Semi-inclusive lepto-production of hidden-charm exotic hadrons

We investigate the semi-inclusive production of hidden-charm exotic states,including the X(3872),Z_(c),Zcs and pentaquark P_(c) states,in lepton-proton scattering processes.These hadrons are close to the thresholds of a pair of charm and anticharm hadrons and are assumed to possess a hadronic molecular structure as their main feature.To provide order-of-magnitude estimates of the cross sections,we use Pythia to simulate the short-distance productions of the constituent hadrons,which then rescatter to form exotic hadrons.The estimates for the X(3872)and Z_(c)(3900)^(±)states are not in conflict with the upper limits measured in the COMPASS experiment for the exclusive photoproduction process.The results indicate that the considered hidden-charm states can be copiously produced at the proposed electron-ion colliders EicC and US-EIC.

Issues and Opportunities in Exotic Hadrons

The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons.Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks,pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented.

Tetraquark and Pentaquark Systems in Lattice QCD

We study multi-quark systems in lattice QCD. First, we revisit and summarize our accurate mass measurements of low-lying 5Q states with J = 1/2 and I = 0 in both positive- and negative-parity channels in anisotropic lattice QCD. The lowest positive-parity 5Q state is found to have a large mass of about 2.24 GeV after the chiral extrapolation. To single out the compact 5Q state from NK scattering states, we use the hybrid boundary condition (HBC), and find no evidence of the compact 5Q state below 1.75 GeV in the negative-parity channel. Second, we study the multi-quark potential in lattice QCD to clarify the inter-quark interaction in multi-quark systems. The 5Q potential V5Q for the QQ--QQ system is found to be well described by the “OGE Coulomb plus multi-Y Ansatz”: The sum of the one-gluon-exchange (OGE) Coulomb term and the multi-Y-type linear term based on the flux-tube picture. The 4Q potential V4Q for the QQ- system is also described by the OGE Coulomb plus multi-Y Ansatz, when QQ and are well separated. The 4Q system is described as a “two-meson” state with disconnected flux tubes, when the nearest quark and antiquark pair are spatially close. We observe a lattice-QCD evidence for the “flip-flop”, i.e., the fluxtube recombination between the connected 4Q state and the “two-meson” state. On the confinement mechanism, the lattice QCD results indicate the flux-tube-type linear confinement in multi-quark hadrons. Finally, we propose a proper quark-model Hamiltonian based on the lattice QCD results.

A discussion on the anomalous threshold enhancement of J/ψ–ψ(3770)couplings and X(6900)peak

The attractive interaction between J/ψandψ(3770)has to be strong enough if X(6900)is of the molecule type.We argue that sinceψ(3770)decays predominantly into a DD^(¯)pair,the interactions between J/ψandψ(3770)may be significantly enhanced owing to the three point DD^(¯)loop diagram.The enhancement originates from the anomalous threshold located at t=−1.288 GeV^(2),whose effect propagates into the s-channel partial wave amplitude in the vicinity of √s≃6.94 GeV.This effect may be helpful in the formation of the X(6900)peak.

对3.9GeV附近0^(++)和2^(++)(类)粲偶素的理解

在过去的20年里,各个实验组在粲偶素能量区间(约3.1~4.5 GeV)观测到了大量的(类)粲偶素,这些粲偶素的发现不仅极大地丰富了强子谱,也将传统的cc介子拓展到了奇特强子态领域.在3.9 GeV能量附近有许多(类)粲偶素的实验候选者,如:X(3915),Z(3930),χc0(3930),χc2(3930)以及X(3960)等,然而它们的本质是什么依然存在争议.本文提出以下猜想:(1)J/φω中观测到的X(3915)与χc2(3930)是同一个态;(2) Ds+Ds-道中观测到的X(3960)是Ds+Ds-体系的S波强子分子态;(3)B+→D+D-K+过程里的JPC=0++组分与X(3960)具有相同来源,质量大约为3.94GeV,并非如《粒子物理综述》中所列来源于X(3915).通过对LHCb实验组在B+→D((s))+D((s))-K+过程以及Belle和BaBar实验组在双光子对撞过程给出的实验数据进行联合拟合,作者发现上述猜想与当前的实验结果都是一致的.本工作不仅对(类)粲偶素能谱提供了新的探索思路,也加深了研究人员对含粲强子之间的相互作用的理解.

利用机器学习研究隐粲五夸克态的性质

机器学习已经在生物、医学、生产等多个领域广泛应用并展现了其优势.最近,机器学习在物理领域也开始逐渐兴起并展现出其独特的优点.该文旨在探索机器学习在强子物理中的应用潜力.作者以隐粲五夸克态Pc(4312)、Pc(4440)和Pc(4457)为例,在强子分子态图像下研究它们的性质.研究表明,神经网络方法和基于χ2的拟合方法都能够阐明基于领头阶接触势的基本物理性质.然而,χ2拟合方法无法区分Pc(4440)和Pc(4457)的量子数,神经网络方法则可以.由此,作者进一步分析了每个实验数据点对于神经网络预测的影响,以及在拟合方法中每个数据点对于关键物理参数的重要性.通过对比研究,作者发现神经网络方法可以多维度地利用实验数据信息,在强子物理中具有巨大的应用前景.

Production of X_(eses)in heavy ion collisions

The yields of X_(cscs)with its two possible configurations,i.e.,the hadronic molecular state and tetraquark state,for Pb-Pb collisions at√sNN=5.02 TeV is studied.A volume effect is found from the centrality distribution of X_(cscs),which could help to distinguish the inner structure of X_(cscs).We also show the rapidity and the transverse momentum distributions of X_(cscs) production as well as its elliptic flow coefficient as a function of the transverse momentum.

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.

Investigating S-wave bound states composed of two pseudoscalar mesons

In this study,we systematically investigated two-pseudoscalar meson systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations.By solving the Bethe-Salpeter equation numerically with the kernel containing the one-particle exchange diagrams,we found that the K■,DK,B■,D■,B■,BD,D■,BK,and■systems withI=0 can exist as bound states.We also studied the contributions from heavy meson(J/ψandΥ)exchanges and found that the contributions from heavy meson exchanges cannot be ignored.

Precise determination of the pole position of the exotic Z_(c)(3900)

We perform a unified description of the experimental data of the π^(+)π^(-)and J/ψπ^(±)invariant mass spectra for e^(+)e^(-)→J/ψπ^(+)π^(-)and the D^(0)D^(*-)mass spectrum for e^(+)e^(-)→D^(0)D^(*-)π^(+)at e^(+)e^(-)center-of-mass energies 4.23 and 4.26 GeV.The analysis takes into account open-charm meson loops that contain triangle singularities,the J/ψπ-DD^(*)coupled-channel interaction respecting unitarity,and the strong ππ-KK final state interaction using dispersion relations.The analysis leads to a precise determination of the Z_(c)(3900)pole with the pole mass and width(3880.7±1.7_(stat)±22.4_(syst))MeV and(35.9±1.4_(stat)±15.3_(syst))MeV,respectively,and hints at that the DD^(*)molecular and non-molecular components are of similar importance in the Z_(c)(3900)formation.

Quantum numbers of the pentaquark states Pc+ via symmetry analysis

We investigate the quantum numbers of the pentaquark states Pc+,which are composed of 4(three flavors)quarks and an antiquark,by analyzing their inherent nodal structure in this paper.Assuming that the four quarks form a tetrahedron or a square,and the antiquark is at the ground state,we determine the nodeless structure of the states with orbital angular moment L≤3,and in turn,the accessible low-lying states.Since the inherent nodal structure depends only on the inherent geometric symmetry,we propose the quantum numbers JPof the low-lying pentaquark states P_c^+may be■,■,■and■,independent of dynamical models.

Interpretation of theη_(1)(1855)as a KK_(1)(1400)+c.c.molecule

An exotic state with J^(PC)=1^(−+),denoted byη1(1855),was observed by BESIII Collaboration recently in J/ψ→γηη′.The fact that its mass is just below the threshold of KK_(1)(1400)stimulates us to investigate whether this exotic state can be interpreted as a KK_(1)(1400)+c.c.molecule or not.Using the one boson exchange model,we show that it is possible for KK_(1)(1400)with J^(PC)=1^(−+)to bind together by taking the momentum cutoffΛ&2 GeV and yield the same binding energy as the experimental value whenΛ≈2.5 GeV.In this molecular picture,the predicted branch ratio Br(η1(1855)→ηη′)≈15%is consistent with the experimental results,which again supports the molecular explanation ofη1(1855).Relevant systems,namely KK_(1)(1400)with JPC=1−−and KK_(1)(1270)with J^(PC)=1^(−±),are also investigated,some of which can be searched for in the future experiments.

Heavy quark spin symmetry and heavy flavor hadronic molecules

We argue that the heavy quark spin symmetry can lead to important consequences for heavy flavor hadronic molecules.It can be used to predict new heavy flavor hadronic molecules and hence provides a method to identify the nature of some newly observed exotic hadrons.For example,if the Y（4660） were an S-wave ψ f 0 （980） shallow bound state,then the mass,width and line shape of its spin partner are predicted.

Note on X(3872) production at hadron colliders and its molecular structure

The production of the X（3872） as a hadronic molecule in hadron colliders is clarified. We show that the conclusion of Bignamini et al., Phys. Rev. Lett. 103（2009） 162001, that the production of the X（3872） at high pT implies a non-molecular structure, does not hold. In particular, using the well understood properties of the deuteron wave function as an example, we identify the relevant scales in the production process.

Towards the establishment of the light J^(P(C))=1^(-(+))hybrid nonet

The observation of the light hybrid candidateη_(1)(1855)by the BESⅢ Collaboration offers great opportunities for advancing our knowledge on exotic hadrons in terms of flavor sector.We demonstrate that this observation provides a crucial clue for establishing the J^(P(C))=1^(−(+))hybrid nonet.Based on the flux tube model picture,the production and decay mechanisms for the J^(P(C))=1^(−(+))hybrid nonet in the J/ψradiative decays into two pseudoscalar mesons are investigated.In the I=0 sector,we deduce that the SU(3)flavor octet and singlet mixing is non-negligible and apparently deviates from the flavor ideal mixing.Because only signals for one isoscalarη_(1)(1855)are observed in theηη′channel,we investigate two schemes of the nonet structure in whichη_(1)(1855)can either be the higher or lower mass state that strongly couples toηη′.Possible channels for detecting the multiplets are suggested.In particular,a combined analysis of the hybrid production in J/ψ→VH,where V and H denote the light vector mesons and 1^(−(+))hybrid states,respectively,may provide further evidence for this nonet structure and ultimately establish these mysterious exotic species in the experiment.

Comment on ‘Note on X(3872) production at hadron colliders and its molecular structure’

We briefly comment on the paper by Albaladejo et al., Chinese Phys. C 41 121001, rejecting its conclusions.

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.

Decay properties of the Zc(3900)through the Fierz rearrangement

We systematically construct all the tetraquark currents/operators of J^PC=1^+− with the quark configurations[cq][cq],[cq][qc],and[cc][qq](q=u/d),and derive their relations through the Fierz rearrangement of the Dirac and color indices.Using the transformations of[qc][qc]→[cc][qq]and[cq][qc],we study decay properties of the Zc(3900)as a compact tetraquark state;while using the transformation of[cq][qc]→[cc][qq],we study its decay properties as a hadronic molecular state.

Hidden-charm pentaquark states through current algebra:from their production to decay

There may be sevenD^((*))Σ_(c)^((*))hadronic molecular states.We construct their corresponding interpolating currents and calculate their masses and decay constants using QCD sum rules.Based on these results,we calculate their relative production rates inΛ^(0)_(b)decays using current algebra,that is,B(Λ^(0)_(b)→P_(c)K^(-)):B(Λ^(0)_(b)→P′_(c)K^(-)),where P_(c)and P′_(c)are two different states.We also study their decay properties via Fierz rearrangement and further calculate these ratios in the J/ψp mass spectrum,that is,B(Λ^(0)_(b)→P_(c)K^(-)→J/ψpK^(-)):B(Λ^(0)_(b)→P′_(c)K^(-)→J/ψpK^(-)).Our results suggest that theD*Σ^(*)_(c)molecular states of JP=1/2^(-)and 3/2^(-)may be observed in future experiments.

Decay properties of the X(3872)through the Fierz rearrangement

We systematically construct all the tetraquark currents of J^(PC)=1^(++) with the quark configurations[cq][cq],[cq][qc],and[cc][qq](q=u/d).Their relations are derived using the Fierz rearrangement of the Dirac and color indices,through which we study decay properties of the X(3872)under both the compact tetraquark and hadronic molecule interpretations.We conduct a search for the X(3872)→χ_(c0)π,η_(c)ππ,and χ_(c1)ππ decay processes in particle experiments.