High Energy Physics Lattice

We introduce novel relations between the derivatives [∂nρ(λ,ml)/∂mnl] of the Dirac eigenvalue spectrum [ρ(λ,ml)] with respect to the light sea quark mass (ml) and the(n+1)-point correlations among the eigenvalues (λ) of the massless Dirac operator. Using these relations we present lattice QCD results for∂nρ(λ,ml)/∂mnl(n=1,2,3) formlcorresponding to pion massesmπ=160−55MeV, and at a temperature of about 1.6 times the chiral phase transition temperature. Calculations were carried out using (2+1) flavors of highly improved staggered quarks with the physical value of strange quark mass, three lattice spacingsa=0.12,0.08,0.06fm, and lattices having aspect ratios4−9. We find thatρ(λ→0,ml)develops a peaked structure. This peaked structure arises due to non-Poisson correlations within the infrared part of the Dirac eigenvalue spectrum, becomes sharper asa→0, and its amplitude is proportional tom2l. We demonstrate that thisρ(λ→0,ml)is responsible for the manifestations of axial anomaly in two-point correlation functions of light scalar and pseudoscalar mesons. After continuum and chiral extrapolations we find that axial anomaly remains manifested in two-point correlation functions of scalar and pseudoscalar mesons in the chiral limit.

Results of a lattice field theory simulation of the single-flavor Thirring model in 2+1 spacetime dimensions are presented. The lattice model is formulated using domain wall fermions as a means to recover the correct U(2) symmetries of the continuum model in the limit where wall separationLs→∞. Simulations on123,163×Ls, varying self-interaction strengthg2and bare massmare performed withLs=8,…48, and the results for the bilinear condensate⟨ψ¯ψ⟩fitted to a model equation of state assuming a U(2)→U(1)⊗U(1) symmetry-breaking phase transition at a criticalg2c. First estimates forg−2aand critical exponents are presented, showing small but significant departures from mean-field values. The results confirm that a symmetry-breaking transition does exist and therefore the critical number of flavors for the Thirring modelNc>1. Results for both condensate and associated susceptibility are also obtained in the broken phase on163×48, suggesting that here theLs→∞extrapolation is not yet under control. We also present results obtained with the associated 2+1dtruncated overlap operator DOL demonstrating exponential localisation, a necessary condition for the recovery of U(2) global symmetry, but that recovery of the Ginsparg-Wilson condition asLs→∞is extremely slow in the broken phase.

We consider the two-dimensional classical XY model on a square lattice in the thermodynamic limit using tensor renormalization group and precisely determine the critical temperature corresponding to the Berezinskii-Kosterlitz-Thouless (BKT) phase transition to be 0.89290(5) which is an improvement compared to earlier studies using tensor network methods.

We investigate the critical endpoints of the finite temperature phase transition of QCD at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and non-perturbatively O(a)-improved Wilson-clover fermion action. The critical endpoints are determined by using the intersection point of kurtosis, employing the multi-parameter, multi-ensemble reweighting method. We present results for the critical endline atNT= 6 and the continuum extrapolation for the critical endpoint of the SU(3)-flavor symmetric point.

TheDDK3-body system is supposed to be bound due to the strongly attractive interaction between theDmeson and theKmeson in the isospin zero channel. The minimum quark content of this 3-body bound state isccq¯s¯withq=u,d. It will be an explicitly exotic tetraquark state once discovered. In order to confirm the phenomenological study of theDDKsystem, we can refer to lattice QCD as a powerful theoretical tool parallel to the experiment measurement. In this paper, a 3-body quantization condition scheme is derived via the non-relativistic effective theory and the particle-dimer picture in finite volume. Lattice spectrum of this 3-body system is calculated within the existing model inputs. The spectrum shows various interesting properties of theDDKsystem, and it may reveal the nature of theD∗(2317). This predicated spectrum is expected to be tested in future lattice simulations.

Elastic scattering amplitudes forI=0DKandI=0,1DK¯are computed inS,PandDpartial waves using lattice QCD with light-quark masses corresponding tomπ=239MeV andmπ=391MeV. TheS-waves contain interesting features including a near-thresholdJP=0+bound state inI=0DK, corresponding to theD∗s0(2317), with an effect that is clearly visible above threshold, and suggestions of a0+virtual bound state inI=0DK¯. TheS-waveI=1DK¯amplitude is found to be weakly repulsive. The computed finite-volume spectra also contain a deeply-boundD∗vector resonance, but negligibly smallP-waveDKinteractions are observed in the energy region considered; thePandD-waveDK¯amplitudes are also small. There is some evidence of1+and2+resonances inI=0DKat higher energies.

We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violatingK???weak decay, the isospin-breakingη???QCD transition, and the electromagneticγ?????amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonicg??.

We present the first determination of the hadronic decays of the lightest exoticJPC=1−+resonance in lattice QCD. Working with SU(3) flavor symmetry, where the up, down and strange quark masses approximately match the physical strange-quark mass givingmπ∼700MeV, we compute finite-volume spectra on six lattice volumes which constrain a scattering system featuring eight coupled channels. Analytically continuing the scattering amplitudes into the complex energy plane, we find a pole singularity corresponding to a narrow resonance which shows relatively weak coupling to the open pseudoscalar--pseudoscalar, vector--pseudoscalar and vector--vector decay channels, but large couplings to at least one kinematically-closed axial-vector--pseudoscalar channel. Attempting a simple extrapolation of the couplings to physical light-quark mass suggests a broadπ1resonance decaying dominantly through theb1πmode with much smaller decays intof1π,ρπ,η′πandηπ. A large total width is potentially in agreement with the experimentalπ1(1564)candidate state, observed inηπ,η′π, which we suggest may be heavily suppressed decay channels.

We study decomposition ofSU(2)gauge field into monopole and monopoleless components. After fixing the Maximal Abelian gauge inSU(2)lattice gauge theory we decompose the nonabelian gauge field into the Abelian field created by monopoles and the modified nonabelian field with monopoles removed. We then calculate respective static potentialis and show that the potential due to the modified nonabelian field is nonconfining while, as is well known, the Abelian field produces linear potential. We further find that the sum of these potentials approximates the nonabelian static potential with good precision at all distances considered. We conclude that at large distances the monopole field potential describes the classical energy of the hadronic string while the static potential due to the modified nonabelian field describes the string fluctuations energy.

I discuss the deconfinement transition in 2+1 flavor QCD in terms of Polyakov loops as well as the hadron resonance gas for hadrons containing static quarks and charm quarks.