A New Hadron Spectroscopy

Front. Phys. 10, 101401 (2015) DOI 10.1007/s11467-014-0449-6 REVIEW ARTICLE A new hadron spectroscopy

Stephen Lars Olsen

Center for Underground Physics, Institute of Basic Science, Daejeon 305-811, Korea E-mail: [email protected] Received August 13, 2014; accepted September 16, 2014

QCD-motivated models for hadrons predict an assortment of “exotic” hadrons that have structures that are more complex than the quark-antiquark mesons and three-quark baryons of the original quark-parton model. These include pentaquark baryons, the six-quark H-dibaryon, and tetraquark, hybrid and glueball mesons. Despite extensive experimental searches, no unambiguous candidates for any of these exotic configurations have been identified. On the other hand, a number of meson states, one that seems to be a proton-antiproton bound state, and others that contain either charmed- anticharmed quark pairs or bottom-antibottom quark pairs, have been recently discovered that neither fit into the quark-antiquark meson picture nor match the expected properties of the QCD- inspired exotics. Here I briefly review results from a recent search for the H-dibaryon, and discuss some properties of the newly discovered states –the proton-antiproton state and the so-called XYZ mesons– and compare them with expectations for conventional quark-antiquark mesons and the predicted QCD-exotic states. Keywords quarks, charmonium, pentaquarks, di-baryons, baryonium, tetraquarks PACS numb ers 14.40.Gx, 12.39.Mk, 13.20.He

Contents gluons are related to mesons and baryons by the long- distance regime of Quantum Chromodynamics (QCD), 1 Introduction 1 which remains the least understood aspect of the the- 2 Pentaquarks and H-dibaryons 2 ory. Since first-principle lattice-QCD (LQCD) calcula- 2.1 Belle H-dibaryon search 2 tions are still not practical for most long-distance phe- 3Whatwedosee 3 nomena, a number of models motivated by the color 3.1 Baryonium in radiative J/ψ → γpp¯ decays? 4 structure of QCD have been proposed. However, so far 3.2 The XYZ mesons 4 at least, predictions of these QCD-motivated models that 3.2.1 Charmoniumlike mesons 4 pertain to the spectrum of hadrons have not had great 3.2.2 Bottomoniumlike mesons 22 success. 3.3 Comments 24 For example, it is well known that combining a q = 3.3.1 Molecules? 25 u, d, s light-quark triplet with aq ¯ =¯u, d,¯ s¯ antiquark an- 3.3.2 Tetraquarks? 28 titriplet gives the familiar meson octet of flavor-SU(3). 3.3.3 QCD-hybrids? 28 Using similar considerations based on QCD, two quark 3.3.4 Hadrocharmonium? 28 triplets can be combined to form a “diquark” antitriplet 3.3.5 A unified model? 29 of antisymmetric qq states and a sextet of symmetric 4 Summary 29 states as illustrated in Fig. 1(a). In QCD, these diquarks Acknowledgements 30 have color: combining a red triplet with a blue triplet – as References and notes 30 shown in the figure – produces a magenta (anti-green) diquark and, for the antisymmetric triplet configurations, 1 Introduction the color force between the two quarks is expected to be attractive. Likewise, green-red and blue-green diquarks The strongly interacting particles of the Standard Model form yellow (anti-blue) and cyan (anti-red) antitriplets are colored quarks and gluons. In contrast, the strongly asshowninFig.1(b). interacting particles in nature are color-singlet (i.e., Since these diquarks are not color-singlets, they can- white) mesons and baryons. In the theory, quarks and not exist as free particles but, on the other hand, the

c The Author(s) 2015. This article is published with open access at link.springer.com REVIEW ARTICLE anticolored diquark antitriplets should be able to com- perimental investigations during the four decades that bine with other colored objects in a manner similar to have elapsed since QCD was first formulated. This ac- antiquark antitriplets, thereby forming multiquark color- tivity peaked in 2003 when the LEPS experiment at the singlet states with a more complex substructure than the SPring-8 electron ring in Japan reported the observa- qq¯ mesons and qqq baryons of the original quark model tion of a peak in the K+n invariant mass distribution [1]. These so-called “exotic” states include pentaquark in γn → K+K−n reactions on a carbon target [2], with baryons, six-quark H-dibaryons and tetraquark mesons, properties close to those that had been predicted for the + as illustrated in Fig. 1(c). Other proposed exotic states S =+1Θ 5 pentaquark [3]. This created a lot of ex- are glueballs, which are mesons made only from gluons, citement at the time [4] but subsequent, high-statistics hybrids formed from a q,¯q and a gluon, and deuteron- experiments [5, 6] did not confirm the LEPS result and, like bound states of color-singlet “normal” hadrons, com- instead, gave negative results. The current “conventional monly referred to as molecules. These are illustrated in wisdom” is that pentaquarks do not exist [7], or at least Fig. 1(d). Glueball and hybrid mesons are motivated by have yet to be found. QCD; molecules are a generalization of classical nuclear The six-quark H-dibaryon, subsequently referred to physics to systems of subatomic partics. as H, was predicted by Jaffee in 1977 to be a doubly strange, tightly bound six-quark structure (uuddss)with isospin zero and J P =0+ [8]. An S = −2 state with baryon number B = 2 and mass below 2mΛ could only decay via weak interactions and, thus, would be long- lived. Although Jaffe’s original prediction that the H would be ∼ 80 MeV below the 2mΛ threshold was ruled out by the observation of double-Λ hypernuclei, most notably the famous “Nagara” event [9] that limited the allowed H region to masses above 2mΛ − 7.7MeV,the theoretical case for an H-dibaryon with mass near 2mΛ continues to be strong, and has been recently strength- ened by two independent LQCD calculations, both of which find an H-dibaryon state with mass near 2mΛ [10, 11].

2.1 Belle H-dibaryon search

The Belle experiment recently reported results of a search for production of an H-dibaryon with mass near 2mΛ in inclusive Υ(1S)andΥ(2S) decays [12]. Decays of narrow Υ(nS)(n =1, 2, 3) bottomonium (b¯b)resonances are particularly well suited for searches for multiquark states with non-zero strangeness. The Υ(nS) states are ﬂavor-SU(3) singlets that primarily decay via Fig. 1 (a) Combining a red and blue quark triplet produces a magenta (anti-green) antitriplet and sextet. (b) The three anticol- annihilation into three gluons. The gluons materialize ored diquark antitriplets. (c) Some of the multiquark, color-singlet into uu¯, dd¯ and ss¯ pairs with nearly equal probabili- states that can be formed from quarks, antiquarks, diquarks and ties, plus additional gluons that also subsequently mate- diantiquarks. (d) Other possible multiquark/gluon systems. rialize as qq¯ pairs. This creates ﬁnal states with a high density of quarks and antiquarks in a limited volume 2 Pentaquarks and H-dibaryons of phase space. A benchmark rate for multiquark-state production in these decays is set by the measured inclu- ¯ 1) All of the above-mentioned candidates for exotic states sive decay branching fractions to antideuterons (D) : −5 have been the subject of numerous theoretical and ex- B(Υ(1S) → D¯ +X)=(2.9±0.3)×10 and B(Υ(2S) →

1) The rates for deuteron and antideuteron production in Υ(nS) decays are almost certainly equal. However, in e+e− experiments, background deuterons are copiously produced by particle interactions in the beam pipe and other material in the inner part of the detector, and these make experimental measurements of their true rate quite diﬃcult. Therefore the rate is quoted for antideuterons, which, because they do not suﬀer from these backgrounds, are easier to measure.

101401-2 Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) REVIEW ARTICLE

D¯ + X)=(3.4 ± 0.6) × 10−5 [13]. If the six-quark H- tence. The absence of pentaquarks led Wilczek to remark dibaryon is produced at a rate that is similar to that “The story of the pentaquark shows how poorly we under- for six-quark antideuterons, there should be many thou- stand QCD” [14]. The absence of any evidence for the sands of them in the 102 million Υ(1S) and 158 million H-dibaryon (among other things) led Jaffe to observe Υ(2S) event samples collected by Belle. that “The absence of exotics is one of the most obvious For H masses below 2mΛ, Belle searched for H → features of QCD” [15]. Λpπ− (& H¯ → Λ¯¯pπ+) signals in the inclusive Λpπ− invariant mass distribution. For masses above 2mΛ,the H → ΛΛ (& H¯ → Λ¯Λ)¯ mode was used. Figure 2 shows 3Whatwedosee the measured Λpπ− (a) & Λ¯¯pπ+ (b) invariant mass spectra for masses below 2mΛ and the ΛΛ (c) and Λ¯Λ(d)¯ Although forty years of experimental searches has failed mass spectra for masses above 2mΛ. Here results from to come up with compelling evidence for specifically the Υ(1S)andΥ(2S) data samples are combined. No QCD-motivated exotic hadrons, strong evidence for signal is observed. The solid red curves show results mesons that do not fit into the simple qq¯ scheme of of a background-only fit to the data; the dashed curve the original quark model has been steadily accumulat- shows the MC expectations for an H-dibaryon produced ing during the past decade. These include a candidate at 1/20th of the antideuteron rate. Upper limits on the for a bound state of a proton and antiproton from the inclusive branching ratios that are at least a factor of BESII experiment [16], so-called “baryonium”, an idea twenty below that for antideuterons are set over the en- that has been around for a long, long time [17], and tire |MH − 2mΛ| < 30 MeV mass interval. the XYZ mesons, charmoniumlike and bottomoniumlike Neither pentaquarks nor the H-dibaryon are seen in states that do not fit into any of the remaining unfilled spite of the stong theoretical motivation for their exis- states in the cc¯-andb¯b-meson level schemes [18].

Fig. 2 (a)–(d) The Λpπ−, Λ¯¯pπ+,ΛΛandΛ¯Λ¯ invariant mass distributions. The solid curves show background-only ﬁt results and the lower panels show the ﬁt residuals. The dashed curves are expected signals for an H production rate that is 1/20th that for D¯ ’s. Reproduced from Ref. [12].

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-3 REVIEW ARTICLE

3.1 Baryonium in radiative J/ψ → γpp¯ decays? ple permitted the application of a partial wave analysis (PWA) that established the J PC =0−+ quantum In 2003, the BESII experiment reported the observation number assignment, in agreement with baryonium ex- of a dramatic near-threshold mass enhancement in the pp¯ pectations. The π+π−η peak in J/ψ → π+π−η decays invariant mass spectrum in radiative J/ψ → γpp¯ decays, was also confirmed and the production-angle distribution shown in the top panel of Fig. 3(a) [16]. The lower panel was found to be consistent with a J PC =0−+ assign- in Fig. 3(a) shows the M(pp¯) spectrum with the effects ment. However, the situation still remains unclear. The of phase-space divided out (assuming an S-wave pp¯ sys- BESIII measurements find a much larger width for the tem). It seems apparent from the phase-space-corrected π+π−η peak than that found for the pp¯ peak in the BE- plot that the dynamical source for this enhancement, SIII partial wave analysis: Γπ+π−η = 190 ± 38 MeV ver- m whatever it may be, is at or below the 2 p mass thresh- sus Γpp¯ < 76 MeV. Another puzzling feature is the lack old. A fit with a Breit–Wigner (BW) line shape modified of any evidence for the pp¯ threshold enhancement in any by a kinematic threshold factor yielded a peak mass of other channels, such as J/ψ → ωpp¯ [25], Υ(1S) → γpp¯ +6 m 1859−27 MeV, about 18 MeV below 2 p, and an upper [26] or in B decays [27]. BESIII is actively looking at var- 2) limit of Γ < 30 MeV on the width . It was subsequently ious other radiative J/ψ decay channels for evidence for pointed out that the BW form used by BESII should be or against other signs of resonance behaviour near 1835 modified to include the effect of final-state-interactions MeV [28]. on the shape of the pp¯ mass spectrum [19, 20]. When this was done, it was found that the effects of FSI are 3.2 The XYZ mesons not sufficient to explain the observed structure and the peak mass of the BW term shifted downward, from 1859 The XYZ mesons are a class of (somewhat haphazardly MeV to 1831 ± 7 MeV while the range of allowed widths named) hadrons that are seen to decay to final states increased to Γ < 153 MeV. that contain a heavy quark and a heavy antiquark, i.e., Soon after the BESII publication appeared, Yan Q and Q¯,whereQ is either a c or b quark, but can- and Ding proposed a Skyrme-like model for proton- not be easily accommodated in an unassigned QQ¯ level. antiproton interactions in which the BESII pp¯ mass- Since the c and b quarks are heavy, their production from threshold enhancement is an S-wave pp¯ bound state with the vacuum in the fragmentation process is heavily sup- binding energy around 20 MeV [21]. Since the p and the pressed and, thus, any heavy quarks seen among the de- p¯ in such a system would annihilate whenever they came cay products of a hadron must have been present among within close proximity of each other, such a state would its original constituents. In addition, the heavy quarks in have a finite width, creating a situation illustrated by conventional QQ¯ “quarkonium” mesons are slow and can the cartoon in panel (b) of Fig. 3: for masses above the be described reasonably well by non-relativistic quantum 2mp threshold, the state would decay essentially 100% mechanics. Indeed it was the success of non-relativistic of the time by “falling apart” into a p andp ¯; for masses charmonium potential-model descriptions of the ψ and below 2mp, the decay would proceed via pp¯ annihilation χc states in the mid-1970’s that led to the general ac- into mesons. Since a preferred channel for low-energy S- ceptance of the reality of quarks and the validity of the + − wave pp¯ annihlation is π π η , Yan and Ding advocated quark model. Quarkonium models specify the allowed + − asearchforπ π η decays of this same state in radiative states of a QQ¯ system; if a meson decays to a final state + − J/ψ → γπ π η decays. A subsequent BESII study of containing a Q and a Q¯ but does not match the expected + − J/ψ → γπ π η decays found a distinct peak at 1834±7 properties of any of the unfilled levels in the associated MeV and width 68 ± 21 MeV as shown in panel (c) of QQ¯ spectrum, it is necessarily exotic. Fig. 3 [22], in good agreement with the mass and width results from the FSI-corrected fit to the pp¯ mass spec- 3.2.1 Charmoniumlike mesons trum. The pp¯ mass-threshold enhancement was confirmed at Charmoniumlike XYZ mesons were first observed start- the same mass with much higher statistics by BESIII ing in 2003 and continue to be found at a rate of about [23]. The signal, shown in panel (d) of Fig. 3, has a sig- one or more new ones every year. There is a huge theo- nificance that is > 30σ3) . The large BESIII event sam- retical and experimental literature on this subject that

2) This report only lists quadrature sums of statistical and systematic errors. Refer to the cited papers for details. 3) With apologies to Tommaso Dorigo: http://www.science20.com/a quantum diaries survivor/a useful approximation for the tail of a gaussian-141353

101401-4 Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) REVIEW ARTICLE

Fig. 3 (a) The upper panel shows the M(pp¯) distribution for J/ψ → γpp¯ decays from BESII [16]. The lower panel shows the same distribution with the kinematic threshold suppression factor removed. (b) A cartoon showing a BW line shape and a threshold-attenuated BW line-shape for a hypothesized baryonium state. The solid curve shows the expected pp¯ line shape. Below threshold, where the dashed curve dominates, the state decays via pp¯ annihilation into mesons. (c) The M(π+π−η) mass distribution for J/ψ → γπ+π−η decays from Ref. [22]. (d) The M(pp¯) distribution for J/ψ → γpp¯ from BESIII [23] with PWA results shown as histograms. will not be repeated here [29, 30]. Instead I restrict my- by Belle [31] as a peak in the distribution of masses (MX ) J/ψ e+e− → J/ψX self to a few remark on subsets of the measurements and recoiling against√ a in inclusive an- outstanding issues. nihilations at s 10.6 GeV shown in panel (a) of Fig. Figure 4 shows the current state of the charmonium 5. In this figure, there are four distinct peaks: the lower + − and charmoniumlike meson spectrum below 4500 MeV. three are due to the exclusive processes e e → J/ψηc, + − + − Here the yellow boxes indicate established charmonium e e → J/ψχc0 and e e → J/ψηc. The fourth peak states. All of the (narrow) states below the 2mD open- near 3940 MeV cannot be associated with any known charm threshold have been established and found to have or expected charmonium state and has been named the properties that are well described by the charmonium X(3940). The curve shows results of a fit that includes model. In addition, all of the J PC =1−− states above the three known charmonium states plus a fourth state; the 2mD open-charm threshold have also been identified. the fit returned a mass M = 3943±6 MeV and an upper The gray boxes show the remaining predicted, but still limit on the total width of Γ 52 MeV. unassigned, charmonium states. The red boxes show elec- Belle also did a study of exclusive e+e− → trically neutral X and Y mesons and the purple boxes J/ψD(∗)D¯ (∗) decays in the same energy region. Here, show the charged Z mesons, aligned according to my to compensate for the low detetction efficiency for D best guess at their J PC quantum numbers. In the fol- and D∗ mesons, a partial reconstruction technique was lowing, I briefly comment on each of the XYZ entries in used that required the reconstruction of the J/ψ and (roughly) clockwise order, starting at the left with the only one D or D∗ meson4), and determined the presence X(3940) and X(4160). of the D¯ or D¯ ∗ from energy momentum conservation [32]. X(3940) and X(4160) The X(3940) was first seen With this technique, the X(3940) was seen in the DD¯ ∗

4) In the remainder of this report, the inclusion of charge conjugate states is always implied.

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-5 REVIEW ARTICLE

Fig. 4 The spectrum of charmonium and charmoniumlike mesons invariant mass distribution in e+e− → J/ψDD¯ ∗ annihi- under variations of the background shape parameteriza- lations [32], as can be seen in the lower panel of Fig. 5(b) tion and the bin size, Belle makes no claims about this and the upper panel in Fig. 5(c). Here the fits shown in distribution other than that it is inconsistent with phase the plots return a mass and width of M = 3942 ± 9MeV space or pure background. On the other hand, Chao [33] +27 + − ∗ ∗ and Γ =37−17 MeV. The e e → J/ψD D¯ study un- suggests that this may be the χc0, which is discussed covered another, higher mass state decaying to D∗D¯ ∗ below in conjunction with the X(3915). as can be seen in the lower panel of Fig. 5(c). The fitted The absence of signals for any of the known spin non- mass and width of this state, which is called the X(4160), zero charmonium states in the inclusive spectrum of Fig. +113 is M = 4156 ± 27 MeV and Γ = 139−65 MeV [32]. 5(a) provides circumstantial evidence for J = 0 assign- Neither the X(3940) nor the X(4160) show up in the ments for the X(3940) and X(4160). The X(3940) → DD¯ invariant mass distribution for exclusive e+e− → D∗D¯ decay mode then ensures that its J PC values are J/ψDD¯ at the same energies. Instead, the M(DD¯) spec- 0−+. The absence of any signal for X(4160) → DD¯ de- trum exhibits a broad excess of events over an equally cay supports a 0−+ assignment for this state as well. In broad background as shown in the upper panel of Fig. both cases, the measured masses are far below expec- 5(b). A fit to a resonant shape, shown as a curve in the tations for the only available 0−+ charmonium levels: figure, returns a signal of marginal significance (3.8σ) the ηc(3S)andηc(4S). Since there are no strong rea- with a peak mass of M = 3780 ± 48 MeV and a width sons to doubt the generally accepted identifications of +316 Γ = 347−143 MeV. Since the fitted values are unstable the ψ(4040) peak seen in the inclusive cross section for

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√ Fig. 5 (a) The distribution of masses recoiling from a J/ψ in inclusive e+e− → J/ψX annihilations near s 10.6GeV. DD¯ DD¯ ∗ The curve is the result of a fit described√ in the text. (b) The (upper)and (lower) invariant mass distributions from e+e− → J/ψDD¯ (∗) annihilations near s 10.6 GeV. Here the J/ψ and a D meson are reconstructed, and the presence D¯ D¯ ∗ D∗D¯ D∗D¯ ∗ of the or is inferred from kinematics.√ (c) The (upper)and (lower) invariant mass distributions from e+e− → J/ψD∗D¯ (∗) annihilations near s 10.6 GeV. Here the J/ψ and a D∗ are reconstructed and the presence of the D¯ or D¯ ∗ is inferred from kinematics. The hatched histograms in the center and right panels show backgrounds estimated from the J/ψ and D(∗) mass sidebands; the insets in the center panels show background-subtracted fits. e+e− → hadrons as the ψ(3S)andtheψ(4415) peak as tern conflicts with expectations from potential models, the ψ(4S) [34, 35], these assignments would imply hy- where hyperfine splittings are proportional to the square perfine n3S − n1S mass splittings that increase from the of the radial wavefunction at r = 0 and decrease with measured value of 47.2±1.2MeVforn = 2 [13], to ∼ 100 increasing n [36]. MeV for n =3and∼ 350 MeV for n = 4 [33]. This pat- Y (4260), Y (4360) and Y (4660): BaBar

+ − + − + − Fig. 6 (a) The M(π π J/ψ)frome e → γisrπ π J/ψ events from BaBar (upper) and Belle (lower). (b) The + − + − + − M(π π ψ )frome e → γisrπ π ψ events from BaBar (upper) and Belle (lower). (c) The total inclusive Born cross + − + − + − section for e e → hadrons in units of σQED(e e → μ μ )fromBESII.

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-7 REVIEW ARTICLE discovered the Y (4260) as a peak near 4260 MeV in the bution in B → Kπ+ψ decay events that survive this M(π+π−J/ψ) distribution from initial-state-radiation K∗ veto, shown an open histogram in Fig. 7(b), exhibits + − + − + e e → γisrπ π J/ψ events [37] shown in the upper a distinct peak near M(π ψ ) 4.43 GeV. A fit to a panel of Fig. 6(a), and the Y (4360) in the π+π−ψ sys- smooth background plus a BW signal function to de- + − + − tem produced via e e → γisrπ π ψ [38], shown in the scribe the peak returns a mass and width of M = 4433±5 +35 upper panel of Fig. 6(b). These states were confirmed MeV and Γ =45−18 MeV; the statistical significance of by Belle, as shown in the lower panels of the same fig- the peak is 6.5σ. However, a 2009 analysis by BaBar ures [39, 40]. Belle found another peak, the Y (4660), at failed to confirm the Belle signal [55]. Figure 7(c), taken higher mass in the M(π+π−ψ) distribution. There is from the BaBar paper, presents a direct comparison be- no sign of the Y (4260) in the M(π+π−ψ) distributions: tween the Belle and BaBar results with the same K∗ the expected shape for Y (4260) → π+π−ψ is shown veto requirements. A BW fit by BaBar that used Belle’s as a dashed curve in the upper panel of Fig. 6(b). Nei- Z(4430) mass and width values found a signal with a ther is there any sign of the Y (4360) or Y (4660) in the statistical significance of only 2σ. M(π+π−J/ψ) distributions of Fig. 6(a). One concern about the Z(4430) was that neither the These states have to be considered exotic because their BaBar nor the 2008 Belle analysis considered the pos- production mechanism ensures that J PC =1−− and all sibility of interference between B → KZ(4430) and of the 1−− cc¯ states near their masses have already been B → K∗ψ amplitudes. Because of this, Belle did two assigned. Moreover, there is no evidence for them in any subsequent analyses that explicitly accounted for the exclusive [41–44] or the inclusive [34, 35] charmed-meson possibility of such interference [56, 57]. The decay chain B → Kπ+ψ ψ → + − production√ cross section, where there is a pronounced dip ; can be completely described at s 4.26 GeV and no striking feature near 4.36 GeV, by four variables5), which can be taken as M(π+ψ), as can be seen in BESII cross section data shown in Fig. M(Kπ+), the ψ helicity angle θ and the angle between 6(c) [34, 35]. This implies large partial decay widths to the Kπ+ and + − planes in the B rest frame φ. Belle’s π+π−J/ψ(ψ); for example: a specific analysis for the first amplitude analysis integrated over θ and φ and Y (4260) finds Γ (Y (4260) → π+π−J/ψ) > 1 MeV [45], only considered the Kπ+ and π+ψ masses [56]; the which is huge by charmonium standards. Some authors second analysis used all four variables [57]. Both ampli- have proposed that the Y (4260) is a cc¯-gluon hybrid tude analyses found strong signals (6.4σ in both cases) state [46, 47] while others have suggested that it is a for a resonance in the π+ψ channel, with a somewhat molecule-like DD¯1(2420) bound-state [48]. The Y (4260) higher peak mass and much broader width than that is discussed in more detail below. reported in the 2008 Belle paper; the four-dimensional + The electrically charged Zc(3900), Zc(4020), analysis, based on 2010 ± 50 B → Kπ ψ signal events, +36 +49 Z1(4050), Z2(4250) and Z(4430) states: Since reported M = 4485±−25 MeV and Γ = 200−58 MeV. the Zc(3900) [49, 50], Zc(4020) [51, 52], Z1(4050) [53], These amplitude analyses show strong interference be- + ∗ + Z2(4250) [53] and Z(4430) [54] are electrically charged tween the Z → π ψ and K → Kπ channels, as is and decay to hidden charm final states, their minimal evident in Fig. 8(a) where the M 2(π+ψ) distribution for quark structure is a ccu¯ d¯ four-quark combination and, the data surviving the K∗ veto (points with errors) are therefore, if they are mesons, they must be exotic. shown with projections of the four-dimensional fit results The Z(4430): The first electrically charged, charmo- superimposed6) . The fit that includes the Z+ → π+ψ niumlike state to be reported was the Z(4430), which was resonance is shown as a solid histogram and the best found by Belle in 2008 in a study of B → Kπ+ψ decays fit with no Z+ resonance is shown as a dashed curve. [54]. An M 2(π+ψ)vs. M 2(Kπ+) Dalitz plot for these For masses below the Z+ resonance peak, the interef- decays is shown in Fig. 7(a). There, the most prominent erence is constructive and there is a clear positive en- feature is a strong vertical band near M 2(Kπ+) 0.8 hancement; for masses above the peak the interference is GeV2 corresonding to B → K∗(890)ψ decays. A second destructive and produces a depletion of events. The orig- vertical band near M 2(Kπ+) 2GeV2 corresponds to inal Belle result, which was based on a one-dimensional ∗ + B → K2 (1430)ψ . To reduce the influence of these struc- fit to the M(π ψ ) distribution, only fit the low-mass tures, Belle studied events with M(Kπ+) more than 100 positive lobe and this resulted in a lower mass and a ∗ ∗ MeV away from the K (890) and K2 (1430) peak mass narrower width. The four-dimensional analysis strongly values (the K∗ veto). The π+ψ invariant mass distri- favored the J P =1+ quantum number assignment for

5) This neglects the ﬁnite width of the ψ resonance. 6) For the four-dimensional analysis, only the ψ → +− decay channel was used.

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Fig. 7 (a) An M 2(π+ψ)(vertical)vs. M 2(Kπ+)(horizontal) Dalitz plot for B → Kπ+ψ events from Belle. The vertical dashed red lines indicate the boundaries of K∗ veto requirement described in the text. (b) The π+ψ invariant mass distribution from B → Kπ+ψ decays from Belle [54] for events with the K∗ veto requirement applied is shown as the open histogram. The shaded histogram is non-ψ background, estimated from the ψ mass sidebands. The curves represent results of a fit described in the text. (c) A comparison of the Belle data (upper) and BaBar data (lower) [55] with the the ∗ ∗ K and K2 vetoed. the Z(4430). amplitude and directly measure the real and imaginary In 2014, the LHCb experiment repeated the Belle four- parts of the amplitude as a function of mass. The results dimensional analysis with a sample of more than 25 K are shown as data points in Fig. 8(c). There the phase B¯0 → K−π+ψ decays [58] and confirmed the Belle sig- motion near the resonance peak agrees well with expec- nal with a significance greater than 14σ. A comparison tations for a BW amplitude as indicated by the nearly of their M(π+ψ) data distribution with projections of circular red curve superimposed on the plot. This rapid their fit results superimposed is shown in Fig. 8(b), where phase motion is a clear signature for a BW-like resonance strong interference effects, similar in character to those behavior but, by itself, does not necessarily rule out ex- reported by Belle, are apparent. The LHCb results for planations of the Z(4430) structure as being due to a P +17 the mass, width and J values, M = 4475−26 MeV, rescattering process [59, 60]. +39 P + Γ = 172−36 MeV and J =1 , agree well with the Belle The Belle and LHCb product branching fractions for four-dimensional fit results but with smaller errors. With Z(4430)+ production in B¯0 decays are their ten-fold larger event sample, the LHCb group was 0 − + + + + B(B¯ → K Z(4430) ) ×B(Z(4430) → π ψ ) able to relax the assumption of a BW form for the Z +3.0 −5 =6.0−2.4 × 10 Belle, and

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-9 REVIEW ARTICLE

Fig. 8 (a) The data points show the Belle M 2(π+ψ) distribution with the K∗ veto applied. The solid (blue) histogram shows four-dimensional fit results with a Z+ → π+ψ resonance included. The dashed (red) curve shows best fit results with no resonance in the π+ψ channel. (b) The LHCb group’s M 2(π+ψ) distribution for all events (no K∗ veto), together with projections from the four-dimensional fits. The solid red histogram shows the fit that includes a Z+ → π+ψ resonance term; the dashed brown histogram shows the fit with no resonance in the π+ψ channel. (c) The Real (horizontal)and Imaginary (vertical) parts of the (1+) Z+ → π+ψ amplitude for different mass bins spanning the 4430 MeV mass region from LHCb [58]. The red curve shows expectations for a BW resonance amplitude.

B(B¯0 → K−Z(4430)+) ×B(Z(4430)+ → π+ψ) 181 ± 31 MeV), gives a lower limit on the partial width + + +1.1 −5 Γ (Z(4430) → π ψ ) > 7.5 MeV, which is very large =3.4−2.4 × 10 LHCb; by charmonium standards: for example, the largest mea- −5 the weighted average is 4.4 ± 1.7 × 10 . There is no ex- sured hadronic transition width between well established 0 − + perimental value for B(B¯ → K Z(4430) ), although charmonium states is Γ (ψ → π+π−J/ψ) = 102 ± 3keV − we expect that it cannot be larger than B(B → [13]7). − K X(3872)), for which BaBar has set a 90% CL up- Another striking feature of the Z(4430) is that its −4 per limit of 3.2 × 10 [61]. This seems reasonable be- π+ψ partial decay width is much stronger than that for cause the leading quark-line diagram for B → KX(3872) π+J/ψ. In 2009, BaBar reported B(B¯0 → K−Z(4430))× is a “factorizable” weak interaction process that is fa- B(Z(4430) → π+J/ψ) < 0.4 × 10−5, an order of mag- vored in B meson decays, while the leading-order dia- nitude lower than the Belle-LHCb average value for gram for producing a charged charmoniumlike state is Z(4430) → π+ψ. Belle recently reported the ﬁrst ob- “non-factorizable”, and expected to be suppressed in B servation of the Z(4430) → π+J/ψ decay mode in meson decays [63–65]. Thus, it is probably safe to expect B → Kπ+J/ψ decays with a product branching frac- B B¯0 → KZ < B B− → K−X < +4.1 −6 that ( (4430)) ( (3872)) tion of 5.4−1.3 × 10 [62], which is near the BaBar up- −4 3.2 × 10 . In that case, the Belle-LHCb average given per limit and about an order of magnitude smaller than + + abovegivealower limit B(Z(4430) → π ψ ) > 5.3% the corresponding rate for Z(4430)+ production in the that, when coupled with our average of the Belle and B → Kπ+ψ channel. LHCb measurements of the Z total width (ΓZ(4430) = The Z1(4050) and Z2(4250) : The Z1(4050) and

7) Hadronic transitions between charmonium states are OZI suppressed. This is not the case for four-quark charmoniumlike states.

101401-10 Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) REVIEW ARTICLE

+ + Z2(4250) are resonances in the π χc1 channel that A BaBar study of B → Kπ χc1 decays did not con- + + were found by Belle in a two-dimensional (M(Kπ ) firm the Belle claim of resonances in the π χc1 channel + + vs. M(π χc1)) amplitude analysis of B → Kπ χc1 de- [66]. Figure 10(a) shows BaBar’s background-subtracted 2 + + cays [53]. Figure 9(a) shows the M (π χc1) distribution M(π χc1) distribution for events with 1.0GeV < for events with 1.0GeV 1.54 GeV (lower) with the best fit jection of the BaBar fit with no Z+ resonances in the + for a model with all known Kπ resonances but no reso- π χc1 channel. This fit obviously overshoots the data in + + nance in the π χc1 channel. Figure 9(b) shows the same the M(π χc1) ∼ 3.9 GeV region and undershoots the + + data with a fit that includes one resonance in the π χc1 data near M(π χc1) ∼ 4.1 GeV. The red curve shows + + channel. Here the fit quality improves substantially; the the result when two Z → π χc1 resonance terms with + statistical significance of the Z → π χc1 term is more the Belle mass and width values are added; this im- than 10σ. The use of different parameterizations of the proves the agreement with the data, but not markedly. + Kπ scalar amplitude or the inclusion of an additional The BaBar report claims that, overall, the M(π χc1) J P =1− or 2+ K∗ resonance with a mass and width left distributions in the data [including those in the regions as free parameters do not reduce the significance of the of M(Kπ+) that are not shown in Fig. 10(a)] are ade- + + Z → π χc1 term to below 6σ. quately described by resonances in the Kπ sector only, It is evident in Fig. 9(b) that the inclusion of a single and the inclusion of Z+ resonances does not signficantly Z → πχc1 amplitude does not reproduce the details of improve the fit quality. Based on this they set 90% CL the data. Because of this, Belle repeated the fit with two product branching fraction upper limits of [66] + BW amplitudes in the Z → π χc1 channel. This model 0 − + + B(B¯ → K Z1(4050) ) ×B(Z1(4050) fits the data well, as can be seen in Fig. 9(c); the signifi- + −5 cance of the two Z model relative to the single Z model → π χc1) < 1.8 × 10 and . σ Z 0 − + + is 5 7 . The masses and widths of the two sare B(B¯ → K Z2(4250) ) ×B(Z2(4250) +24 +51 + −5 Z1(4050): M1 = 4051−43 MeV, Γ1 =82−28 MeV → π χc1) < 4.0 × 10 , Z M +185 , Γ +321 . 2(4250): 2 = 4248−45 MeV 2 = 177−72 MeV which are below, but not in strong contradiction with,

2 + + + Fig. 9 (a) The M (π χc1) distribution for B → Kπ χc1 events with 1.0GeV 1.54 GeV (lower) from Belle. The solid histograms are projections of the two-dimensional fit with no resonance + in the π χc1 channel. The dashed histogram indicates the background level determined from the χc1 mass sidebands. (b) + + The same data with results of the fit with a single Z → π χc1 resonance amplitude. Here the dotted histogram indicates + + + the sum of all fit components other than the Z . (c) The same data with results of the fit that includes two Z → π χc1 resonanceswithmassandwidthvaluesgiveninthetext.

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-11 REVIEW ARTICLE the Belle measurements [53] ran with such high luminosity (L > 1034 cm−2 · s−1), 0 − + + the measurements were feasible. A more efficient way to B(B¯ → K Z1(4050) ) ×B(Z1(4050) produce Y (4260) mesons would be to run a high lumi- → π+χ . +4.0 × −5 + − c1)=30−1.8 10 and nosity e e collider as a “Y (4260) factory,” i.e., at a cm 0 − + + B(B¯ → K Z2(4250) ) ×B(Z2(4250) energy of 4260 MeV, corresponding to the peak mass of + +19.8 −5 the Y (4260). This was done at the upgraded, two-ring → π χc1)=4.0−1.0 × 10 . Beijing electon-positron collider (BEPCII) [67] in 2013, For comparison, Fig. 10(b), from Ref. [53], shows the and large numbers of Y (4260) decays were detected in + Belle data with the same M(Kπ ) requirement and the the new BESIII spectrometer [68]. + results of a fit with no Z resonances (dashed blue curve) The first channel to be studied with these data was + and the fit with the two Z resonances described above. e+e− → π+π−J/ψ, where a distinct peak, called the The Belle and BaBar data, and the results of their no Zc(3900), was seen near 3900 MeV in the distribution + Z fits are qualitatively very similar, while the results of of the larger of the two π±J/ψ invariant mass combi- + the fits that include Z terms are quite different. This nations in each event (Mmax(πJ/ψ)), as can be seen in + is because in Belle fits, the Z amplitudes are coherent Fig. 11(a) [49]. A fit using a mass-independent-width BW + with those for the Kπ channel and, as in the case of function to represent the π±J/ψ mass peak yielded a Z + Z+ M . ± . the (4430) analysis, interference between the and mass and width of Zc(3900) = 3899 0 6 1MeVand Kπ+ Γ ± ∼ amplitudes is very strong, in this case resulting in Zc(3900) =46 22 MeV, which is 24 MeV above the strong destructive interference below and above the peak mD∗+ + mD¯ 0 (or mD+ + mD¯ ∗0 ) threshold. The Zc(3900) region. A comparison of Figs. 10(a) and (b) clearly shows was observed by Belle in isr data at about the same time that by neglecting the possibility of interference between [50]. + + the Z and Kπ amplitudes, the BaBar analysis under- A subsequent BESIII study of the (DD¯ ∗)± systems + + ∗ ± ∓ estimates the strength of possible Z1 and Z2 signals in produced in (DD¯ ) π final states in the same data their data. sample found very strong near-threshold peaks in both 0 ∗− + ∗0 The Zc(3900) : The discovery and early measure- the D D and D D¯ invariant mass distributions [69], ments of the Y (4260) were based on measurements of as shown in Figs. 11(b) and (c), respectively. The curves e+e− → γ Y the√ initial state radiation process, isr (4260) in the two figures show the results of fits to the data at s 10.6 GeV. This reaction requires that either the with threshold-modified BW line shapes to represent the − + incident e or e radiates a ∼ 4.5 GeV photon prior to peaks. The average values of the mass and widths from annihilating, which results in a strong reduction in event these fits are used to determine the resonance pole posi- rate. However, since the PEPII and KEKB B-factories tion (Mpole +iΓpole) with real and imaginary values of

2 + + Fig. 10 (a) The data points show the background-subtracted M (π χc1) distribution for B → Kπ χc1 events with 1.0GeV

Fig. 11 (a) Invariant mass distributions for π+J/ψ from e+e− → π+π−J/ψ events from Ref. [49]; (b) M(D0D∗−)and(c) M(D+D¯ ∗0)fore+e− → (DD¯ ∗)+π− events from Ref. [69]; (d) The eﬃciency corrected production angle distribution compared with predictions for J P =0− (dashed-red), J P =1− (dotted blue)andJ P =1+ (solid black) quantum number assignments.

− − Mpole = 3883.9 ± 4.5MeVandΓpole =24.8 ± 12 MeV. signment is clearly preferred and the 0 and 1 assign- Since the pole mass position is 2σ lower than the ments are ruled out with high confidence. Zc(3900) mass reported in Ref. [49], BESIII cautiously The Zc(4020) : With data accumulated at the peaks ∗ named this DD¯ state the Zc(3885). In the mass deter- of the Y (4260), Y (4360) and nearby energies, BESIII + − minations of both the Zc(3885) and Zc(3900), effects of made a study of π π hc(1P ) final states. Exclusive possible interference with a coherent component of the hc(1P ) decays were detected via the hc → γηc tran- background are ignored, which can bias the measure- sition, where the ηc was reconstructed in 16 exclusive ments by amounts comparable to the resonance widths, hadronic decay modes. With these data, BESIII ob- ± and this might account for the different mass values. In served a distinct peak near 4020 MeV in the Mmax(π hc) any case, we consider it highly likely that the Zc(3885) distribution that is shown in Fig. 12(a). A fit to this + is the Zc(3900) in a different decay channel. If this is peak, which the BESIII group called the Zc(4020) , ∗ P + the case, the partial width for Zc(3900) → DD¯ decays with a signal BW function (assuming J =1 )plus is 6.2 ± 2.9 times larger than that for J/ψπ+,whichis a smooth background, returns a ∼ 9σ significance signal M . ± . small compared to open-charm vs. hidden-charm decay- with a fitted mass of Zc(4020) = 4022 9 2 8MeV, width ratios for established charmonium states above the about 5 MeV above mD∗+ + mD¯ ∗0 ,andawidthof ψ ψ Γ . ± . σ e+e− → open-charm threshold, such as the (3770) and (4040), Zc(4020) =79 3 7 MeV [51]. The product ( π−Z + ×B Z + → π+h where corresponding ratios are measured to be more than c(4020) ) ( c√(4020) c)ismeasuredto an order-of-magnitude larger [13]. be 7.4±2.7±1.2pbat s = 4260 MeV, where the second ∗ Since the Z(3885) → DD¯ signals are so strong, the error reflects the uncertainty of B(hc → γηc). J P quantum numbers can be determined from the depen- The inset in Fig. 12(a) shows the result of including + + dence of its production on θπ, the bachelor pion produc- a Zc(3900) → π hc term in the fit. In this case, a + − + + tion angle relative to the beam direction in the e e cm marginal ∼ 2σ signal for Zc(3900) → π hc is seen to P − 2 system. For J =0 ,dN/d| cos θπ| should go as sin θπ; the left of the Zc(4020) peak. This translates into an up- − 2 + + − − + for 1 it should follow 1 + cos θπ and for 1 it should per limit on the product σ(e e → π Zc(3900) ) × + + + be flat (0 is forbidden by Parity). Figure 11d shows the B(Zc(3900) → π hc) of 11 pb. Since the product + − − + + + efficiency-corrected Zc(3885) signal yield as a function of σ(e e → π Zc(3900) ) ×B(Zc(3900) → π J/ψ) P + | cos θπ|, together with expectations for J =0 (dashed is measured to be 62.9 ± 4.2 pb [49], this limit implies − P + P + + + red), 1 (dotted blue) and J =1 .TheJ =1 as- that the Zc(3900) → π hc decay channel is suppressed

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+ + − + − Fig. 12 (a) The Mmax(π hc) distribution for e e → π π hc events from BESIII. The shaded histogram is background estimated from the hc mass sidebands. The curves are results of fits described in the text. (b) The corresponding M π0h e+e− → π0π0h max( c) distribution for c√events from BESIII. (c) The distribution of masses recoiling from a detected D+ and π− for e+e− → D+π−π0X events at s = 4260 MeV. The peak near 2.15 MeV corresponds to e+e− → π−D∗+D¯ ∗0 + − − events. The red dashed histogram shows the expected recoil mass distribution for e e → π Zc,withMZc = 4025 GeV; the open, dash-dot histogram shows results for MC π−D∗+D¯ ∗0 three-body phase-space events. The shaded histogram is combinatoric background from wrong-sign combinations in the data. (d) M(D∗D¯ ∗)fore+e− → (D∗D¯ ∗)+π− events, i.e., events in the 2.25 MeV peak in panel (c). The curves are described in the text. relative to that for π+J/ψ by at least a factor of five. shown as data points in Fig. 12(d), shows a strong near- BESIII recently reported observation of the neu- threshold peaking behavior with a shape that cannot be tral member of the Zc(4020) isospin triplet [70]. The described by a phase-space-like distribution, shown as 0 + − 0 0 Mmax(π hc) distribution for e e → π π hc events in a dash-dot blue curve, or by combinatoric background, ± the same data set used for the Zc(4020) ,showninFig. whichisdeterminedfromwrong-sign(WS)eventsinthe + 12(b), looks qualitatively like the Mmax(π hc) distribu- data (i.e., events where the bachelor pion and charged tion with a distinct peak near 4020 MeV. A fit to the D meson have the same sign) that are shown as the data that includes a BW term with a width fixed at the shaded histogram. The solid black curve shows the re- + value measured for the Zc(4020) and floating mass results of a fit to the data points that includes an ef- turns a mass of 4023.9 ± 4.4 MeV; this and the signal ficiency weighted S-wave BW function, the WS back- yield are in good agreement with expectations based on ground shape scaled to measured non-D∗+D¯ ∗0π− back- isospin symmetry. √ ground level under the signal peak in Fig. 12(d), and a A study of e+e− → D∗+D¯ ∗0π− events in the s = phase-space term. The fit returns a 13σ signal with mass 4.26 GeV data sample using a partial reconstruction and width M = 4026.3 ± 4.5MeVandΓ =24.8 ± 9.5 technique that only required the detection of the bach- MeV, values that are close to those measured for the − + ∗+ 0 + + + elor π ,theD from the D → π D decay and one Zc(4020) → π hc channel. Although BESIII cautiously 0 ∗+ ∗0 ∗ ∗ + π , either from the D or the D¯ decay, to isolate the calls this (D D¯ ) signal the Zc(4025), in the follow- process and measure the D∗+D¯ ∗0 invariant mass [52]. ing we assume that this is another decay mode of the ∗+ ∗0 − The signal for real D D¯ π final states is the dis- Zc(4020). tinct peak near 2.15 MeV in the D+π− recoil mass spec- From the numbers provided in Ref. [52], we deter- ∗ ∗ + − − ∗ ∗ trum shown on Fig. 12(c). The measured D D¯ invari- mine σ(e e → π Zc(4020)) ×B(Zc(4020) → D D¯ )= ant mass distribution for events in the 2.15 MeV peak, 89 ± 19 pb. This implies that the partial width for

101401-14 Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) REVIEW ARTICLE

∗ ∗ ZC(4020) → D D¯ is larger than that for Zc(4020) → have some relation to the Zc(4020)’s proximity to the πh ± m ∗ c, but only by a factor of 12 5, not by the large 2 D threshold. However, until BESIII√ provides a limit ∗ factors that are characteristic of open charm decays of on a Zc(4020) → DD¯ signal at s = 4260 MeV, this conventional charmonium. effect cannot be quantified. ∗ There is no sign of Zc(4020) → DD¯ in either X(3915) The X(3915) is an ωJ/ψ mass peak with Figs. 11(b) or (c), where ∼ 500 and ∼ 700 event M = 3918 ± 2MeVwithΓ =20± 5 MeV [13] seen in 0 ∗− + ∗0 Zc(3885) signals in the D D and D D¯ distribu- B → KωJ/ψ decays by both Belle [71] and BaBar [72, tions, respectively, correspond to the product σ(e+e− → 73] [see Figs. 13(a) and (b)] and in the two-photon pro- − ∗ π Zc(3900)) ×B(Zc(3900) → DD¯ )=84± 23 pb, cess γγ → ωJ/ψ also by Belle [74] and BaBar [75] [Fig. about the same as the corresponding product for 13(c)]8) . BaBar measured its J PC quantum numbers to ∗ ∗ ++ the Zc(4020)D D¯ signal mentioned in the previous be 0 . The PDG currently assigns this as the χc0(2P ) paragraph. This absence of any evident signals for charmonium level (i.e., the χc0), an assignment that has ∗ Zc(4020) → DD¯ in Figs. 11(b) and (c) suggests that a number of problems [77]: ∗ the Zc(4020) → DD¯ partial width is considerably i) The J =2memberoftheχc0,1,2 multiplet, the ∗ ∗ smaller than that for Zc(4020) → D D¯ ,whichmay χc2(2P )(χc2), was seen by Belle [78] and confirmed by

Fig. 13 (a) The X(3915) → ωJ/ψ signals in B → KωJ/ψ decays from Belle. (b) The corresponding distributions from + + 0 BaBar, where the upper panel shows results for B → K ωJ/ψ and the lower panel shows those for B → KSωJ/ψ.The inset in the upper panel shows an expanded view of the low end of the ωJ/ψ mass scale, where the smaller, low-mass peak is due the X(3872) → ωJ/ψ and the larger, higher mass peak is the X(3915) → ωJ/ψ signal. (c) The X(3915) → ωJ/ψ signals in γγ → ωJ/ψ fusion reactions from Belle (upper) and BaBar (lower).

8) Some of the literature refers to this state as the Y (3940).

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BaBar [79] as a distinct peak in the DD¯ invariant mass 14(c)]. Since neither group reported a X(3915) → DD¯ distribution near 3930 MeV in γγ → DD¯ events. The limit, I formed my own conservative estimate of an up- mass, production rate and production angle dependence per bound by scaling the total number of Belle events agree quite well with expectations for the χc2 [see Figs. in the two mass bins surrounding 3915 MeV in the up- 14(a) and (b)], and there are no known reasons to doubt per panel of Fig. 14(c) to the ψ(3770) signal while as- this assignment. The weighted averages of the Belle and suming constant acceptance. This gives B(X(3915) → BaBar mass and width measurements are M = 3927 ± 3 ωJ/ψ) > B(X(3915) → D0D¯ 0), which strongly contra- MeV and Γ =24± 6 MeV [13]. With the χc2 well estab- dicts the theoretical expectation that the χc0 → DD¯ lished with a reliably known mass, the X(3915) = χc0 decay channel should dominant [76]. 3 3 assignment implies a 2 P2 − 2 P0 ﬁne splitting of only iii) Since branching fractions cannot exceed unity, χ ± c2 9 4 MeV, which is very small in comparison with the the measured quantity Γγγ ×B(χc2 → DD¯)= corresponding n = 1 splitting of 141.4 ± 0.3 MeV [13] 0.21 ± 0.04 keV [78, 79], translates to a ∼90% CL χ and theoretical predictions for n = 2 that range from 69 c2 lower limit Γγγ > 0.16 keV. Using the assumption MeV [36] to 80 MeV [76]. χc0 χc2 χ χ Γγγ /Γγγ = Γ c0 /Γ c2 =4.5 ± 0.6 [13], which is ii) There is no sign of X(3915) → DD¯ decay, which γγ γγ valid for pure charmonium states, I infer a lower limit is expected to be a favored decay mode. Belle [80] and χc0 Γγγ > 0.80 keV that, when taken with the measured BaBar [81] have studied the process B → KDD¯ and Γ X(3915)B X → ωJ/ψ . ± . both groups see prominent signals for ψ(3770) → DD¯, value γγ ( (3915) )=0054 0 009 B χ → ωJ/ψ < . but no hint of a DD¯ mass peak near 3915 MeV [see Fig. keV [82], gives an upper limit ( c0 ) 5 6% if

Fig. 14 (a) The DD¯ invariant mass distribution for γγ → DD¯ events in Belle. The narrow peak is attributed to χc2 → DD¯ . ∗ (b) The | cos θ | distribution for events in the region of the χc2 peak. The solid line show expectations for spin=2, helicity=2; the dashed line shows the spin zero expectation. (c) The M(D0D¯ 0) distribution from B → KD0D¯ 0 decays from Belle [80] (upper); the M(DD¯ ) distribution from B → KDD¯ decays from BaBar [81] (lower). The near-threshold peak in both plots is due to the ψ(3770). (d) The M(DD¯ ) distribution from γγ → DD¯ two-photon annihilation from BaBar [79] (upper); the same distribution from Belle [78] (lower). The narrow peak is due to the γγ → χc2 → DD¯ and the curves show results of ﬁts described in Ref. [77].

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PC ++ X(3915) = χc0. The PDG value for the X(3915) to- vector-vector interactions. They find a J =0 state tal width of 20 ± 5 MeV and the above-mentioned limit near 3940 MeV with a 17 MeV width [86] that is domi- ∗ ∗ ∗ ∗ B(X(3915) → DD¯) < B(X(3915) → ωJ/ψ)implyan nantly D D¯ and Ds Ds .TheX(3915) mass is below the upper limit Γ (χc0 → DD¯) < 1.5MeVfortheX(3915) = threshold for decays to these final states and the authors χc0 assignment. This upper limit is below the range of findastrongdecaytoωJ/ψ plus a strong suppression theoretical predictions that range from 7 MeV [83] to 187 of decays to DD¯, consistent with what is seen experi- MeV [84]. mentally. This paper also predicts other states, including iv) The average of the Belle and BaBar measure- some with isospin=1, but none of these can be as easily ments for X(3915) production in B meson decay is associated with any of the XYZ peaks that are seen in +0.9 −5 B(B → KX3915)×B(X3915 → ωJ/ψ)=(3.0−0.7)×10 . experiment. If I make the (reasonable?) assumption that B(B → Y (4140) In 2009, the CDF group reported 3.8σ ev- −4 Kχc0) < B(B → Kχc0)=(1.3 ± 0.2) × 10 [13], I idence for a near-threshold peak in the φJ/ψ invariant + + find the lower limit B(χc0 → ωJ/ψ) > 14%, in strong mass distribution from B → K φJ/ψ decays based contradiction to the 5.6% upper limit established in the on an analysis of a 2.7 fb−1 data sample [87]. CDF previous paragraph. subsequently reproduced this signal with a larger, 6.0 Some authors have identified another candidate for the fb−1 data sample and with a significance that increased χc0. Guo and Meissner [77] propose that the broad back- to more than 5σ [88] [see Fig. 15(a)]. The mass and ground under the γγ → χc2 → DD¯ peak in the M(DD¯) width were reported as M = 4143.4 ± 3.0MeVand +10.7 distribution in γγ → DD¯ events as seen in Fig. 14(a) is Γ =15.3−6.6 MeV. The CDF group’s fit, shown as a due to γγ → χc0 → DD¯. Their fits to BaBar and Belle red curve in Fig. 15(a), includes a second structure with +8.6 +23.2 data, shown as dashed curves Fig. 14(d), yield a “χc0” mass and width M = 4274.4−7.0 MeV and Γ =32.3−17.1 mass and width of M = 3838±12 MeV and Γ = 221±21 MeV, with a significance estimated to be 3.1σ. MeV, which is in general agreement with charmonium The existence of the Y (4140) has been somewhat con- model expectations. This fit is almost certainly biased troversial because it was not seen in B → KφJ/ψ decays because the authors do not consider contributions to the by LHCb [89], which set an upper limit on the Y (4140) ∗ DD¯ signal from χc2 → DD¯ decays where the π or γ production rate in B decays that is about a factor of two from D¯ ∗ → Dπ¯ (γ) decay is missed. Nevertheless, their below the CDF group’s central value for the same quan- suggestion that a broad and light χc0 might be responsi- tity. Figure 15(b) shows the LHCb group’s M(φJ/ψ)dis- ble for at least part of the measured DD¯ “background” tribution as a histogram with expectations for the two should be carefully considered. With enough data, con- peaks reported by CDF superimposed as blue dashed ∗ tributions from χc0 → DD¯ and χc2 → DD¯ can be curves. While the agreement between the LHCb data and sorted out from the relative rates for D0D¯ 0, D∗+D∗− the CDF-inspired curves is pretty poor, there does seem and D0D∗− final states and the shapes of their associ- to be excesses in the LHCb distribution in the vicinity ated pT distributions. This is a good candidate for a “day of both of the CDF peaks. The excess near threshold is one” measurement for the BelleII experiment [85]. pretty broad and suggests that if there is a state decay- Chao [33] suggested that χc0 → DD¯ may be the source ing to φJ/ψ in that mass region, it may have a broader of the broad peak in the M(DD¯) spectrum seen by Belle width than the CDF group’s measured Γ value. in e+e− → J/ψDD¯ events [32], as discussed above and This year, the CMS group published the M(φJ/ψ)dis- shown in the upper panel of Fig. 5(b). The Belle group’s tribution in B+ → K+φJ/ψ shown in Fig. 15(c), where fit to this distribution yielded a broad signal with a peak there are distinct signals near the positions of both of mass at 3780 ± 48 MeV and a significance of 3.8σ. the CDF peaks [90]. Their fit to the data, shown as red This mass is closer to expectations for the χc0 than that curves in the figure, give a Y (4140) mass an width of +24 of the X(3915). Belle is now investigating this reaction M = 4148.0 ± 6.7MeVandΓ =28−22 MeV, which with about twice as much data than was used in the Ref. agree within errors with the CDF measurements. The es- [32] analysis. timated significance of the Y (4140) peak is greater than Although these suggestions are not definitive, they, 5σ. Note that the central value of the CMS width mea- plus the arguments from the previous paragraph, show surement, while consistent with the CDF value, is higher that the PDG’s assignment of the X(3915) to the χc0 by nearly a factor of two, and has a large positive-side charmonium level is premature and possibly misleading. error. If the X(3915) is not an ordinary cc¯ charmonium state, The fitted mass of the second peak, M = 4314 ± 9 what is it? Molina and Oset proposed a molecule-like MeV, is about 3σ higher than the CDF value, while +34 picture with states that are dynamically generated from the fitted width, Γ =38−22 MeV, is in good agreement,

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-17 REVIEW ARTICLE

Fig. 15 (a) The CDF 6.0 fb−1 M(φJ/ψ)− M(J/ψ) distribution for B+ → K+φJ/ψ decays is shown as a histogram. The red curve shows the results of a fit that includes the Y (4140), a possible second resonance near 4275 MeV and a phase-space non-resonant term (shown as a dashed line). (b) The same distribution from LHCb, with expectations based on the CDF results shown as a dashed blue curve. The LHCb upper limit is based on the results of the fit to their data shown as a solid red curve. (c) The same distribution from the CMS group with the results of their fits superimposed. albeit with large errors. The CMS paper also provides a that the two states may be related: e.g., the X(3915) plot that compares the K+K−K+ invariant mass distri- may be a D∗D¯ ∗ molecule and the Y (4140) is its hid- + − + ∗+ ∗− bution for B → K K K J/ψ decays with phase-space den charm counterpart Ds Ds molecule [92, 93]. In expectations [see Fig. 16(a)], where there is some indica- this case the Y (4140) would have the same J PC quan- tion of structure around 1.7 ∼ 1.8 GeV. The CMS group tum numbers as the X(3915), namely 0++,andthis warns that if such a structure actually exists, it could cre- implies that the Y (4140) could be accessible in γγ fu- ate a reflection peak in the M(K+K−J/ψ) distribution sion reactions. The M(φJ/ψ) distribution from a Belle near 4.3 GeV that could distort the measured param- study of γγ → φJ/ψ near the mφ + mJ/ψ threshold eters of the second φJ/ψ mass peak. As was the case is shown in Fig. 16(c), where there is no sign of the + +4.6 for the Z(4430) parameter extraction from B → Kπ ψ Y (4140) but ∼ 3σ evidence for a peak at M = 4350.6−5.1 +18 decays, a better understanding of this second peak prob- MeV with width Γ =13−10 MeV [94]. The mass value ably needs an experiment with a data sample that is is ∼ 4σ above that of the second peak seen by CDF large enough to support an amplitude analysis. and CMS in B → KφJ/ψ decays and, so, if both obser- The BaBar group recently reported on a search for the vations are from real meson states, they are not likely Y (4140) in B → KφJ/ψ decays [91]. Figure 16(b) shows to be from the same source. The absence of any events their efficiency-corrected M(φJ/ψ) distribution together in the Y (4140) region translates into the upper limit Y (4140) PC ++ with results of a fit that includes two resonances with the Γγγ ×B(Y (4140) → φJ/ψ) < 41 eV for J =0 , CDF group’s mass and width values. Although there are which is smaller, but not much smaller, than the mea- signs of signals both for the Y (4140) and the Y (4275), sured value (54 ± 9 eV) of the corresponding quantity the statistical significance in each case is less that 2σ for the γγ → X(3915) → ωJ/ψ signal discussed above. after systematic errors are considered. However, it is much lower than theoretical expectations Y m m ∗+ ∗− +137 PC ++ The (4140) shows up just above the φ + J/ψ mass for a Ds Ds molecule: 176−93 eV for J =0 or X +147 PC ++ threshold and e.g., the (3915) mass is just above the 189−100 eV for J =2 [94]. mω +mJ/ψ mass threshold. This led to some speculation 101401-18 Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) REVIEW ARTICLE

Fig. 16 (a) The data points show the CMS experiment’s M(K+K−K+) distribution from B+ → K+K−K+J/ψ decays; the histogram shows the expectations for a four-body phase-space distribution. (b) The efficiency corrected M(φJ/ψ) distribution for B → KφJ/ψ decays from BaBar. The red curve shows the results of a fit that includes two resonances with mass and width fixed at the CDF values. (c) The open histogram shows the M(φJ/ψ) distribution for γγ → φJ/ψ events from Belle; the shaded histogram shows the background estimated from the φ and J/ψ mass sidebands. The solid curve shows the results of the fit described in the text.

The LHCb results discussed here were based on an value, 3871.68±0.17 MeV, is indistinguishable from that −1 analysis of a 0.17 fb data sample, which is only about for the mD0 +mD∗0 = 3871.84±0.27 MeV threshold [13]; one tenth of their current total. Hopefully new results a recent result from LHCb is MX(3872) −(mD0 +mD∗0 )= based on all of the available data will soon be available. −0.09 ± 0.28 MeV [101]. It is also narrow, Belle has X(3872) The X(3872) was ﬁrst seen in 2003 as reported a 95% C.L. upper limit on its total width of apeakintheπ+π−J/ψ invariant mass distribution in Γ < 1.2 MeV [102]. B → Kπ+π−J/ψ decays [95] as shown in Fig. 17(a). It While LHCb and CDF have conclusively established is well established and has been seen and studied by a the J PC quantum numbers as 1++ [103, 104], its isospin number of experiments [96–100]. The PDG average mass is less well understood. Both CDF [105] and Belle [102]

Fig. 17 (a) The π+π−J/ψ invariant mass distribution for B → Kπ+π−J/ψ events from Belle’s original X(3872) paper. (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. The dashed (solid) curve is for even (odd) X(3872) parity. (c) M(D0D¯ ∗0) distributions from B → KD0D¯ ∗0 decays. The upper plot is for D¯ ∗0 → D¯ 0γ decays, the lower plot is for D¯ ∗0 → D¯ 0π0 decays. The peaks near threshold are attributed to X(3872) → D0D¯ ∗0 decays.

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-19 REVIEW ARTICLE have shown that the π+π− system in X → π+π−J/ψ The X(3872) has also been seen to decay to D0D¯ ∗0 decays originates from ρ0 → π+π− decay, which is con- [108–110]. Since its J PC =1++,theX(3872) couples sistent with the J PC =1++ assignment reported by to a DD¯ ∗ pair in an S- and/or D-wave. The D0D¯ ∗0 LHCb. The decay X → ρJ/ψ implies that either the system is right at threshold and, so, the S-wave should X(3872) has isospin I = 1 or 0: if it has isospin zero, be dominant, in which case some very general univer- its decay to ρJ/ψ is isospin violating; if it has I =1, sal theorems apply [111–113]. One consequence of these it should have charged partners. Searches for narrow, theorems is that, independently of its dynamical ori- charged partner states decaying to ρ±J/ψ by BaBar [106] gin, the X(3872) should exist for some fraction of the and Belle [102] set branching ratio limits well below ex- time as a DD¯ ∗ molecule-like state (either bound or pectations for isospin conservation. However, these lim- virtual) with size determined by its scattering length its should probably be viewed with some caution be- a00, which in turn depends upon the mass diﬀerence

X δm m − m 0 − m ∗0 − . ± . cause if charged partners of the neutral (3872) exist 00 = X√(3872) D D (= 0 09 0 28 MeV) ∗ and have masses that are even just a few MeV higher, as a00 = / μδm00,whereμ is the DD¯ reduced mass. their decays to DD¯ ∗ final states would probably be This, taken with the experimentally allowed range of 0 0∗ significantly stronger than those for their neutral part- δm00 values, suggests that for the D D¯ configuration, ± 0 ∗0 ner; these higher rates could suppress the ρ J/ψ decay the mean D -D¯ separation is huge, of order a00 ∼ 10 branching fraction below isospin expectations and pro- fm, and much larger than the extent of the D+D∗− con- duce a significantly broader width. However, other evi- figuration, for which δm+− = mX(3872) −mD+ −mD∗− dence against I = 1 comes from observations by Belle 8MeVanda+− 2 fm. The very different properties [107] and BaBar [72, 73] of X(3872) → ωJ/ψ decays of the D0D¯ ∗0 and D+D∗− configurations imply that the with a branching fraction that is nearly equal to that X(3872) isospin is not very well defined [114]. for ρJ/ψ decays; the PDG average is B(X(3872) → The BESIII experiment recently reported the observa- ωJ/ψ)/B(X(3872) → π+π−J/ψ)=0.8 ± 0.3 [13]. Since tion of the process e+e− → γX(3872) at cms energies in MX(3872) − mJ/ψ 775 MeV, and ∼ 7MeVbelowmω, the region of the Y (4260) peak [115]. The X(3872) was the decay X(3872) → ωJ/ψ can only proceed via the low detected via its π+π−J/ψ decay channel; a π+π−J/ψ energy tail of the ω peak and is, therefore, kinematically invariant mass plot summed over the data at all of the suppressed. I estimate a suppression factor of ∼ 1/1209). energy points is shown in Fig. 18(a), where a 6.3σ peak The fact that this strongly suppressed I = 0 final state at the mass of the X(3872) is evident. Figure 18(b) shows is accessed at nearly the same rate as the I =1,ρJ/ψ the energy dependence of the X(3872) production rate final state – which is also kinematically suppressed, but where there is some indication that the observed signal is only by a factor that I estimate to be ∼ 1/5–suggests associated with the Y (4260). Assuming that Y (4260) → that the X(3872) is (mostly) an isospin singlet and that γX(3872) decays are the source of this signal, and using the ρJ/ψ decay mode violates isospin symmetry. the PDG lower limit B(X(3872) → π+π−J/ψ) > 0.026

Fig. 18 (a) The data points show the BESIII experiment’s M(π+π−J/ψ) distribution for e+e− → γπ+π−J/ψ events +1.7 at energies near the Y (4260) resonance. The ﬁtted peak has a mass and width of M = 3871.9 ± 0.7MeVandΓ =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 σB (e+e− → γX(3872)) ×B(X(3872) → π+π−J/ψ), measurement where σB denotes the Born cross section. The solid curve is the Y (6260) line shape ﬁtted to the data; the dashed curves show phase-space and linear production model expectations.

9) This estimate neglects the possible eﬀects of ρ-ω interference.

101401-20 Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) REVIEW ARTICLE

[13], we determine X(3872) as a molecule [118–129], an idea that predates even Törnqvist’s 1994 paper [130–133]. However, the B(Y (4260) → γX(3872)) > 0.05, (1) CDF group reported that only (16.1 ± 5.3)% of their B(Y (4260) → π+π−J/ψ) X(3872) signal are produced via B meson decays; most which is substantial and suggestive of some commonality of their observed signal is produced promptly in high en- in the nature of the Y (4260), X(3872) and Zc(3900). ergy pp¯ interactions [134]. In addition, the D0 experiment Various interpretations for the X(3872) have been pro- showed that the many of the characteristics of X(3872) posed. The only viable candidate for a charmonium as- production in these high energy pp¯ collisions, such as 3 p signment is the 2 P1 state, i.e., the χc1, which is the only the rapidity- and T -dependence of the inclusive pro- charmonium level with the right quantum numbers and duction cross section, are very similar to those for the an expected mass that is anywhere near 3872 MeV. The ψ . The LHCb [99] and CMS [135] experiments report X measured mass is below the range of the theoretically ex- similar√ characteristics for inclusive (3872) production pected values discussed in Ref. [76], where a computation in s = 7 TeV proton-proton collisions. If the X(3872) using a non-relativistic potential model (NR) gives 3925 is a large and fragile molecule with a miniscule binding MeV while that based on a relativized potential model energy, why would its production characteristics in high (GI) [36] gives 3953 MeV. Potential model calculations energy pp and pp¯ collisions match those of the nearly of masses of charmonium states that are above the open- point-like and tightly bound ψ cc¯ state? This issue is charm thresholds at 2mD and mD + mD∗ do not explic- discussed in detail in Ref. [136], where the authors use itly take into account effects of virtual, but on-mass-shell the powerful software tools that successfully model par- DD¯ and DD¯ ∗ states and, so, it is not too surprising that ticle production in high energy hadron colliders to show both models miss the mass of the well measured multi- that the prompt production cross section for a loosely D0D¯ ∗0 plet partner χc2 by a substantial amount: NR gives 3972 bound molecule should be about two-orders-of- MeV and GI gives 3979 MeV, while the PDG average of magnitude smaller than the production rates measured measured values is ∼ 50 MeV lower at 3927.2±2.7MeV. by CDF. In the absence of any computation that incorporates the Both Belle [138] and BaBar [137] reported similar X γJ/ψ measured χc2 as input, I estimate a range of expected strengths for (3872) decay to final states; the av- χ m erage of their measured branching fractions correspond c1 mass values pegged to the χc2 measurement to be X → γJ/ψ 3880 MeV M(χc1) 3901 MeV by subtracting the NR to a (3872) partial width that is less than X → π+π−J/ψ . ± . and GI calculated δm2−1 = m(χc2) − m(χc1) splittings, that for (3872) by a factor of 0 24 0 05. namely δm2−1(NR) = 47 MeV and δm2−1(GI) = 26 This is in good agreement with a calculation based on a MeV, from the χc2 measurement. The X(3872) mass is molecular picture by Aceti, Molina and Oset [139], where 0 ∗0 below this range, but not by much. The biggest problem they find this ratio to be 0.18. In addition to D D¯ , D+D∗− D+D∗− with the χc1 charmonium assignment for the X(3872) is this calculation includes and s s compo- the strength of the ρJ/ψ discovery decay channel, which, nents in the X(3872) wave function. Interestingly, the + − for charmonium, is isospin- and OZI-violating and ex- authors find that the Γ (γJ/ψ)/Γ (π π ψ) partial width pected to be strongly suppressed. ratio is very sensitive to these extra terms: if only the 0 ¯ ∗0 The close match between the X(3872) mass and mD0 + D D term is considered, the ratio becomes very much 4 −4 mD∗0 – they are equal to within 1 part in 10 – suggests smaller, of order ∼ 10 . Since many calculations based + ∗− that there is some close relation between the X(3872) on a molecule picture ignore the D D and (especially) 0 ∗0 + ∗− and the D D¯ system. In 1994, Törnqvist proposed the the Ds Ds terms, their reliability may be questionable. existence of deuteron-like DD¯ ∗ isoscalar states bound Swanson pointed out that the relative partial widths by pion exchange with J PC =0−+ and 1++ and mass for the X(3872) → γψ and X(3872) → γJ/ψ decay near 3870 MeV that he called “deusons” [116]. In Au- channels would be a powerful diagnostic for the X(3872) gust 2003, shortly after the X(3872) discovery was an- [140]. For a pure χc1 charmonium state, he estimates nounced by Belle at the Fermilab Lepton-Photon 2003 that this ratio would be in the range 0.7–6.8, while ∗ meeting, he identified it with the 1++ DD¯ ∗ deuson pre- for pure DD¯ molecular state the expectations are dis- −3 dicted in his 1994 paper. Because of its proximity to tinctly smaller, at ∼ 3 × 10 . Until recently, the situ- the D0D¯ ∗0 threshold, the deuson wave function is pre- ation with X(3872) → γψ was not very clear. BaBar dominantly D0D¯ ∗0, and not a very pure isospin eigen- reported 3.5σ evidence for this mode at a rate that is state as discussed above [114], and this can account for 3.4 ± 1.4timesthatforγJ/ψ [137]; Belle reported no the strong isospin violation. There has been a consid- signal and a 90% CL upper limit on this ratio of 2.1 erable number of subsequent reports that describe the [138]. This year LHCb study of this mode measured a

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-21 REVIEW ARTICLE

4.4σ signal for X(3872) → γψ, and a ratio relative to an cays. The proponents of this model have not made any X(38972) → γJ/ψ signal in the same data of 2.5 ± 0.7 X(3872)-specific predictions. [141], much higher than expectations for a pure DD¯ ∗ The defects in all of the above-mentioned pictures molecular state. for the X(3872) have inspired models that incorpo- Maiani and collaborators advocate a QCD-type rate combinations of the different ideas. For example, tetraquark structure (i.e., a cq diquark and ac ¯q¯ dian- a charmonium-molecular hybrid10) model by Takizawa tiquark, where q = d or u)fortheX(3872) [142]. In and Takeuchi finds a specific X(3872) wave function their first paper on the subject, they predicted that the [148]: X(3872) would be one of two neutral states that dif- |X(3872) =0.237|cc¯−0.944|D0D¯ ∗0 fer in mass by 8 ± 3 MeV, a value that is related to + ∗− the u-andd-quark mass difference; one of the states −0.228|D D , (2) B+ → K+X was predicted to be produced in 1(3872) ¯ ∗ 0 0 which translates into about 6% cc¯, 69% of isoscalar DD and the other in B → K X2(3872) decays. They also and 26% isovector DD¯ ∗. Hadronic production is hypoth- predicted the existence of charged partner states, X±, esized to proceed via the cc¯ core component and this nearby in mass. BaBar [106] and Belle [102] studied these could explain why X(3872) production properties are possibilities and found no evidence for different X(3872) similar to those of the ψ . This calculation uses a high χc1 mass differences in B+ and B0 decays and put limits on input mass, namely 3950 MeV, which may result in an B(B → KX±) ×B(X± → π±π0J/ψ that are well below underestimate of the cc¯ component, but does not negate isospin-based predictions. However, the recent discovery ±,0 the basic idea. Note that similar numerical results are of the Zc(3900) triplet has supplied the “missing” par- found in Ref. [113]. ticles, albeit with different G-parity and at somewhat There are two related states that are orthogonal to the higher masses. This revived interest in QCD-tetraquark one given in Eq. (2). Reference [148] discusses one that ideas [143]. Among other things, this model has a natu- is mostly cc¯ and probably should be considered to be ral explanation for the Z(4430) [144] and, since QCD- the χc1 charmonium state. This is pushed up in mass to tetraquarks are tightly bound, compact objects, their well above both DD¯ ∗ thresholds and becomes wide and prompt production in high hadron collisons with proper- not easily identifiable. Presumably the other state would ties can be expected to be similar to that for the ψ .On ∗ be dominantly isovector DD¯ , and this might be the the other hand, Ref. [143] proposed a second Zc state at 0 ±,0 Zc(3900) , the neutral Iz =0memberoftheZc(3900) about 100 MeV below the Zc(3900) mass and contrasted isospin triplet. If so, the residual cc¯ core and isoscalar this prediction with a molecule expectation for a second ¯ ∗ + ∗ ∗ DD components may result in a measureable isospin Zc existence of another π J/ψ near the D D¯ thresh- 0 0 ∗0 violating differences between Zc(3900) → D D¯ and old. The subsequent observation by BESIII [51] of the 0 + ∗− Zc(3900) → D D decays. higher mass Zc(4020) near the 2mD∗ threshold clearly The X(3872) has a long interesting story that we can- favors the molecule scheme. not do justice to in this brief report and, instead, refer QCD-hybrid mesons are color-octet quark-antiquark the readers to a recent review [149]. combinations with an excited gluon degree of freedom [145]. While there is considerable literature that identi- 3.2.2 Bottomoniumlike mesons fies the Y (4260) as a charmonium hybrid, i.e., a cc¯-gluon structure [46, 47], there have been no suggestions that Figure 19 indicates the recent status of the b¯b bottomo- X this idea may apply to the (3872) as well. This may be nium and bottomoniumlike mesons. Here the beige boxes partly due to the fact that LQCD calculations find the ++ indicate the well established bottomonium mesons, the lowest 1 charmonium hybrid mass to be near 4400 green boxes show those that were recently established, X MeV and far above that of the (3872) [146]. and the red and purple boxes indicate anomalous states QQ¯ Hadrocharmonium is a model in which a pair that are discussed below. forms a tightly bound system embedded in a light The large Y (4260) → π+π−J/ψ signal discovered in mesonic cloud that it interacts with via QCD analogs the charmonium mass region by BaBar motivated a Belle QQ¯ of Van der Waals forces [130, 147]. The core states search for similar behavior in the bottomonium system have wave functions that are closely related to conven- π+π− nS [150]. This uncovered anomalously large Υ(√ ) tional Quarkonium states. This would explain, for ex- (n =1, 2, 3) production rates that peak around s = Z → πψ πJ/ψ ample, the dominance of (4430) over de- 10.89 GeV as shown in the upper panel of Fig. 20(a)

10) This “hybrid” is not the same as the previously discussed QCD hybrid.

101401-22 Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) REVIEW ARTICLE

[151]. This peak energy is about 2σ higher than that tigate the source of this anomaly. By the end of Belle e+e− → hadron −1 of√ the peak in the cross section at operations, a 121.4 fb data sample√ had been accumu- s 10.87 GeV that is usually associated with the con- lated near the peak of the Υ(5S)( s =10.87 GeV) and ventional Υ(5S) bottomonium meson (and shown in the data taken in energy scans around the peak accounted for lower panel of Fig. 20(b). If the peak in the π+π−Υ(nS) an additional sample of 12 fb−1. One of the first studies cross section is attributed to Υ(5S) decays, it implies done with this Υ(5S) data sample was an investigation of Υ(5S) → π+π−Υ(nS)(n =1, 2, 3) partial widths that the inclusive missing-mass spectrum recoiling from π+π− are hundreds of times larger than theoretical predic- pairs. tions [152], and the corresponding measured rates for the The upper right panel of Fig. 20 shows the distribu- Υ(4S) [13]. This suggests the presence of a new, non-b¯bb- tion of masses recoiling against all of the π+π− pairs in quark-sector equivalent of the Y (4260) with mass around events collected near the peak of the Υ(5S) resonance 10.89 GeV [153] and referred to in the following as the [154]. The combinatoric background is huge – there are Υ(10890). typically 106 entries in each 1 MeV bin – and the statisti- The large cross sections for e+e− → π+π−Υ(nS) cal errors are tiny (∼ 0.1%). The data were fit piece-wise (n =1, 2, 3) near the Υ(5S) motivated Belle to take a with sixth-order polynomials, and the residuals from the large sample of data at this energy in order to inves- fits are shown in the lower panel of Fig. 20(b), where, in

Fig. 19 The spectrum of bottomonium and bottomoniumlike mesons.

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-23 REVIEW ARTICLE

Fig. 20 (a) Cross sections for e+e− → π+π−Υ(nS)(n =1, 2, 3) (upper)ande+e− → hadrons (lower) in the vicinity of the Υ(5S) resonance (from Ref. [151]). (b) Distribution of masses recoiling against π+π− pairs at cms energies near 10.87 GeV (upper) and residuals from piecewise fits to the data with smooth polynomials (lower) (from Ref. [154]). The hb(1P ) and hb(2P ) peaks, shaded in yellow, are first observations. addition to peaks at the Υ(1S), Υ(2S), Υ(3S) masses A study of π0π0Υ(nS), (n =1, 2, 3) found a 6.5σ signal 0 and some expected reflections, there are unambiguous for the neutral Zb(10610) isospin partner state with a 1 1 h P h P P P M 0 ± signals for the b(1 )and b(2 ), the 1 1 and 2 1 mass Zb(10610) = 10609 6 MeV and a production rate bottomonium states. This was the first observation of that is consistent with isospin-based expectations [157]. these two elusive levels [154]. One puzzle is that the The lower mass state is just 2.6 ± 2.2MeVabovethe + − π π hb(mS), (m =1, 2) final states are produced at mB + mB∗ mass threshold and the higher mass state is + − rates that are nearly the same as those for π π Υ(nS) only 2.0 ± 1.6MeVabove2mB∗ . Dalitz-plot analyses of + − + − P + (n =1, 2, 3), even though the π π hb transition requires the π π Υ(nS) final states establish J =1 quan- a heavy-quark spin flip that should result in a strong sup- tum number assignments for both states [158, 159]. The pression. This motivated a more detailed investigation of close proximity of the BB¯∗ and B∗B¯∗ thresholds and the these channels. J P =1+ quantum number assignment is suggestive of + − Figure 21(a) shows the π π hb yields versus the max- virtual S-wave molecule-like states. ± (∗) ∗ imum hbπ invariant mass for hb = hb(1P ) (upper) and The B B¯ molecule picture is supported by a Belle + − (∗) ∗ hb = hb(2P ) (lower), where it can be seen that all of study of e e → B B¯ π final states in the same data + − ∗ ∗ ∗ the π π hb events are concentrated in two Mmax(hbπ) sample [160], where BB¯ and B B¯ invariant mass peaks peaks near 10 610 MeV and and 10 650 MeV [155]. are seen at the Zb(10610) and Zb(10650) mass values, re- Studies of fully reconstructed π+π−Υ(nS), (n =1, 2, 3) spectively, as shown in the right panels of Fig. 21. From Υ(nS) → + − events in the same data sample found these data, preliminary values of the branching fractions + ∗0 0 ∗+ peaks at the same masses in the Mmax(Υ(nS)π) distri- B(Zb(10610) → B B¯ + B¯ B + c.c.)=(86.0 ± 3.6)% ∗+ ∗0 butions for all three Υ(nS) states; these are shown in and B(Zb(10610) → B B¯ + c.c.)=(73.4 ± 7.0)% the three center panels of Fig. 21. Here the fractions of are inferred. The B(∗)B¯∗ “fall apart” modes are stronger π+π−Υ(nS) events in the two peaks are substantial – than the sum total of the π+Υ(nS)andπ+h(mP )modes, ∼ 6% for the Υ(1S), ∼ 22% for the Υ(2S)and∼ 43% but only by factors of ∼ 6fortheZb(10610) and ∼ 3 + − for the Υ(3S) – but, unlike the case for the π π hb(mP ) for the Zb(10650). The measured branching fraction for + − ∗ ∗ channels, they do not account for all of the π π Υ(nS) Zb(10610) → B B¯ is consistent with zero. This pat- ∗ event yield [156]. Fitted values of the peak masses and tern, where BB¯ decays dominate for the Zb(10610) and ∗ ∗ widths in all five channels are consistent with each other; B B¯ decays are dominant for the Zb(10650) are consis- the weighted average mass and width values are tent with expectations for molecule-like structures.

Z1(10610): M1 = 10607.2 ± 2.0MeV, 3.3 Comments Γ1 =18.4 ± 2.4MeV;

Z2(10650): M2 = 10552.2 ± 1.5MeV, Table 1 provides a tabulation of recently discovered

Γ2 =11.5 ± 2.2MeV.

101401-24 Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) REVIEW ARTICLE

+ + + − + − Fig. 21 (a) Invariant mass distributions for hb(1P )π (upper)andhb(2P )π (lower)frome e → π π hb(nP )events. (b) Invariant mass distributions for Υ(1S)π+ (upper), Υ(2S)π+ (center)andΥ(3S)π+ (lower)ine+e− → π+π−Υ(nS) B∗B¯∗ events. The figures are from Ref. [155], and scaled to make the make the horizontal scales√ (almost) match. (c) The (upper)andBB¯∗ (lower) invariant mass distributions for e+e− → B(∗)B¯∗π events near s =10.86 GeV (from Ref. [160]). mesons (and candidate mesons), together with observed threshold with J P =1+ and a significant coupling to ∗ ∗ production & decay channels, averages of mass and width DD¯ .Thisisconsistentwithavirtual√ S-wave DD¯ measurements and the J PC values when they are known. molecule of the form (DD¯ ∗ − D∗D¯)/ 2. The X(3872) + P + ∗ For simplicity, I assume the Zc(3900) → π J/ψ and also has J =1 and couples to DD¯ with mass right ∗ + 0 ∗0 Zc(3885) → (DD¯ ) are the same state and average the at the D D¯ threshold and seems to be an isospin sin- + ∗ measured mass and width values, the Zc(4020) → π hc glet [102]. This suggests√ an S-wave DD¯ molecule of the ∗ ∗ + ∗ ∗ and Zc(4025) → (D D¯ ) measurements are treated in form (DD¯ + D D¯)/ 2. (Note that although they both the same way. have J P =1+,theX(3872) has even C parity, while the Iz =0memberoftheZc(3900) triplet must have odd C 3.3.1 Molecules? parity.) The Zc(4020)/Zc(4025) observations (assuming they The recent BESIII findings, taken together with previous are the same state) establish the existence of another experimental results, establishes a concentration of char- isospin triplet just above the D∗D¯ ∗ threshold. If this is ∗ ∗ ∗ moniumlike states crowding the DD¯ and D D¯ mass the charmed-sector equivalent of the Zb(10650), it also threshold regions and bottomoniumlike isospin triplets has J P =1+ and could be considered as a virtual D∗D¯ ∗ ∗ ∗ ∗ near the BB¯ and B B¯ thresholds, which are sugges- molecule for which the Iz = 0 component must have odd tive of molecule-like structures [118–129]. C parity. This suggests that there might be an X(3872)- ∗ ∗ If we assume that the Zc(3900) and Zc(3885) are the like, even C parity isospin singlet D D¯ nearby, and la- same state, it corresponds to an isospin triplet with a beled as Xc2 in the lower part of the level diagram shown pole mass that is about ∼15 MeV above the D0D∗− in the left panel of Fig. 22.

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Table 1 New cc¯ and b¯b mesons above open-flavor threshold. The masses M and widths Γ are weighted averages of measurements with uncertainties added in quadrature. For the X(3872), only π+π−J/ψ decays are used in the mass average. Ellipses (...) indicate an inclusive reaction. In the JPC column, question marks indicate my educated guess or no information. For charged states, C is that of the neutral isospin partner. “Υ(5S) is in quotes to reflect the suspicion that the anomalous π+π−Υ(nS) events originate not from the Υ(5S), but from another 1−− meson with a nearby mass, i.e., the Υ(10890). This Table is a modification of one from Ref. [161] via Ref. [29, 30].

State M /MeV Γ /MeV J PC Process (decay mode) Experiment

X(3872) 3871.68±0.17 < 1.21++ B → K +(J/ψ π+π−) Belle [95, 102], BaBar [98], LHCb [103] pp¯ → (J/ψ π+π−)+... CDF [96, 104, 105, 160], D0 [97] B → K +(J/ψ π+π−π0) Belle [107], BaBar [72, 73] B → K +(D0D¯ 0π0) Belle [108, 109], BaBar [110] B → K +(J/ψ γ) BaBar [137], Belle [138], LHCb [141] B → K +(ψ γ) BaBar [137], Belle [138], LHCb [141] pp → (J/ψ π+π−)+... LHCb [99], CMS [100] +10 ++ X(3915) 3917.4 ± 2.728− 9 0 B → K +(J/ψ ω) Belle [71], BaBar [72, 73] e+e− → e+e− +(J/ψ ω) Belle [74], BaBar [75] ++ + − + − χc2(2P ) 3927.2 ± 2.624±62 e e → e e +(DD¯ ) Belle [78], BaBar [79] +9 +27 −(?)+ + − ∗ X(3940) 3942−8 37−17 0(?) e e → J/ψ +(D D¯ ) Belle [32] e+e− → J/ψ +(...) Belle [31] G(3900) 3943 ± 21 52±11 1−− e+e− → γ +(DD¯ ) BaBar [163], Belle [164] +121 −− + − + − Y (4008) 4008− 49 226±97 1 e e → γ +(J/ψ π π ) Belle [39] Y (4140) 4144 ± 317± 9??+ B → K +(J/ψ φ) CDF [87, 88], CMS [90] +29 +113 −(?)+ + − ∗ X(4160) 4156−25 139−65 0(?) e e → J/ψ +(D D¯ ) Belle [32] +8 −− + − + − Y (4260) 4263−9 95±14 1 e e → γ +(J/ψ π π ) BaBar [37, 165], CLEO [166], Belle [39] e+e− → (J/ψ π+π−) CLEO [167] e+e− → (J/ψ π0π0) CLEO [167] Y (4274) 4292 ± 634± 16 ??+ B → K +(J/ψ φ) CDF [88], CMS [90] +4.6 +18.4 ++ + − + − X(4350) 4350.6−5.1 13.3−10.0 0/2 e e → e e (J/ψ φ) Belle [94] Y (4360) 4361 ± 13 74±18 1−− e+e− → γ +(ψ π+π−) BaBar [38], Belle [40] +9 +41 −− + − + − X(4630) 4634−11 92−32 1 e e → γ (Λc Λc ) Belle [168] Y (4660) 4664±12 48±15 1−− e+e− → γ +(ψ π+π−) Belle [40] + +− − + Zc (3900) 3890 ± 333± 10 1 Y (4260) → π +(J/ψ π ) BESIII [49], Belle [50] Y (4260) → π− +(DD¯ ∗)+ BESIII [69] + +(?)− − + Zc (4020) 4024 ± 210± 31(?) Y (4260) → π +(hc π ) BESIII [51] Y (4260) → π− +(D∗D¯ ∗)+ BESIII [52] + +24 +51 ?+ + Z1 (4050) 4051−43 82−55 ? B → K +(χc1 π ) Belle [53], BaBar [66] + +35 +99 +− + Z (4200) 4196−32 370−149 1 B → K +(J/ψ π ) Belle [62] + +185 +321 ?+ + Z2 (4250) 4248− 45 177− 72 ? B → K +(χc1 π ) Belle [53], BaBar [66] Z+(4430) 4477 ± 20 181 ± 31 1+− B → K +(ψ π+) Belle [54, 56, 57], LHCb [58] B → K +(Jψπ+) Belle [62] +8.9 −− + − + − Yb(10890) 10888.4±3.0 30.7−7.7 1 e e → (Υ(nS) π π ) Belle [152] + +− − + Zb (10610) 10607.2±2.0 18.4±2.4 1 “Υ(5S) → π +(Υ(nS) π ), n =1, 2, 3 Belle [155, 158, 159] − + “Υ(5S) → π +(hb(nP ) π ), n =1, 2 Belle [155] “Υ(5S) → π− +(BB¯∗)+, n =1, 2 Belle [160] 0 +− 0 0 Zb (10610) 10609± 61“Υ(5S) → π +(Υ(nS) π ), n =1, 2, 3 Belle [157] + +− − + Zb (10650) 10652.2±1.5 11.5±2.2 1 “Υ(5S) → π +(Υ(nS) π ), n =1, 2, 3 Belle [155] − + “Υ(5S) → π +(hb(nP ) π ), n =1, 2 Belle [155] “Υ(5S) → π− +(B∗B¯∗)+, n =1, 2 Belle [160]

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Fig. 22 (a) Level diagram for the X(3872), the recently discovered Zc(3900) & Zc(4020) isotopic triplets, and the Z(4430) isospin triplet. The salmon-colored boxes indicate other states that are suggested by the molecule picture. (b) Level diagram for the recently discovered Zb states, a conjectured b-sector equivalent of the X(3872) at the mB + mB∗ threshold and an additional isoscalar partner of the Zb(10650) at the 2mB∗ theshold. The transition between a mB + mB∗ threshold state to the Υ(1S)wouldhaveaQ-value of 1145 MeV, well above the mass of the ρ and ω mesons.

∗ ∗ P If the Xc2 exists with a mass that is below the D D¯ old. We do not know their J – we do not even know threshold and a relatively narrow width, it might have a if the two states have the same J P values – but if the + P − significant branching fraction to ωJ/ψ final states. If its π -χc1 system is in an S-wave, J =1 .Wedoknow mass is above 2mD∗ and it is relatively narrow, it might that their neutral I3 = 0 partner, which has not yet be accessible in B− → K−D∗D¯ ∗ decays. BaBar has re- been seen, has to have even C parity. If we assume − − 0∗ ∗0 P − ported large branching fractions for B → K D D¯ J =1 ,aDD¯ 1(2420) would give the right quantum − ∗+ ∗− (1.1±0.1%) and K D D (0.13±0.02%) but did not numbers and a nearby mass threshold for the Z2(4250), P + ∗ publish any invariant mass distributions [169]. where the D1 is a J =1 , D π resonance with mass The Zc mesons have a minimal four-quark structure M = 2421.3 ± 0.6MeVandwidthΓ =27.1 ± 2.7MeV. of ccq¯ iq¯j (i =1, 2, j =1, 2&q1 = u, q2 = d). The One could imagine a situation where the Y (4260) is the locations of the Zc(3900) and the Zc(4020) near the C odd isosinglet and the Z√2(4250) is the C even isotriplet ∗ ∗ ∗ DD¯ and D D¯ thresholds and the similarity of the DD¯ 1 molecular states 1/ 2(DD¯1 ± D1D¯). However, the M − M . ± . Y DD¯ Zc(4020) Zc(3900) = 133 9 4 0 MeV mass split- scenario where the (4260) is a 1 molecule [48] was ting with the mD∗ − mD141 MeV mass difference examined by BESIII as part of their study of Y (4260) → (∗) ∗ indicates that configurations where cq¯j form a D and πDD¯ [69]. Since the Y (4260) mass is ∼ 30 MeV below ∗ ¯ cq¯ j form a D are important, as is the case for molec- mD +mD1 4290 MeV, a prominant DD1 component of ular pictures. The BaBar group has recently identified its wave function should show up as a distinct clustering ∗ ∗ the nr = 2 excitations of the D and D with masses of πD¯ invariant masses near their upper kinematic limit. MD(2S) = 2540 ± 8MeVandMD∗(2S) = 2609 ± 4MeV BESIII reports no evidence for such clustering and, thus, ∗ [1708]. An S-wave DD¯ (2S) combination would have no indication of a DD¯ 1 component of the Y (4260). On have J P =1+ and a “threshold” mass around 4480 MeV, the other hand, there are no interesting nearby D(∗)D¯ (∗) P − very close to the Belle-LHCb average MZ(4430) = 4477± mass thresholds for the Z1(4020), especially for J =1 . 19 MeV. In the b-quark-sector, the Zb states are isospin triplets + + P + ∗ ∗ ∗ The charged Z1(4050) and Z2(4250) states that de- with J =1 near the BB and B B¯ threshold and + ∗ ∗ ∗ cay to π χc1 are less easy to associate with a thresh- suggestive of virtual S-wave BB¯ and B B¯ molecules.

Stephen Lars Olsen, Front. Phys. 10, 101401 (2015) 101401-27 REVIEW ARTICLE

Here we might expect C-even equivalents of the X(3872) would be 4 MeV, and small compared to that for π+J/ψ, and Xc2 (labeled as Xb1 and Xb2 in the right panel of Fig. which they estimated to be 29 MeV. Subsequently the 22), but finding them may be difficult with existing data. DD¯ ∗ decays have been seen, with a decay with that is The CMS group searched for a b-quark version of the 6.2 ± 2.9 times larger than that for π+J/ψ [69], not six X π+π− S 11) (3872) in the inclusive Υ(1 ) invariant mass√ dis- times smaller . tribution produced in proton-proton collisions at s =8 One attractive feature of the tetraquark feature is TeV, but found no evidence for peaks other than those that it can explain the large partial width for transi- due to Υ(2S)andΥ(3S)toπ+π−Υ(1S) transitions [171]. tions such as Y (4260) → π+π−J/ψ, X(3915) → ωJ/ψ, However, if, as expected, the b-quark-sector equivalent of Z(4430) → π+ψ, etc., in a natural way. The corre- the X(3872) has J PC =1++, zero isospin, and is near sponding transitions in the charmonium system are OZI- the BB¯∗ mass threshold, the π+π−Υ(1S) decay mode, suppressed, and the partial widths are relatively small for which the π+π− would have to originate from ρ → 100 keV. In molecular models, although OZI- π+π−, would violate isospin and be suppressed relative suppression can be evaded, the Q and Q¯ reside in dif- to decays to the isospin-conserving ωΥ(1S) final state. ferent constituent mesons with small spatial overlap. In This is not the case for the X(3872) where the isospin- addition they have uncorrelated colors and spins. In allowed ωJ/ψ decay mode is kinematically suppressed: contrast, tetraquarks are compact. The the Q and Q¯ i.e., Qc mD0 +mD∗0 −mJ/ψ = 776 MeV, which is about necessarily have a large overlap and tightly correlated one ω natural width below its peak mass mω = 783 MeV. color and spin and the presence of the additional light In the b-quark-sector, mB + mB∗ − mΥ(1S) = 1145 MeV, quarks eliminates OZI suppression. A tetraquark inter- which is well above mω.Thus,ωΥ(1S) final states are pretation of the charged bottomoniumlike Zb(10610) and + − probably more relevant than π π Υ(1S) for searches for Zb(10650) states is advocated by Ali and collaborators X(3872) counterparts of the Zb(10610) and Zb(10650). [172, 173]. This would require studies of decay final states that contain a π0, which may be difficult to do with existing LHC 3.3.3 QCD-hybrids? experiments, but could be done at BelleII [85]. Since QQ¯-gluon hybrid mesons cannot account for any of 3.3.2 Tetraquarks? the charged Z states, their role in explaining the XYZ meson puzzles described here has to be limited. As men- Maiani and collaborators note that the MZ(4430) − tioned above, there has been a number of papers that M ± −− Y Zc(3900) = 589 30 MeV mass difference is the same identify the 1 states as charmonium hybrids. In −− as mψ − mJ/ψ = 589 MeV, with not such a large er- 1 hybrids, the Q and Q¯ are in a relative P -wave, which + ror. This, together with the preference for the Z(4430) suppresses their Γe+e− partial widths. The experimental + + to decay to π ψ rather than π J/ψ, suggests that in 90% CL upper limit Γe+e− (Y (4260)) < 580 eV [45] is 3 the Z(4430), configurations where the c andc ¯ form a smaller than corresponding width for the nearby 3 S1 ψ are important. This is in line with QCD tetraquark state: Γe+e− (ψ(4040)) = 860 ± 7 eV and about the same 3 expectations as discussed in Ref. [144]. as that for the 4 S1 state: Γe+e− (ψ(4415)) = 580 ± 70 In Ref. [143], which appeared shortly after the eV [13]. For similar reasons, decays to S-wave plus P - Zc(3900) discovery was announced, Maiani and collabo- wave open charmed mesons are supposed to be domi- rators proposed a test between the tetraquark and molec- nant. As mentioned above in the discussion related to ∗ ∗ ular model: their model predicted a second charged the study of Zc(3885) → DD¯ in Y (4260) → πDD¯ Zc state with a mass that is about 100 MeV lower, decays, there is no strong evidence for subthreshold while the molecular picture predicted a second state at Y (4260) → DD¯ 1(2420) decays in these final states [69]. higher mass, close to the 2mD∗ threshold. The BESIII Thus, although there is a lot of theoretical enthusi- group’s subsequent discovery of the Z(4020) confirmed asm for identifying the 1−− Y states as cc¯-gluon hy- the molecular picture. However, the Ref. [143] prediction brids, there is not much experimental evidence to sup- of a lower mass partner state was based on a particu- port this assignment. Perhaps theoretical analyses of the lar model for diquark-diantiquark spin-spin interactions. recent BESIII observations of strong decay widths for + − + − Perhaps modifications that incorporate measured prop- Y (4260) → π Zc(3900) & π Zc(4020) [49, 52] and erties of the Zc(4020) can fix this. The same paper also the radiative transition Y (4260) → γX(3872) [115] will ∗ + predicted that the DD¯ decay width of the Zc(3900) clarify the situation.

11) Here I assume that the Zc(3885) and Zc(3900) are the same state.

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3.3.4 Hadrocharmonium? this approach, Friedmann is able to categorize all of the established hadrons as designated by the PDG at the Voloshin points out that the 23 MeV mass difference time of her publication, including many of the “exotic” + between the Zc(3900) (measured in the π J/ψ channel) ones listed above, in an elegant concise way. A striking + ¯ ∗0 ∗+ ¯ 0 and the D D (or D D ) threshold is not that small feature of this scheme is that all of the states can be in- (∗) [147]. The momenta of the “constituent” D mesons in corporated in her scheme without invoking any radial ex- 12) the Zc restframe would be substantial, ∼ 200 MeV/c . citations. In conventional models, radial excitations are P + Since J =1 , the mesons would be in an S-wave with essential features but, with them, the model runs into no centrifugal barrier to hold them together, in which lots of problems, especially with the categorization of the 13) case, the total width 29 ± 10 MeV seems too small. baryon spectrum. For example, the J P =1/2+, N(1440) ¯ ∗ Also, in a DD bound state, the spins of the c and the “Roper” resonance, which defies any compelling classi- c¯ quarks would be uncorrelated and, thus, the cc¯ system fication in the quark model, is naturally accommodated S S should consist of equal amounts of =0and =1. in Freidmann’s scheme as a (qq)A(qq)Aq¯ state, where the Z → πJ/ψ This suggests that the decays c(3900) and two asymmetric, spin-zero diquarks ((qq)A)areinarel- πhc should occur at a similar rate, contrary to the ob- ative P -wave. The ψ, which is the quintessential radi- servation reported in Ref. [51]. As discussed above, BE- ally excited meson in the quark model, is identified as a Z → πh SIII measurements show that the c(3900) c rate (qq)A(¯qq¯)A pair in a P -wave. Of course this is just a clasi- is suppressed relative to that for the πJ/ψ mode by at fication scheme and it remains to be seen if a tetraquark least a factor of five. While the hadrocharmonium model picture of the ψ can reproduce the success of the charmo- fixes the above problems, it, like the tetraquark model, nium model description of the ψ properties such as, for predicts a lower mass partner state while BESIII found example, the ratio of Γe+e− (ψ )/Γe+e− (J/ψ). Neverthe- the Zc(4020) at higher mass. Also, the hadrocharmonium less, no one could accuse Friedmann of being a “prisoner ¯ ∗ 14) prediction for the DD decay width is similar to the 4 of conventional thinking.” MeV value predicted by the tetraquark model, and is in strong contradiction with experimental observatiions. 4 Summary 3.3.5 A unified model? The QCD exotic states that are much preferred by the- None of the models discussed above gives a compelling orists, such as pentaquarks, the H-dibaryon, and meson picture of all the observed data. Thus, in our current hybrids with exotic J PC values continue to elude confir- situation, we are forced to a attribute some of the ob- mation even in experiments with increasingly high levels served states to one picture and others to a different sce- of sensitivity. On the other hand, a candidate pp¯ bound nario. In some cases, like the X(3872), mixtures of dif- state and a rich spectroscopy of quarkoniumlike states ferent models have been invoked. In all cases, these pic- that do not fit into the remaining unassigned levels for cc¯ tures accept the standard potential-model based quark charmonium and b¯b bottomonium states has emerged. No model ideas and apply molecule or tetraquark, etc., ideas compelling theoretical picture has yet been found that to those states where the conventional approach fails. provides a comprehensive description of what is seen, Thus, molecular models work for near-threshold “exotic” but, since at least some of these states are near D(∗)D¯ ∗ (∗) ∗ states, tetraquarks for scalar mesons, cc¯-gluon hybrids or B B¯ thresholds and couple to S-wave combinations for the 1−− Y states, etc. Since all these approaches have of these states, molecule-like configurations necessarily problems, the situation is not very satisfying. have to be important components of their wave functions An exception to these piecemeal approaches is an [112]. This has inspired a new field of “flavor chemistry” ambitious project by Friedmann that eschews potential that is attracting considerable attention both by the ex- model and non-relativistic quantum mechanics ideas al- perimental and theoretical hadron physics communities together and, instead, attempts to build the spectrum of [29, 30]. With the increased emphasis of the BESIII and hadrons directly from QCD principles alone, using quark LHC experiments on this subject and the imminent op- and diquark constituents on an equal footing [174]. With eration of BelleII [85], the high luminosity reincarnation

12) Z M ± Z With my average of all c(3900) mass measurements, ZC (3900) = 3890 3 MeV, and the diﬀerence between the c(3900) mass ∗ (∗) and the D¯ mass threshold is lower, at 14 MeV, and the constituent D momentum in the Zc restframe decreases to 170 MeV. 13) This is my average of the measurements reported in Refs. [49] and [69]. 14) http://scitation.aip.org/content/aip/magazine/physicstoday/news/10.1063/PT.5.3012

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of Belle, and the future operation of the PANDA exper- 12. B. H. Kim, et al. (Belle Collaboration), Search for an H- iment at FAIR [175], we can expect a continuous flow dibaryon with a mass near 2mΛ in Υ(1S) and Υ(2S) decays, of interesting experimental results including, probably, Phys. Rev. Lett. 110, 222002 (2013) many new surprises and, hopefully, new, groundbreaking 13. J. Beringer, et al. (Particle Data Group), Review of particle insights into the long-distance behavior of QCD. physics, Phys. Rev. D 86(1), 010001 (2012) 14. Reported by T. E. Barnes, HADRON05 summary: Heavy Acknowledgements While preparing this report I benefited quark hadrons and theory, arXiv: hep-ph/0510365 (2005) from communications from Eric Braaten, Sookyung Choi, Tamar 15. R. L. Jaffe, Exotica, arXiv: hep-ph/0409065v2 (2004) Friedmann, Pyungwon Ko, Tomasz Skwarnicki, Sachiko Takeuchi, Kai Yi, Qiang Zhao and colleagues on the Belle & BESIII exper- 16. J. Z. Bai, et al. 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