were produced in high energy pp colli- states have essentially the same internal structure, differ- sions (382). The averages of the BaBar and LHCb mass ing only by a radial excitation. and width measurements for this state, which is called ∗ Molecules are not likely explanations for most of the the DJ (2600), are 2622 ± 12 MeV and 104 ± 20 MeV, ∗ ∗ other hidden-charm non-standard mesons. For example, respectively (9). If we assume D (2S) = DJ (2600), the DD¯ ∗(2S) “threshold” is at ' 4490 MeV, and ' 12 MeV when the Y (4260) was first reported by BaBar with a +8 ¯ above the Z(4430) mass. This association with a radially mass of 4259−10 MeV, its interpretation as a DD1(2420) excited D∗ meson may account for the observed prefer- molecule with a binding energy of ' 25 MeV might have been plausible (301). But recent high-statistics measure- 57 ments by BESIII have shown that single resonance fits to 2. Diquarks the Y (4260) were na¨ıve and the peak is, in fact, best fit by two resonances (see Fig. 38) with masses 4220±4 MeV QCD, which explains the existence of qq¯ mesons and and 4320 ± 13 MeV (301). This implies that the required qqq baryons, also predicts that the short-distance color DD¯ 1(2420) binding energy for the lower-mass peak would force between two quarks in an S = 0 diquark antitriplet be much higher, at ' 65 MeV, while the higher-mass state (see Fig. 6b) is attractive and one-half the strength state would be unbound by ' 35 MeV, making a molec- of the attraction between a quark and antiquark in a ular interpretation for either component of this peak im- standard meson. Therefore, diquarks and diantiquarks plausible. are expected to play a strong role in shaping the spec- The only relevant two-particle threshold with J PC = troscopy of multi-quark hadrons, when pairs of quarks 0++ S-wave quantum numbers that is near the X(3915) exist inside the confinement volume (10). + − In 2004, Maiani et. al (126) proposed that the X(3872) meson is the Ds Ds threshold at 3937 MeV. However, since three-pseudoscalar-meson couplings are forbidden is formed from a symmetric combination of an S = 0 by parity plus rotation invariance, π-meson exchange and S = 1 diquark and diantiquark in a relative S-wave: forces, which provide the bulk of the binding for the [cq]S=0[¯cq¯]S=1 + [cq]S=1[¯cq¯]S=0, with q = u or d. This deuteron, are not applicable. Thus, there is no plausi- implies the existence of two nearly degenerate neutral states, Xh and Xl, that are mixtures of Xu = [cu][¯cu¯] ble deuson-like model that can account for the nature ¯ of the X(3915). Likewise, before the LHCb group es- and Xd = [cd][¯cd], with a mass difference: PC ++ tablished the J of the X(4140) resonance as 1 , M(Xh) − M(Xl) = 2(md − mu)/ cos 2θ there were a number of suggestions that it was an S- = (7 ± 2) MeV/ cos 2θ, (20) ∗+ ∗− wave D D molecule (2m ∗− = 4224 MeV). But an s s Ds S-wave D∗+D∗− system can only have J PC = 0++ or where θ is the mixing angle. Here, an unequal mixture of s s 0 2++ (since C = (−1)L+S) (224). The LHCb measure- the two states (i.e., θ 6= 45 ) would generate isospin vio- ment (49) rules out this possibility and, in addition, they lation in Xh and Xl decays. Tetraquarks made out of di- reported three additional candidates for ccs¯ s¯ states: the quarks must be compact due to the confinement of color, X(4274), X(4500) and X(4700). None of these are close which naturally can explain the large X(3872) prompt production rate at hadron colliders. However, this model to the thresholds of any S-wave combinations of Ds excitations that would reproduce their measured quantum predicted the existence of three additional states: two ++ ++ numbers. 0 states with lower mass values and a 2 state at a higher mass. The production of two neutral X(3872) Some authors have suggested that the narrow Pc(4450) states differing in mass by an amount consistent with P − pentaquark might be an S-wave, J = 3/2 molecule the Eq. 20 prediction was ruled for high energy pp¯ pro- ¯ ∗ comprised of a Σc baryon and a D meson, with a binding duction by CDF (60) and for production in B meson energy of ' 13 MeV (342; 383). This, taken alone, might decays by BaBar (386) and Belle (54). Compelling can- be a reasonable suggestion. However, if the Pc(4450) is didates for the predicted 0++ and 2++ states have yet − 3/2 , the LHCb data indicate that the Pc(4380) should to be identified. Similar to the case for molecular mod- + be 5/2 (47). The lightest meson-baryon combinations els, the significant X(3872) → γψ(2S) rate relative to that can produce spin 5/2 in an S-wave are pχc2 (for the X(3872) → γJ/ψ(1S) decays is not naturally ex- ∗ ¯ ∗ which π-exchange forces are not allowed) and Σc D , with plained by the tetraquark model, unless it also includes mass thresholds that are 115 and 145 MeV above the mixing with the χc1(2P) charmonium state or dynamical Pc(4380) mass, respectively. Moreover, the ∼ 200 MeV effects (387) discussed below. Moreover, unlike molecu- width of the lower-mass Pc(4380) state makes it pretty lar models, the tetraquark picture does not offer natural short-lived for a molecular state with c andc ¯ spatially explanations for the X(3872) mass coincidence with the separated into two different confining volumes, resulting D0D¯ ∗0 threshold, or its very narrow width. The lat- in a small overlap of its wave function with the J/ψ state ter led to hybridized-tetraquark model, which explains that is produced in its decay (384). These thresholds are the near-threshold states as an interplay between bound also too high to provide a plausible molecular explanation molecules and compact tetraquark states (255). P ± for the case where the J = 5/2 assignment is associ- Diquark interpretations have been proposed to ex- ated with the heavier and narrower Pc(4450) peak. This plain most of the observed states. For example, in is not only the case for a bound molecule interpretation, this model, the Y (4260) is a symmetric [cq]S=0[¯cq¯]S=1 but also for cusp or triangle anomaly mechanisms, which diquark-diantiquark combination, like the X(3872), but require S-wave interactions to make significant contribu- in a relative P-wave (297). The ' 350 MeV mass differ- tions (385). ence between the two states is consistent with the typical Thus, a reasonable conclusion is that while molecule mass penalty that is associated with the addition of one models have relevance for some of the observed candi- unit of orbital angular momentum (see, e.g., Table III) dates, they are not the whole story. and the strong Y (4260) → γX(3872) transition reported 58 by BESIII (73) would be an allowed electric dipole tran- and only occurs if this overlap is well matched to an acces- sition between the two related states (388). Likewise the sible configuration of final-state hadrons. In this way the Zc(3900) can be naturally accommodated as the antisym- process has a complex and intricate dependence on the 0 metric, S-wave [cq]S=0[¯cq¯ ]S=1 diquark-diantiquark com- production mechanism and decay final states that sup- bination, and the Z(4430) as its first radial excitation. presses all the unwanted states. But this comes at the The diquark picture also can explain states that molecu- cost of stripping the dynamical diquark picture of virtu- lar models have trouble with, such as the X(3915) (290) ally all of its ability to predict the existence of additional and the four states seen decaying to J/ψφ (329; 389), and states. provide a common origin for the Pc(4380) and Pc(4450) Baryons with heavy quarks are an interesting testing pentaquarks that can accommodate their opposite pari- ground for diquark models. For example, in heavy-light- ties (390; 391). light quark baryons, spin couplings of the heavy quark are These successes can be attributed to a larger number expected to be suppressed by its heavy mass creating fa- of degrees of freedom in strong color binding as com- vorable conditions for formation of a light diquark, [qq]Q. pared to weak, Yukawa-type exchange forces. Orbital Since a good diquark would be in the same color state as excitations between colored objects can reach higher spin q¯, meson-like radial and orbital-angular-momentum ex- states at lower masses. Slight changes in free parameters citation spectrum is expected for such a system. The that describe the strength of the color forces, can shift known excitations of charmed and beauty baryons fol- predicted masses to any value, while molecular models low these predictions. For example, the LHCb has re- can only accommodate structures near hadron-hadron cently observed five narrow Ωc excitations (392), that lie mass thresholds. However, the free parameters of di- in the mass range of 1P and 2S states predicted in diquark models are usually readjusted when moving from quark models (393; 394). Their masses extend to just the description of one exotic hadron system to another, below mΞ + mD, which is the threshold for decays that resulting in no single unified diquark model that can de- leave the ss diquark intact. Therefore, their strong de- + − scribe all of the observed states at once. The universal cays to Ξc K requires the disintegration of the ss di- prediction of large prompt production rates for tightly quark, which can explain their narrow widths (0.8-8.7 bound tetraquarks and pentaquarks at hadron colliders MeV) in spite of the fact that there is no OZI suppres- are in some conflict with the reality that to date, only sion. the X(3872) and X(4140) states have been seen in this In doubly-heavy baryons, the heavy quark pair is likely production mode (224). to form a diquark, [QQ]q, acting like an effective heavy One big problem with the diquark picture is that, since antiquark. Using an approach based on this idea, Kar- the strong radial color force between the diquark and liner and Rosner (395) predicted with good precision the ++ the diantiquark is universal, it has the same strength for mass of the Ξcc baryon, that was recently observed by q, q0 = u, d, s independently of their flavor or spin state. LHCb (181). They have extended this model to pre- Therefore, every successful application of the idea to an dict that the mass of the lightest 1+ [bb][¯ud¯] tetraquark experimentally observed state carries with it predictions system would be well below the threshold for decays to for a large number of related states that typically are not B−B¯0γ, and therefore be stable under strong and elec- seen, as was the case for the original diquark-diantiquark tromagnetic decays (see also refs. (396)). The similar interpretation of the X(3872) discussed above. Another [bc][¯ud¯] tetraquark state is also likely to be stable, while problem is that in this picture, diquark separations are [bc][¯ud¯] may be right below, or right above the D0D∗+ comparable to the diquark sizes, and there is nothing in threshold. Almost the same predictions for these states the model to prevent fast fall-apart widths to individu- were obtained a year earlier by Francis et al. employ- ally confined mesons and baryons, thereby precluding the ing LQCD calculations with diquark interpolators (192). existence of narrow states. Therefore, these are now perhaps the most firm theoret- Brodsky, Hwang and Lebed (387) address these prob- ical predictions offering hope for unambiguously estab- lems with a scheme that creates separation between di- lishing the existence of diquark tetraquarks in not too quarks, severely restricts the number of observed states, distant future. and suppresses the superfluous ones. Their basic idea, which they call dynamical diquarks, is that at production, the diquark and diantiquark move rapidly apart, a 3. QCD hybrids motion that is opposed by the increasingly stronger confinement force. By the time the motion stops, the diquark The existence of hybrid states is among the most in- diantiquark separation is large and there is no substantial triguing predictions of QCD. The most striking experi- overlap between the quarks in one and the antiquarks in mental signature for QCD hybrids is the possible exis- the other. Hadronization of diquarks separated dynami- tence of mesons with exotic quantum numbers. How- cally by this production mechanism depends on the over- ever, since all the states discussed in this report have lap of the tails of the quark and antiquark wave-functions non-exotic quantum numbers, there is no smoking gun 59 candidate for a hybrid state. The state that has been tion measurements (89), shown in Fig. 39, find a strong + − most strongly promoted as a candidate for a cc¯-gluon π π hc decay rate for the lower mass resonant compo- charmonium hybrid is the 1−− Y (4260) (302; 303; 304). nent, but no signal for the higher mass component. Even However, this assignment is not unique, and this state with the above-described mixing, the hadrocharmonium is also considered to be a good QCD tetraquark candi- model will have a hard time reproducing this decay pat- date. Charmonium hybrids are expected to have strong tern. decays to S-wave D(∗)D¯ ∗∗ final states, where D∗∗ designates the P-wave charmed mesons described in Ta- ble III. For the Y (4260), the only possible accessible fi- 5. Kinematically induced resonance-like peaks ∗ ¯ ∗ nal state of this type would be D D0(2400), where the ∗ ++ D0(2400) is a 0 Dπ resonance with mass and width As mentioned above in the discussion of molecular M = 2318 ± 29 MeV and Γ = 267 ± 40 MeV. In princi- models, some authors have suggested that the Zc and Zb ple, a high-statistics study of Y (4260) → D∗Dπ¯ might peaks are due to kinematic effects caused by the nearby ∗ ¯ ∗ (∗) ¯ ∗ (∗) ¯∗ see evidence for a D D0 final state but, since it is a D D and B B mass thresholds (146; 147; 148; 372). broad S-wave state, it would probably be difficult to Other authors claim that the same data show that the distinguish from a non-resonant background. As men- peaks are are associated with poles in the correspond- tioned in Section V.C, the latest lattice QCD study of ing D(∗)D¯ ∗ or B(∗)B¯∗ scattering t-matrix and, therefore, charmonium states has a lowest-mass 1−− hybrid candi- qualify as genuine physical states (149; 377). This seems date at M = 4285 ± 14 MeV (186). This is ' 65 MeV to be a controversy that only more, and higher-precision above the recent BESIII measurement of the Y (4260) data can resolve. For example, although both mecha- mass (4220 ± 4 MeV). However, given that the LQCD nisms produce strong phase motion that can be displayed calculations are missing simulations of couplings to the in Argand plots, the detailed mass dependence of this available decay channels, this difference should probably phase motion is distinctly different for the two models. be considered small. Another suggestion requires the application of sophis- ticated coupled-channel data analysis techniques (157). However, distinguishing between the two scenarios with 4. Hadrocharmonium either method will require huge data samples, with increases over existing data sets by factors that approach In the hadrocharmonium model, the strong preference two orders of magnitude. This would require at least for the Y (4260) (Y (4360)) meson to decay to π+π−J/ψ a year-long dedicated BESIII run at energies near the (π+π−ψ0) over the fall-apart D(∗)D¯ (∗) modes is accom- Y (4260) peak and a long period of BelleII operation at modated by a meson structure that contains a color- the Υ(10860) peak. singlet charmonium-state core surrounded by a light quark excitation (141). In the case of the Y (4260) (Y (4360)), this core state was taken to be the J/ψ (ψ0). 6. Comments Since the J/ψ (ψ0) state is present in its constituents, the Y (4260) (Y (4360)) naturally prefers to decay to final At this point, the challenges posed by the observed states that include it. However this model had trouble heavy quarkonium-like states with unusual properties with BESIII observations of substantial rates for Y (4260) have not been answered well by any theory for hadronic + − and Y (4360) decays to π π hc final states (93). In the states. J/ψ and ψ0, the c- andc ¯-quarks are in a spin-triplet state, In general the successful theoretical work in this area while in the hc they are in a spin-singlet. By themselves, has been reactive rather than predictive. Different ap- the triplet and singlet cores cannot mix and a hadrochar- proaches have had some success for some states but fail monium state should have strong rates for decays to one or are not applicable to others. This could be because the of them, but not both. In an attempt to fix this prob- non-standard hadrons that are observed are due to a vari- lem, the model was revised to include two hadrocharmo- ety of different, unrelated mechanisms, or that the actual nium states, one with a spin-triplet core and one with underlying mechanism has not yet been discovered. The a spin-singlet core, and these two states mix, producing lack of good understanding of the nature of these states, the observed Y (4260) and Y (4360), which now can both sheds doubts into our understanding of hadronic struc- decay to singlet and triplet states with relative rates de- tures in general. Open-flavor thresholds in light hadron termined by the (unspecified) mixing angle (397). But, spectroscopy are usually right above the ground states subsequent to the appearance of this modification to the of such systems and whatever mechanisms that are in model, the BESIII group found that in the two resonance play for above-open-flavor-threshold heavy quarkonium- Y (4260) → π+π−J/ψ structure shown in Fig. 38 (52), like hadrons are likely having a strong influence on light both resonant components have strong decay rates to hadron spectroscopy. + − + − π π J/ψ, while the latest BESIII π π hc cross sec- More theoretical and experimental work is required in 60 all areas of hadron spectroscopy to overcome this crisis. tude analyses of B → KJ/ψω and Kχc1π are needed to establish the J PC quantum numbers of the X(3915), and the Z(4050)+ and Z(4250)+. B. Experiment Fortunately there are powerful experiments that are currently running and producing important and unique To date, the progress in the field has mainly been results. For example, B → Kχc1π and KJ/ψω are driven by experiments. Although Törnqvistproposed accessible to the LHCb even with their existing data the existence of a J PC = 1++ state with mass near the sample. Their recent discoveries of J/ψφ mesons and ¯ ∗ −1 DD threshold ten years before its discovery (138), the Pc pentaquarks were based on analyses of their 3 fb 0 ¯ ∗0 X(3872)’s narrow width, close proximity to the D D , Run-I data sample that was accumulated at Ecm(pp) = large isospin violation, and its strong production in B- 7 and 8 TeV. In Run-II, which is now underway and meson decays and high-energy pp¯ collisions were big sur- will finish in 2018, they will accumulate an additional −1 prises. Likewise, the discovery of the Y (4260) as a huge 8 fb at Ecm(pp) = 13 TeV. Since the b-quark pro- peak in the e+e− → π+π−J/ψ cross section with no duction cross section at 13 TeV is about twice that at hints of a corresponding signal in the open charmed me- 7 TeV (398), the Run-II data set will be equivalent to son channel was totally unexpected. Subsequent discov- approximately five times that for Run-I. Thus, we can eries, both in the c-quark and b-quark sectors, were simi- anticipate the discovery of additional states and signifi- larly unanticipated. New developments in this field have cant improvements of existing results, including substan- closely tracked increases in the size and improvements in tial improvements in the precision of the Z(4430) and the quality of the available data samples plus advances Pc Argand plots. A LHCb detector upgrade in 2021 will in the sophistication of analysis techniques. The discov- enable it to accumulate higher luminosities. After that ery of the Pc(4380) and Pc(4450) pentaquarks was pos- they expect that the total data sample accumulated by −1 sible because of the unprecedentedly large sample of Λb 2030 will be 50 fb (collected at Ecm(pp) = 14 TeV). decays that was accumulated by the LHCb experiment. The LHCb collaboration is also discussing a major detec- Likewise, the two-resonance structure of the Y (4260) was tor/luminosity upgrade after 2030 with an ultimate goal seen by BESIII only because they had a larger data sam- of 300 fb−1. Even larger integrated luminosities will be ple and better mass resolution than the earlier measure- collected at the LHC by the CMS and ATLAS detectors. ments. The clear demonstration of BW-amplitude-like Therefore, it is expected that these experiments will also phase motion for the Z(4430) meson and the Pc(4450) continue to contribute to advances in exotic hadron spec- pentaquark was the result of complex, multidimensional troscopy in spite of their lack of hadron identification and amplitude analyses. their more restrictive triggers. There are huge differences in what we know about vari- BESIII is planning long data runs in the Y(4260) peak ous candidate states. For some, like the X(3872) and the region during the next few years, and these should pro- Y (4260), we know the quantum numbers and a number of vide sufficient data to support studies of the phase mo- + − decay modes, while for others we do not even know their tion across the Zc peaks in Y (4260) → π π J/ψ and + − quantum numbers. Even the ones with a lot of available π π hc decay channels, and enable amplitude analyses information have important pieces of information that of Y (4260) → πD(∗)D¯ ∗ decays. Long-term future BE- are unknown. For example, we still do not know the nat- SIII running plans include high luminosity scans over the + − ural width of the X(3872) or whether its mass is above 2mD ≤ Ecm(e e ) ≤ 2mΛc + 50 MeV range to com- or below the mD0 + mD∗0 mass threshold. We have not pletely map out c-quark production in the threshold re- seen phase motion for the Y (4260), or convincing phase gion in a large assortment of decay channels. motion for the Pc(4380). While we learned a great deal The BelleII experiment will start physics operation about the nature of the X(3872) from the fact that it is in late 2017. The first year of running will be used to produced promptly in high energy pp¯ and pp collisions, develop experience with machine operations without ei- we only have limited information about prompt hadro- ther the inner pixel or the silicon-strip vertex detector production of other states. in place. Since this configuration has limited capabilities For experimental reasons, most of the states seen so far for doing B-meson physics, which is the main motivation were first discovered in decay modes that include a J/ψ for the project, operation at the Υ(10860) and higher en- 0 or a ψ the final state. Future experiments that access ergies for detailed studies of the Zb mesons and searches pairs of open-charm or beauty particles may uncover a for possible additional states is planned (224). Over the interesting dimensions of this spectroscopy that might anticipated ten-year operational lifetime of BelleII, a to- give important clues about the underlying dynamics. tal data sample of 50 ab−1 will be accumulated, mostly + − In addition to finding new states, it would be very use- at Ecm(e e ) = 10.58 GeV. Thus, the final BelleII data ful if our level of knowledge of all of the candidate states sample will be a factor of 50 larger than the Belle data set. could be brought to the same high level as the currently The strengths of BelleII, i.e. superior photon, π0, ω and 0 best known ones. For example, multidimensional ampli- η( ) detection capabilities and higher absolute reconstruc- 61 tion efficiencies, are complementary to those of LHCb. of strong interactions, they expose the phenomenological High reconstruction efficiencies are especially essential for disconnect between its Lagrangian and types of struc- (∗) ¯ (∗) tures it can produce at large distances, with possible im- studies of D(s) D(s) systems. In addition, the B-factory environment provides a unique opportunity for making plications to strongly coupled theories proposed as ex- precise measurements of inclusive branching fractions tensions of the Standard Model. Often in the history of + + such as B → K Xcc¯; Xcc¯ → anything decays (213), physics, puzzles and their eventual resolution have pro- where Xcc¯ designates relatively narrow charmonium-like duced important advances in our understanding of na- states such as the X(3872) or X(3915). Inclusive branch- ture. We hope that this will ultimately be the case for ing fractions are required input for converting product the issues that are discussed here. branching fraction and total width measurements into decay partial width values, which are usually the theo- Acknowledgements: This work was supported by the retically relevant quantities. Institute for Basic Science (Korea) by project code IBS- There are several current and future medium-energy R016-D1 and by the National Science Foundation (USA) experiments designed to explore non-standard hadrons Award Number 1507572. We would like to thank Steven and to provide information on the properties of the still Gottlieb for reading the manuscript and providing a num- enigmatic states complementary to e+e− and hadron col- ber of useful comments. lider experiments. 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