Photo-and electro-production of narrow exotic states:From light quarks to charm and up to bottom

Accessing a full image of the inner content of hadrons represents a central endeavour of modern particle physics,with the main scientific motivation to investigate the strong interaction binding the visible matter.On the one hand,the structure of known exotic candidates is a fundamental open issue addressed widely by scientists.On the other hand,looking for new states of exotic nature is a central component for theoretical and experimental efforts from electron-positron machine and electron accelerator with fixed target to heavy ion and electron-ion colliders.In this article we present a succinct short overview of the attempt to search for exotic narrow N∗and Z states containing light quarks only or also charm,and its connotation for bottom regions(the latter two are also known as Pc(Zc)and Pb(Zb)states,respectively in the literature).We address the effort of searching for exotic narrow N∗and Z states in light quark sector.We focus on recent progress in searching for signal of Pc and Zc states photoproduction and its implication into the Pb and Zb photoproduction and their decay properties.We also discuss future perspectives for the field in electron-ion colliders,a good place to disentangle the nature of some of these states and investigate some other enlightening topics including QCD trace anomaly and quarkonium-nucleon scattering length.

Possible J^(PC)=0^(+-) exotic states

We study possible exotic J^（PC）=0~＋- states using tetraquark interpolating currents with the QCD sum rule approach. The extracted masses are around 4.85GeV for the charmonium-like states and 11.25 GeV for the bottomonium-like states. There is no working region for the light tetraquark currents, which implies that the light 0~＋- state may not exist below 2GeV.

D-wave excited cscs tetraquark states with J^(PC)=1^(++)and 1^(+-)

We study the mass spectra of D-wave excited cscs tetraquark states with J^(PC)=1^(++)and 1^(+-)in both symmetric 6cs@6cs and antisymmetric 3cs@3cs color configurations using the QCD sum rule method.We construct the D-wave diquark-antidiquark type of cscs tetraquark interpolating currents in various excitation structures with(L_(λ),Lp{p_(1),p_(2)})=(2,0(0,0),(1,1(1,0),(1,1(0,1),(0,2(1,1),(0,2(2,0),(0,2(0,2).Our results support the interpretation of the recently observed X(4685)resonance as a D-wave cscs tetraquark state with JPC-1++in the(2,O(0,O))or(0,2(2,O))excitation mode,although some other possible excitation structures cannot be excluded exhaustively within theoretical errors.Moreover,our results provide the mass relations 6_(ρρ)<3_(λλ)<3_(λρ)<3_(ρρ)and 6pp<3au<6aa<3pp for the positive and negative C-parity D-wave cscs tetraquarks,respectively.We suggest searching for these possible D-wave cscs tetraquarks in both the hidden-charm channels J/o and nc,as well as open-cham channes such as D_(s)D_(x)nd D_(s)D_(s1).

Exotic D_(s)^(*)D^(*) molecular states and scqc tetraquark states with J^(P)=0^(+),1^(+),2^(+)

We have calculated the mass spectra for the D_(s)^(*)D^(*) molecular states and scqc tetraquark states with J^(P)=0^(+),1^(+),2^(+).The masses of the axial-vector D_(s)^(*)D^(*),D_(s)^(*)D molecular states and 1_([sc])㊉0_([qc]),0_([sc])©1_([qc])tetraquark states are predicted to be approximately 3.98 GeV,in good agreement with the mass of Z_(cs)(3985)^(-)from BE-SIII.In both the molecular and diquark-antidiquark scenarios,our results suggest that there may exist two almost degenerate states,as the strange partners of X(3872)and Z_(c)(3900).We propose to carefully examine Z_(cs)(3985)in future experiments to verify this.One may also search for more hidden-charm four-quark states with strangeness in not only the open-charm D_(s)^(*)D^(*) channels but also the hidden-charm channels η_(c)K/K^(*),J/ψK/K^(*).

Study of the XYZ states at the BESIII

With its unique data samples at energies of 3.8-4.6 GeV, the BESIII experiment made a significant contribution to the study of charmonium and charinonium-like states, i.e., the XYZ states. We review the results for observations of the Zc（3900） and Zc（4020） states, the X（3872） in e^＋e^- annihilation, and charmonium ψ（13D2） state, as well as measurements of the cross-sections of ωχcJ and ηJ/ψ, and the search for e^＋e^-→γχcJ and γY（4140）. We also present data from BESIII that may further strengthen the study of the XYZ and conventional charmonium states, and discuss perspectives on future experiments.

Study of the structures of four-quark states in terms of the Born-Oppenheimer approximation

In this work, we use the Born-Oppenheimer approximation, where the potential between atoms can be approximated as a function of distance between the two nuclei, to study the four-quark bound states. By this approximation, Heitler and London calculated the spectrum of the hydrogen molecule, which includes two protons （heavy） and two electrons （light）. Cenerally, the observed exotic mesons Zb（10610）, ZD（10650）, Zc（3900） and Zc（4020） （Zc（4025）） may be molecular states made of two physical mesons and/or diquark-anti-diquark structures. Analogous to the Heitler-London method for calculating the mass of the hydrogen molecule, we investigate whether there exist energy minima for these two structures. Contrary to the hydrogen molecule case where only the spin-triplet possesses an energy minimum, there exist minima for both of these states. This implies that both molecule and tetraquark states can be stable objects. Since they have the same quantum numbers, however, the two states may mix to result in the physical states. A consequence would be that partner exotic states co-existing with ZD（10610）, Zb（]0650）, Zc（3900） and Zc（4020） （Zc（4025）） are predicted and should be experimentally observed.

Production of hidden-charm and hidden-bottom pentaquark states in electron-proton collisions

Electro-production of several pentaquark states is investigated in this study.The eSTARlight package is adapted to study the electro-production of J/ψand γ(1S)via pentaquark P_(c)and P_(b)resonance channels in ep→eJ/ψp and ep→eγ(1S)p scattering processes at the proposed electron-ion colliders(EICs).The results obtained in this study are compared to those of non-resonance t-channels,which are described in the pomeron exchange model developed in our studies.Some pseudo-rapidity and rapidity distributions of J/ψand γ(1S)are presented for the proposed EICs,including EicC and EIC-US.It is found that EicC is a good platform to identify P_(b) states in the future.

Search for exotic state 1^(-+) π_1(1400) at BESⅢ

The J/ψ hadronic decays provide good laboratory to search for the hybrid states with exotic quantum numbers. A full Partial Wave Analysis （PWA） is performed to the generated Monte Carlo J/ψ→ ρηπ data, based on the design of BESⅢ detector, to study the sensitivity of searching for a possible exotic state at BESⅢ.

Glueballs at physical pion mass

Glueballs are investigated through gluonic operators on two N_(f)=2+1RBC/UKQCD gauge ensembles at the physical pion mass.The statistical errors of glueball correlation functions are considerably reduced through the cluster decomposition error reduction(CDER)method.The Bethe-Salpeter wave functions are obtained for the scalar,tensor,and pseudoscalar glueballs by using spatially extended glueball operators defined through the gauge potential A_(μ)(x)in the Coulomb gauge.These wave functions exhibit similar features of non-relativistic two-gluon systems and are used to optimize the signals of the related correlation functions at the early time regions,where the ground state masses are extracted.These masses are close to those from the quenched approximation and indicate the possible existence of glueballs at the physical point.The resonance feature of glueballs and the mixing with conventional mesons and multi-hadron systems should be considered in a more systematic lattice study.

Experimental review of the T(1S,2S,3S)physics at e^(+)e^(-) colliders and the LHC

The three lowest-lying r states,ie,r(1S),T(2S),and r(35),composed of b pairs and below the BB threshold,provide a good platform for the researches of hadronic physics and physics beyond the Standard Model.They can be produced directly in ete--colliding experiments,such as CLEO,Babar,and Belle,with low continuum backgrounds.In these experiments,many measurements of the exclusive r(1S)and r(2S)decays into light hadrons,which shed light on the"80%rule"for the Okubo-Zweig-lizuka suppressed decays in the bottomonium sector,were carried out.Meanwhile,many studies of the charmonium and bottomonium productions in r(1S,2S,3S)decays were performed,to distinguish different Quantum Chromodynamics(QCD)models.Besides,exotic states and new physics were also extensively explored in r(1S,2S,3S)decays at CLEO,BaBar,and Bell.The r(1S,2S,3S)states can also be produced in p collisions and in ollisions involving heavy ions.The precision measurements of their cross sections and polarizations at the large hadron collider(LHC),especially in the CMS,ATLAS,and LHCb experiments,help to understand r production mechanisms in Pp collisions.The observation of the sequential r suppession in heavy ion collisions at CMS,LHCb,and ALICE is of great importance for verifying the quark-gluon plasma predicted by QCD.In this article,we review the experimental results on T(1S,2S,3S)at e+e-colliders and the LHC,and summarize their prospects at Belle II and the LHC.

Predictions of γ(4S)→h_b(1P,2P)π^+π^- transitions

We study the contributions of intermediate bottomonium-like Zb states and the bottom meson loops in the heavy quark spin flip transitionsγ(4 S)→hb(1 P,2 P)π+π-.Depending on the constructive or destructive interferences between the Zb-exchange and the bottom meson loops mechanisms,we predict two possible branching ratios for each process:BRγ(4 S)→hb(1 P)π+π-≈(1.20.40.8×10^-6)or(0.5-0.20.5×10^-6),and BRγ(4 S)→(2 P)π+π-≈(7.1-1.1+1.7×10^-10)or(2.4-0.10.2×10^-10)).The contribution of the bottom meson loops is found to be considerably larger than that of the Zbexchange in the T(4 S)→hb(1 P)ππtransitions,while its decay rates are not comparable to those of heavy quark spin conservedγ(4 S)→γ(1 S,2 S)ππprocesses.We also predict the contribution of the charm meson loops in the branch fractions ofΨ(3 S,4 S)→hc(1 P)ππ.

Electron-ion collider in China

Lepton scattering is an established ideal tool for studying inner structure of small particles such as nucleons as well as nuclei.As a future high energy nuclear physics project,an Electron-ion collider in China(EicC)has been proposed.It will be constructed based on an upgraded heavy-ion accelerator,High Intensity heavy-ion Accelerator Facility(HIAF)which is currently under construction,together with a new electron ring.The proposed collider will provide highly polarized electrons(with a po-larization of 80%)and protons(with a polarization of 70%)with variable center of mass energies from 15 to 20 GeV and the luminosity of(2–3)×1033 cm^(−2)·s^(−1).Polarized deuterons and Helium-3,as well as unpolarized ion beams from Carbon to Uranium,will be also available at the EicC.The main foci of the EicC will be precision measurements of the structure of the nucleon in the sea quark region,including 3D tomography of nucleon;the partonic structure of nuclei and the parton interaction with the nuclear environment;the exotic states,especially those with heavy flavor quark contents.In addition,issues fundamental to understanding the origin of mass could be addressed by measurements of heavy quarkonia near-threshold production at the EicC.In order to achieve the above-mentioned physics goals,a hermetical detector system will be constructed with cutting-edge technologies.This document is the result of collective contributions and valuable inputs from experts across the globe.The EicC physics program complements the ongoing scientific programs at the Jefferson Laboratory and the future EIC project in the United States.The success of this project will also advance both nuclear and particle physics as well as accelerator and detector technology in China.

Can X(5568) be a tetraquark state?

Very recently, the D0 collaboration has reported the observation of a narrow structure, X（5568）, in the decay process X（5568）→ Bs^0π^±using the 10.4fb^-1 data of pp collision at √s= 1.96 TeV. This structure is of great interest since it is the first hadronic state with four different valence quark flavors, b, s, u, d. In this work,we investigate tetraquarks with four different quark flavors. Based on the diquark-antidiquark scheme, we study the spectroscopy of the tetraquarks with one heavy bottom/charm quark and three light quarks. We find that the lowest-lying S-wave state, a tetraquark with the flavor [su][bd] and the spin-parity J^P= 0^＋, is about 150 MeV higher than the X（5568）. Further detailed experimental and theoretical studies of the spectrum, production and decays of tetraquark states with four different flavors are vital to gain a better understanding of the nature and classification of hadron exotic states.

Is J^(PC)=3^(-+) molecule possible?

The confirmation of charged charmonium-like states indicates that heavy quark molecules should exist. Here we discuss the possibility of a molecule state with ^PC=3^-＋. In a one-boson-exchange model investigation for the S wave C=＋ D^＊D2^＊ states, one finds that the strongest attraction is in the case J= 3 and I=0 for both π and σ exchanges. Numerical analysis indicates that this hadronic bound state might exist if a phenomenological cutoff parameter around 2.3 GeV （1.5 GeV） is reasonable with a dipole （monopole） type form factor in the one-pion- exchange model. The cutoff for binding solutions may be reduced to a smaller value once the σ exchange contribution is included. If a state around the D^＊D2^＊ threshold （≈4472 MeV） in the channel J/ψω （P wave） is observed, the heavy quark spin symmetry implies that it is not ace meson and the jPC are likely to be 3^-＋.

Experimental review of e+e-→ππhc

We review the recent BESIII measurement of e＋e-→ππhc in which its line shape is studied between the center-of-mass energies of 3.9 to 4.42 GeV and an iso-vector charmonium-like state Zc（4020） is observed in the invariant mass of 7rhc at the BESIII experiment. The charged Zc（4020）± is the second observed Zc state following Zc（3900）, while the Zc（4020）0 is the first observed neutral Zc state. The line shape of δ（e＋e-→ππhc）is also re-analyzed in view of searching for the Y state and the existence of the Y（4220） state is confirmed and compared with the previous work of the BESIII experiment.

Disentangling the nature of resonances in coupled-channel models

We present severM possible hadronic states found in coupled-channel models within the on-shell approx- imation. The interaction potential is constructed as a sum of the tree-level Feynman diagrams calculated with the effective Lagrangians. Based on the recent empirical data, we illustrate the possible existence of severM baryonic and mesonic states with definite quantum numbers in the model. We give their properties for the purpose of further study and discuss the potential of finding them in future experiments.