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.

Study of the topological quantities of lattice QCD using a modified DCGAN frame

A modified deep convolutional generative adversarial network(M-DCGAN)frame is proposed to study the N-dimensional(ND)topological quantities in lattice QCD based on Monte Carlo(MC)simulations.We construct a new scaling structure including fully connected layers to support the generation of high-quality high-dimensional images for the M-DCGAN.Our results suggest that the M-DCGAN scheme of machine learning will help to more efficiently calculate the 1D distribution of topological charge and the 4D topological charge density compared with MC simulation alone.

Exploring hidden-charm and hidden-strange hexaquark states from lattice QCD

Based on five different ensembles of newly generated(2+1)-flavor configurations with pion mass of approximately mπ■(140-310)MeV,we present a lattice analysis of hidden-charm and hidden-strange hexaquarks with the quark content■.The correlation matrices of two types of operators with JPC=0++,0-+,1++and 1--are simulated to extract the masses of the hexaquark candidates,which are subsequently extrapolated to the physical pion mass and continuum limit.The results indicate that ground state masses are below the■threshold and provide a characteristic signal for the experimental discovery of hexaquark candidates,which may enrich the versatile structure of multiquarks;moreover,it is an indispensable step to decipher the nonperturbative nature of the fundamental interactions of quarks and gluons.

^(3)S_(1)–^(3)D_(1) coupled channel Λ_(c)N interactions:chiral effective field theory versus lattice QCD

We study the lattice QCDΛ_(c)N phase shifts for the^(3)S_(1)-^(3)D_(1)coupled channel using both the leading order covariant chiral effective theory and the next-to-leading order non-relativistic chiral effective field theory(ChEFT).We show that although it is possible to describe simultaneously the^(3)S_(1)and^(3)D_(1)phase shifts and the inelasticityη_(1),the fitted energy range is quite small,only up to E_(c.m.)=5 MeV.This raises concerns regarding the consistency between leading/next-to-leading order ChEFT and the lattice QCD simulations.

Charmed andϕmeson decay constants from 2+1-flavor lattice QCD

On a lattice with 2+1-flavor dynamical domain-wall fermions at the physical pion mass,we calculate the decay constants of D_s^(*) , D^(*) ,and φ .The lattice size is 48^3×96 ,which corresponds to a spatial extension of -5.5 fm,with a lattice spacing of a\approx a≈0.114 fm.For the valence light,strange,and charm quarks,we use overlap fermions at several mass points close to their physical values.Our results at the physical point are f_(D)=213(5) MeV, f_(D)_(s)=249(7) MeV, f_(D)^(*)=234(6) MeV, f_(D)_(s)^(*)=274(7) MeV,and f_(D)_(s)=241(9) MeV.The couplings of D^(*) and D_s^(*) to the tensor current( f_(V)^(T) )can be derived from ratios f_(D)^(*)^T/f_(D)^(*)=0.91(4) and f_(D)_(s)^(*)^T/f_(D)_(s)^(*)=0.92(4) ,respectively,which are the first lattice quantum chromodynamics(QCD)results.We also obtain ratios f_(D)^(*)/f_(D)=1.10(3) and f_(D)_(s)^(*)/f_(D)_(s)=1.10(4) ,which reflect the size of heavy quark symmetry breaking in charmed mesons.Ratios f_(D)_(s)/f_(D)=1.16(3) and f_(D)_(s)^(*)/f_(D)^(*)=1.17(3) can be taken as a measure of SU(3)flavor symmetry breaking.

Exotic and excited-state meson spectroscopy and radiative transitions from lattice QCD

We discuss recent progress in extracting the excited meson spectrum and radiative transition form factors from lattice QCD.We mention results in the charmonium sector,including the first lattice QCD calculation of radiative transition rates involving excited charmonium states,highlighting results for high spin and exotic states.We present recent results on a highly excited isovector meson spectrum from dynamical anisotropic lattices.Using carefully constructed operators we show how the continuum spin of extracted states can be reliably identified and confidently extract excited states,states with exotic quantum numbers and states of high spin.This spectrum includes the first spin-four state extracted from lattice QCD.We conclude with some comments on future prospects.

Baryon-Baryon interactions from lattice QCD

We report on new attempt to investigate baryon-baryon interactions in lattice QCD.From the Bethe-Salpeter （BS） wave function,we have successfully extracted the nucleon-nucleon （NN） potentials in quenched QCD simulations,which reproduce qualitative features of modern NN potentials.The method has been extended to obtain the tensor potential as well as the central potential and also applied to the hyperonnucleon （YN） interactions,in both quenched and full QCD.

First lattice QCD calculation of semileptonic decays of charmed-strange baryonsΞc

While the standard model is the most successful theory to describe all the interactions and constituents of elementary particle physics,it has been constantly scrutinized for over four decades.Weak decays of charm quarks can be used to measure the coupling strength between quarks in different families and serve as an ideal probe for CP violation.As the lowest charm-strange baryons with three different flavors,Ξ;baryons(composed of csu or csd)have been extensively studied in experiments.In this study,we use state-of-the-art lattice QCD techniques to generate 2+1 clover fermion ensembles with two lattice spacings,a=(0.108,0.080 fm).Then,we present the first ab-initio lattice QCD calculation of the Ξ;→Ξ form factors.Our theoretical results for the Ξc→Ξl;v;decay widths are consistent with and approximately two times more precise than the latest measurements by the ALICE and Belle collaborations.Based on the latest experimental measurements,we independently obtain the quark-mixing matrix element |V;|,which is in good agreement with results from other theoretical approaches.

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2＋1flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. The scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. The light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects. The coarse and fine lattices are of sizes 24^3 ×64 and 32^3 ×64 with inverse spacings 1/a= 1.75（4） GeV and 2.33（5） GeV, respectively.

Baryon structure from Lattice QCD

We present recent lattice results on the baryon spectrum, nucleon electromagnetic and axial form factors, nucleon to △ transition form factors as well as the △ electromagnetic form factors. The masses of the low lying baryons and the nucleon form factors are calculated using two degenerate flavors of twisted mass fermions down to pion mass of about 270 MeV. We compare to the results of other collaborations. The nucleon to △ transition and △ form factors are calculated in a hybrid scheme, which uses staggered sea quarks and domain wall valence quarks. The dominant magnetic dipole nucleon to △ transition form factor is also evaluated using dynamical domain wall fermions. The momentum frame are extracted using the form factors transverse density distributions of the △ in the infinite determined from lattice QCD.

Calculation of disconnected quark loops in lattice QCD

Calculation of disconnected quark loops in lattice QCD is very time consuming.Stochastic noise methods are generally used to estimate these loops.However,stochastic estimation gives large errors in the calculations of disconnected diagrams.We use the symmetric multi-probing source(SMP)method to estimate the disconnected quark loops,and compare the results with the Z(2)noise method and the spin-color explicit(SCE)method on a quenched lattice QCD ensemble with lattice volume 12^3×24 and lattice spacing a≈0.1 fm.The results show that the SMP method is very suitable for the calculation of pseudoscalar disconnected quark loops.However,the SMP and SCE methods do not have an obvious advantage over the Z(2)noise method in the evaluation of the scalar disconnected loops.

Full lattice QCD study of the κ scalar meson

We studied the K light scalar meson in 2＋1 flavor full QCD with sufficiently light u and d quarks. Via lattice simulation we measured the correlators for the K channel in the ＂Asqtad＂ improved staggered fermion formulation. After chiral extrapolation we obtained the mass of the K meson with 826± 119 MeV, which is within recent experimental values of 800-900 MeV. The simulations were carried out with the MILC 2＋1 flavor gauge configurations at lattice spacing a ≈ 0.15 fm.

One-pion-exchange potential with contact terms from lattice QCD simulations

Pion-mass-dependent nucleon-nucleon(NN)potentials are obtained in terms of the one-pion exchange and contact terms from the latest lattice QCD simulations of the two-nucleon system.They assume the forms of the leading order(LO)NN potential from the chiral effective field theory and thus are referred to as the LO chiral potential in this study.We extract the coefficients of contact terms and cut-off momenta in these potentials,for the first time,by fitting the phase shifts of 1S0 and 3S1 channels obtained from the HALQCD collaboration with various pion masses from 468.6 to 1170.9 MeV.The low-energy constants in the 1S0 and 3S1 channels become weaker and approach each other for larger pion masses.These LO chiral potentials are applied to symmetric nuclear and pure neutron matter within the Brueckner-Hartree-Fock method.Presently,however,we do not yet have the information of the P-wave NN interaction to be provided by the lattice QCD simulations for a complete description of nuclear matter.Our results enhance understanding of the development of nuclear structure and nuclear matter by controlling the contribution of the pionic effect and elucidate the role of chiral symmetry of the strong interaction in complex systems.

The QCD Ground State Chiral Tetrahedron Symmetry

We propose that the exotic meson tetraquark ud~dũintroduced in previous papers, may be a pseudo-Goldstone boson having a tetrahedron geometry and symmetry. The transition from the neutral pion superposition of two free mesons, dd~ and uũ, to the tetrahedron geometry with optional two chiral states may be the symmetry breaking of the QCD ground state. The ud~dũtetrahedron mass may be calculated by measuring the β decay rate variability. We assume that electrons and positrons are composite particle exotic tetraquarks, dũdd~ for the electrons and ud~dd~ for the positrons and confined by the strong force. We propose that the QCD tetrahedrons play a central role in electron pairing mechanism in both chemical bond forming and superconductor Cooper pairs. We propose a hypothesis where the QCD ground state tetrahedrons play a central role in low energy physics where quark exchange reactions between particles and the QCD tetrahedrons via gluon junctions transfer all the forces. The QCD ground state ud~dũtetrahedrons hypothesis provides a symmetry breaking and a mass gap may be created by the ground state QCD tetrahedrons Bose-Einstein condensate.

An Effective Way for Determining the Transition Points in Lattice QCD at Finite Temperature

The transition points of lattice quantum chromodynamics（QCD） with two degenerate flavors of Wilson quarks at finite temperature T and small imaginary quark chemical potential μ are determined by using the reweighting technique.Under the positive fermion determinant,i.e.,the chemical potential is pure imaginary,the simulations are performed at hopping parameter κ = 0.165.The comparison between the reweighting technique and the conventional point-by-point scanning method is presented.The results prove that the reweighting technique is an effective and efficient method in investigating the critical phenomenon.

Semileptonic decays B_c■(η_c, J/ψ)l■_l in the “PQCD+Lattice” approach

We study the semileptonic decaysBc-→(ηc,J/ψ)l-■lusing the PQCD factorization approach with the newly defined distribution amplitudes of the B c meson and a new kind of parametrization for extrapolating the form factors which takes into account the recent lattice QCD results.We find the following main results:(a)the PQCD predictions of the branching ratios of theBc→(ηc,J/ψ)l■decays are smaller by about 5%-16%when the lattice results are taken into account in the extrapolation of the relevant form factors;(b)the PQCD predictions of the ratio Rηc,RJ/ψand of the longitudinal polarization PτareRηc=0.34±0.01,RJ/ψ=0.28±0.01,Pτ(ηc)=0.37±0.01and Pτ(J/ψ)=-0.55±0.01;and(c)after including the lattice results,the theoretical predictions slightly change:Rηc=0.31±0.01,RJ/ψ=0.27±0.01,Pτ(ηc)=0.36±0.01andPτ(J/ψ)=-0.53±0.01.The theoretical predictions of RJ/ψagree with the measurements within the errors.The other predictions could be tested by the LHCb experiment in the near future.

Strangeonium-like hybrids on the lattice

The strangeonium-like ss^-g hybrids are investigated from lattice QCD in the quenched approximation.In the Coulomb gauge,spatially extended operators are constructed for 1^--and(0,1,2)^-+states with the color octet ss^-component being separated from the chromomagnetic field strength by the spatial distance r,whose matrix elements between the vacuum and the corresponding states are interpreted as Bethe-Salpeter(BS)wave functions.In each of the(1,2)^-+channels,the masses and the BS wave functions are reliably derived.The 1^-+ground state mass is approximately 2.1-2.2 GeV,and that of 2^-+is approximately 2.3-2.4 GeV,whereas the mass of the first excited state is approximately 1.4 GeV higher.This mass splitting is much larger compared to that expected based on the phenomenological flux-tube model or constituent gluon model for hybrids,which is usually a few hundred MeV.The BS wave functions with respect to r exhibit clear radial nodal structures of a non-relativistic two-body system,which imply that r is a meaningful dynamical variable for these hybrids and motivate a color halo picture of hybrids,in which the color octet ss^-is surrounded by gluonic degrees of freedom.In the 1^--channel,the properties of the lowest two states are consistent with those ofФ(1020)andФ(1680).We did not obtain convincing information with respect toФ(2170).However,we argue that regardless of whetherФ(2170)is a conventional ss^-meson or a ss^-g hybrid in the color halo scenario,the ratio of partial decay widthsΓ(Фη)andΓ(Фη')observed by BESIII can be understood based on the mechanism of hadronic transition of a strangeonium-like meson in addition toη-η'mixing.

Latest lattice results for baryon spectroscopy

Theoretical and computational advances have enabled not only the masses of the ground states,but also some of the low-lying excited states to be calculated using Lattice Gauge Theory.In this talk,I look at recent progress aimed at understanding the spectrum of baryon excited states,including both baryons composed of the light u and d quarks,and of the heavier quarks.I then describe recent work aimed at understanding the radiative transitions between baryons,and in particular the N-Roper transition.I conclude with the prospects for future calculations.

Scalar meson spectroscopy with a fine lattice

With sufficiently light u and d quarks the isovector （a0） and isosinglet （f0） scalar meson propagators are dominated at large distances by two-meson states. In the staggered fermion formulation of lattice QCD, taste-symmetry breaking causes a proliferation of multihadron states that complicates the analysis of these channels. Of special interest is the bubble contribution, which makes a considerable contribution to these channels. Using numerical simulation we have measured the correlators for both a0 and f0 channels in the ＂Asqtad＂ improved staggered fermion formulation in a MILC fine （a = 0.09 fm） lattice ensemble. We analyze those correlators using rooted staggered chiral perturbation theory （rSxPT） and achieve chiral couplings that are well consistent with previous determinations.

Lattice calculation of the κ meson

We study the K meson in 2 ＋ 1 flavor QCD with sufficiently light u/d quarks. Using numerical simulations, we measure the point-to-point K correlators in the ＂Asqtad＂ improved staggered fermion formu- lation. We then analyze these correlators using rooted staggered chiral perturbation theory （rSxPT）, with particular attention paid to bubble contribution. After chiral extrapolation, we obtain the physical K mass with 828＋97 MeV, which is within the recent experimental value of 800-900 MeV. These numerical simulations are carried out with MILC 2 ＋ 1 flavor gauge configurations at a lattice spacing of α = 0.12 fm.