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PoS( 2013)001 http://pos.sissa.it/ ∗ [email protected] Speaker. An overview of recent developments in hadronquark spectroscopy dynamics is and given with heavy an hadron emphasisintroduced as spectroscopy. on important heavy dynamical Heavy contents for heavy quark spinof . symmetry multiquark We also hadrons and discuss with possibilities heavy . are ∗ Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. c

XV International Conference on Hadron Spectroscopy-Hadron4-8 2013 November 2013 Nara, Japan Makoto Oka Department of Physics, H-27, Tokyo InstituteE-mail: of Technology, Meguro, Tokyo, 152-8551, Japan New Aspect of Hadron Spectroscopy PoS(Hadron 2013)001 . ]. ¯ Q 3 QCD Q Λ , which ], about ) 1 states[ ¯ c Makoto Oka c 1405 , they contain ( Λ i.e. bound states, but ¯ Q Q and the ∗− D + ,D 0 ∗ ¯ D 0 ]. Another example of tetra-quarks or and so on. 4 0 2 a , , the color-gauge couplings are common to all the 0 f i.e. component[ components as ingredients, while the meson is com- ¯ ¯ q KN q or qq ]. Those states cannot be explained as (quark-model) 2 ]. 5 , is likely to be a superposition of the D ∗ In this article, I would like to discuss some topics on heavy quark hadrons. In sect. 2, we dis- The QCD lagrangian is flavor blind, At first glance, tetra-quarks and meson molecules are different and independent. The former Many of these new types of hadrons appear in the heavy hadron spectrum, Such new types of hadrons may not be, in fact, new. In the light meson and spectra, Hadron spectroscopy has entered a new era. According to the Data Group[ The most exciting discovery was exotic “” states, X, Y and Z’s, found at Belle, D + cuss distinct dynamical contents of heavy quarkhadron systems, comparing spectroscopy. strangeness Emphases and charm/bottom are onexotic diquark hadron structure with of charm baryon quarks.years. excited In states sect. and Lattice tetra-quark QCD 3,physical we calculations quark review have masses. some been theoretical Excited highly developments statespresented. in sophisticated are In recent also sect. and studied. 4, can conclusions New access are analyses presented. hadrons of at QCD sum the rules are also heavy quarks. It is interesting toby see the dynamics of heavy heavy quark quarks symmetry. haschiral some symmetry It new and features, is its represented in spontaneous contrast breaking.valid to in In the light the large quarks, spectroscopy, quark heavy whose mass quark dynamics limit, spin so is symmetry that is dominated spin by of the heavy quark is conserved. 2. Dynamics of Heavy Quarks flavors. It is, however, known that the scale dependence arises from the trace anomaly and molecules is seen in the light scalar mesons, contains color-non-singlet posed only of color-singlet clusters.not. It Meson is, molecules however, may notFurthermore, look clear QCD just whether does like not they tetra-quarks have are a whenIn distinguishable conserved order two or charge to clusters to dissolve are them distinguish close we theselations need to two inside to kinds each such clarify of other. the multi-quark “hadrons”. dynamics environments.hadrons of and Recently, quarks resonances some and were multi-quark studies made (color) to based corre- operators[ define on compositeness the (wave-function) of renormalization factor of hadron require new dynamical contents, such as tetra-quarks, hadronic molecules and their mixings to we have a few candidates ofis hadronic likely resonances or to multi-quarks. be One dominated of them by is the New Aspect of Hadron Spectroscopy 1. Introduction As an example, recent analysesD show that the X(3872) resonance, sitting just at the threshold of BaBar and BES-III[ 300 mesons and 300(QCD) is are the first known principle in ofQCD, the hadron structures lattice zoo and QCD of interactions. simulations, The hadrons. are first-principle(resonance) well calculations states The in successful are quantum in not explaining chromodynamics well the reproduced.hadrons, ground which Recently, do states, we not have while fit encountered excited in several “new the types” conventional scheme of of the hadron classification. PoS(Hadron 2013)001 6 Σ 3. ( → / ∗ Q 1 with have (2.1) , and Σ i ∗ Q ∼ ¯ ss Σ h qqq ) and the and 8 Makoto Oka Q and and 142 MeV and Σ Q , the soft QCD . This is called ¯ i q ) Σ Q q ¯ Q ) = dd m h is the heavy quark m D , / . i Q 1 − Q ) ( m ¯ a ∗ Σ uu O h A D quarks in ( × m ] = ud ∆ ∇ ∇ ∇ ( belong to the octet ( , where · QCD → ∗ Q Q H Σ m , of the heavy quark, which is a con- a / 2 Q v λ σ σ σ Q and [ σ σ σ Σ † Q 397 MeV ), the splitting is reduced by a factor b Q 1 m come from the interaction between the heavy- ) = → , which leads us to the constituent quark picture K Q − c 3 a 0 Σ − ) becomes independent from → QCD ∗ ). Spectrum of light hadrons has exhibited important ¯ 3 s t QA ( Λ K and , a ( Q 2 b λ ∗ Q m , Λ † Σ c ∆ Q ∼ expansion of the QCD Hamiltonian leads to the conservation of and depends on the velocity µ a 2 is conserved in the limit, Q Q / ) meson are degenerate in the limit. This is indeed the tendency for m m QA σ σ σ / − a 2 λ µ γ ¯ Q ]. This symmetry gives simple relations among the transition amplitudes of heavy 6 46 MeV. At each flavor step ( ), and the heavy flavors ( s ), respectively. Now in the heavy baryon spectrum, the HQSS combines , ) = d 10 B , . Thus in the heavy quark limit, the spin of the heavy quark disappears from the interaction. u − Q ∗ , 65 MeV for charm, and 21 MeV for bottom. Again the ratios are about 1/3 for each step. m On the other hand, the heavy quarks are subjected to heavy-quark symmetry. In particular, the A similar degeneracy is seen in the baryon spectrum (Fig.1). The The heavy-quark interaction can be expanded by 1 This symmetry is important in the heavy hadron spectroscopy. For instance, the pseudoscalar In the heavy quark picture, the classification of the baryons are different from the familiar The quark flavors can be divided into two categories, depending on their masses: the light B / Λ ) meson and the vector (1 ( − m heavy quark spin symmetry plays adynamics key role behind to the classify heavy quark and describe symmetry the is heavy that hadron for spectra. a large The heavy quark mass the constituent (valence) quarks, wheremasses. the hadron masses are roughly given by the sum of quark dynamics is independent from stant of motion[ the total spin 1. Then the splittings of of hadrons. The ground state mesons and baryons can be explained fairly well as The first term is the color-electricthe Coulomb quark spin coupling to and the the color-magnetic secondby field. 1 term One denotes sees the that coupling the spin-dependent of Namely, coupling the is heavy quark suppressed spin (0 SU(3) scheme used in the light hadron sector. In SU(3), the light pseudo-scalar mesons playinduces roles effective of quark the masses (pseudo-) of Nambu-Goldstone order . of The SCSB 2.1 Heavy Quark Spin Symmetry (HQSS) the heavy quark spin symmetry (HQSS). the charm and bottom meson masses, quark spin and the light-quarkand spin. The observed mass splittings are 194 MeV for the strange in SU(3)) into the same “multiplet” and quark decays. Furthermore, 1 the heavy quark spin, as is shown in the next subsection. flavors ( New Aspect of Hadron Spectroscopy sets the typical momentum of theat quark-gluon the correlations. low As energy the region, the effective gauge interaction coupling is grows weaker for heavier quarks. mass, giving ∆ decuplet ( roles of chiral symmetry and its spontaneousus breaking that (SCSB) the in low-energy QCD QCD. vacuum The has SCSB non-zero tells quark condensates of light flavors, PoS(Hadron 2013)001 - P , of (2.2) (2.3) ρ and Makoto Oka λ excited states λ ) diquark, called 6 modes are degenerate, and ρ 3 2 -mode is the excitation from 1 r r r ) pair of light quarks. This is λ √ 2 2 ¯ 3 and m m λ + + ∞ 1 1 → . The r r r m Q 1 Q −→ m m m limit, they split so that the − = q Q Q 3 . In the SU(6) scheme of the for m r r m r ) channel. − m 2 Q − 2 = m / + 4 3 λ λ λ Q form a spin 1, isospin 1 (or flavor √ m ∗ Q and 5 Σ √ , − attraction is weaker in this channel compared to the scalar 2 2 = r r r and / q ρ λ − Q (the SU(3) limit), then the − interaction via a gluon exchange or the instanton-light-quark , 3 ω ω 1 Σ 2 q − r r r q 2 m = / − = ρ λ = ]. q ρ ρ ρ E E 7 1 in the pseudoscalar (0 m ¯ q forms a spin 0 and isospin 0 (or flavor Heavy baryon spectrum for strange, charm and bottom sectors. = − Q q excited states. The ratio of the excitation energies can be roughly estimated q Λ m ρ ) diquark. The + heavy baryons, the light quarks form a diquark state. It is straightforward to see q -mode. Figure 1: ) diquark. The ρ quarks, they are identified as 70-dimensional representation. − + s q quarks in is equal to 1 of the heavy quark relative to the light diquark, while the internal diquark state is − modes. They correspond to excitations of the individual Jacobi coordinates, Q ud and Q m → ρ d , 0 If Extending these observations to excited states of baryons is very interesting. Consider the The structure of these baryons can be viewed based on the diquark picture in the quark model. In contrast, the light quarks in When one of the quarks is heavy, then they can be classified into two distinct excitation modes: u and = L excited in the mix with each other. On the other hand, in the large that the Here we assign the heavy quark to the particle 3, λ For the the scalar (0 coupling gives strong attraction in thisis channel. a According half to of that the for color the Casimir factor, its strength wave baryons with spin-parity 1 come lower than the 2.2 Diquarks the New Aspect of Hadron Spectroscopy the axial-vector (1 diquark. Some quenchedapproaches lattice give calculations consistent are results availableranging on for about the 100-200 the MeV[ mass diquark splitting spectrum. of the Different scalar and axial vector diquarks, the three-quark system, defined (non-relativistically) by from the harmonic oscillator model of confinement, PoS(Hadron 2013)001 ∗ cc 0) T = in ) ]. We J ]. This ¯ 3 , ( 11 6 10 cc T = Makoto Oka C ( 0). The lowest separately from cc 0) state[ ) = 6 I ]. ( = , 9 I cc 0 T , = + = ), whose strong decay is 1 ]. can be distinguished from J , − ∗ cc ∗ 12 ¯ = 3 2 cc baryons. T / T π 1 = J modes may mix at intermediate , representation, Qqq ¯ C = λ d and ( 6 ¯ u ¯ π d cc J cc u ( T and ( ¯ final states. s ρ cc K T uudc ) + . Exotic hadrons are the ones with quantum Σ ( reactions using the NRQCD approach[ Λ 5 qqq − e threshold. The predicted mass is 2420 MeV and the + e K and ], it is shown that the mixing is reduced rapidly when . If the scalar diquark is light enough to make a bound mode excitations for the 8 . Possible low-lying exotic (multi-quark) hadrons can be ) ¯ + q in λ − c q 1 cc Λ . These two kinds of excitation modes can be generalized to qqq limit. In reality, the ( T b ∗ and Q will be a stable tetra-quark resonance. Recently, we have es- or m D 1) and the scalar diquark ¯ , ρ m . It is pointed out that the ¯ q c cc q T = m ) + qqq The J − , 0 → consists of diquarks with the color ¯ 3 ( or s 0). It is extremely interesting to identify ) ¯ D q m = 6 q ( = C cc I → ( , threshold, T q 3 in the large Figure 2: 1 , because such an “exotic” color configuration is not allowed inside ordinary ∗ may mix as they have the same overall quantum numbers. However, the mixing of cc m √ cc ) = / ¯ 3 T ( ]. It is a state made of DD J , cc where T 13 6 1 , ) = and 6 denotes the harmonic oscillator constant for the relevant mode. This ratio reaches 1 in the ( ) C 6 ( cc ( ω ¯ T d cc An interesting possibility is a double charm meson T QCD does not restrict hadrons to Experimental studies of charm baryon spectroscopy are on-going or planned at several facili- Another interesting suggestion of an exotic heavy hadron was made by Diakonov in the chiral u increases from 1 ∼ . In a recent quark model calculation[ Q Q ∗ cc will be suppressed due to the suppression of the spin-flip interaction of heavy quarks[ found by considering the attraction of the scalar diquark. forbidden if its mass is lowermain than decay the modes are into the Cabibbo allowed numbers that are not realized by m 3. Multi-quark hadrons with heavy quarks state is formed by have also investigated production ofT another possible exotic state of the same , ties. Among them, J-PARC has aexperimental hall plan to to explore utilize charm the baryon new excitations high-momentum up beam to line 3 in GeV the or hadron higher[ where SU(3) limit and 1 higher excitations and their separation is advantageousof in the studying light the effective diquarks, mass as and well dynamics as the interaction between the heavy quark and the light quarks. state below the timated production cross sections of quark model[ New Aspect of Hadron Spectroscopy m strong-decay threshold is and ¯ shapes of the momentum distribution. the ground state hadrons of color-singlet PoS(Hadron 2013)001 , c > T T , and X Makoto Oka ]. Scattering 5 mesons and the or the other non- ]. The situation is D ) 20 , hadrons[ 3827 ( X i.e. On the other hand, the theoretical ap- symmetry, spontaneous chiral symmetry 2 #(antiquark), is not a conserved quantity, f ]. and the other charmonium states, analyses + () is conserved. Nonetheless, 14 ψ / × , whose predicted masses are not completely consistent J 3 cc Ξ 6 = , #(quark) ]. For i.e. states fairly well, although ], where we find that the Upsilon peaks remain above 21 , 21 D 20 , , 1 #(antiquark) S ]. By using MEM, we have succeeded in obtaining the spectral 19 − 18 , 2 P ]. 15 creation and annihilation are suppressed. Conservation of the heavy-quark ¯ Q Q is the critical temperature for the quark-gluon plasma phase[ c T (1) anomaly, heavy quark symmetry and so on. Color confinement does not easily al- A ]. They reproduce 1 ]. Recent developments include application of the maximum entropy method (MEM) to 16 operators strongly and we need to introduce 4-quark operators to generate them. 17 , where I pose a question: Are “exotic” hadrons well defined? Indeed, it is not clear how the various Another hint comes from special roles of color singlet clusters, One possible exception is the double charm baryon Another powerful method to obtain the hadron spectrum based on QCD is the QCD sum Hadrons are elementary excitation modes of the QCD vacuum. Their spectrum is the most The quantum numbers and masses of the ground state hadrons are well reproduced by the c 2 T qq 2 , is growing. We need more than zoology and must construct a unified picture of all the hadrons. . nor an observable, while #(quark) low multi-quark, or multi-gluon “exotic” hadrons, but our list of abnormal hadrons, such as structures, such as tetra-quark, hadronknow molecule, how diquark to molecule, quantify etc., and are determinetion different? experimentally is the We that “exotic-ness” do number of not of hadrons quarks in in QCD. a A hadron, cau- and will dissociate at a higher temperature. breaking, U Z spin in productions and decays may be a key to solve thestates structure of problem. color singletlanguages clusters may are help to well avoid defined the ambiguity. in the asymptotic region, and bases in hadronic the reason is not known whyground-state the hadrons. constituent quark A model hint worksserved, would extremely because well be for that describing the the number of heavy quarks are approximately con- with the observed one at SELEX[ rules[ important clue of the dynamicsdom and of symmetries confined of quarks low energy and QCD, . such as SU(3) It gives the key degrees of free- standard excited states are notto given. A ¯ conjecture is that those non-standard states do not couple charmonium at finite temperature[ show that the temperaturestrongly. dependences of It is the found gluon1 that condensates sharp modify peaks the of spectral the functions spectral functions disappear quickly at around 5. Conclusion – Goals and Issues – analyses of the QCD sumfunctions rules[ from the sumform. rule without So making far the the pole+continuum method has assumption been for applied its to functional the ordinary mesons, , quark model as well as the lattice QCD calculations[ New Aspect of Hadron Spectroscopy 4. QCD analyses proaches on the excitedculations states of are the quite heavy limited. mesonsstates[ in There lattice are QCD, which some give attempts excitations of spectra first of principle the charmonium cal- different in the bottomonium spectrum[ PoS(Hadron 2013)001 Makoto Oka (2006) (2013) 043. 97 (1979) 448. (2013) 034027. B147 Bormio2013 (1986) 242. D87 ]. 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