Focus on lattice QCD

The structure of the tetraquark candidate ${Z}_{{\rm{c}}}(3900)$, which has been experimentally reported in ${e}^{+}{e}^{-}$ collisions, is studied by s-wave meson–meson coupled-channel scattering on the lattice. The s-wave interactions among the $\pi J/\psi$, $\rho {\eta }_{{c}}$ and $D{\bar{D}}^{* }$ channels are derived from (2 + 1)-flavor dynamical QCD simulations at ${m}_{\pi }=410$–700 MeV. It is found that the interactions are dominated by the off-diagonal $\pi J/\psi$–$D{\bar{D}}^{* }$ and $\rho {\eta }_{{c}}$–$D{\bar{D}}^{* }$ couplings. With the interactions obtained, the s-wave two-body amplitudes and the pole position in $\pi J/\psi$–$\rho {\eta }_{{c}}$–$D{\bar{D}}^{* }$ coupled-channel scattering are calculated. The results show that ${Z}_{{c}}(3900)$ is not a conventional resonance but a threshold cusp. A semiphenomenological analysis with the coupled-channel interaction to the experimentally observed decay mode is also presented to confirm the conclusion.

The influence of centre vortices on dynamical chiral symmetry breaking is investigated through the light hadron spectrum on the lattice. Recent studies of the quark propagator and other quantities have provided evidence that centre vortices are the fundamental objects underpinning dynamical chiral symmetry breaking in $\mathrm{SU}(3)$ gauge theory. For the first time, we use the chiral overlap fermion action to study the low-lying hadron spectrum on lattice ensembles consisting of Monte Carlo, vortex-removed, and vortex-projected gauge fields. We find that gauge field configurations consisting solely of smoothed centre vortices are capable of reproducing all the salient features of the hadron spectrum, including dynamical chiral symmetry breaking. The hadron spectrum on vortex-removed fields shows clear signals of chiral symmetry restoration at light values of the bare quark mass, while at heavy masses the spectrum is consistent with a theory of weakly interacting constituent quarks.

We study the relation between quark confinement and chiral symmetry breaking in QCD. Using lattice QCD formalism, we analytically express the various 'confinement indicators', such as the Polyakov loop, its fluctuations, the Wilson loop, the inter-quark potential and the string tension, in terms of the Dirac eigenmodes. In the Dirac spectral representation, there appears a power of the Dirac eigenvalue ${\lambda }_{n}$ such as ${\lambda }_{n}^{{N}_{t}-1}$, which behaves as a reduction factor for small ${\lambda }_{n}$. Consequently, since this reduction factor cannot be cancelled, the low-lying Dirac eigenmodes give negligibly small contribution to the confinement quantities, while they are essential for chiral symmetry breaking. These relations indicate that there is no direct one-to-one correspondence between confinement and chiral symmetry breaking in QCD. In other words, there is some independence of quark confinement from chiral symmetry breaking, which can generally lead to different transition temperatures/densities for deconfinement and chiral restoration. We also investigate the Polyakov loop in terms of the eigenmodes of the Wilson, the clover and the domain-wall fermion kernels, and find similar results. The independence of quark confinement from chiral symmetry breaking seems to be natural, because confinement is realized independently of quark masses and heavy quarks are also confined even without the chiral symmetry.

We review recent results on the phase structure of quantum chromodynamics (QCD) and bulk QCD thermodynamics. In particular, we discuss how universal critical scaling related to spontaneous breaking of the chiral symmetry manifests itself in recent lattice QCD simulations and how the knowledge on non-universal scaling parameters can be utilized in the exploration of the QCD phase diagram. We also show how various (generalized) susceptibilities can be employed to characterize properties of QCD matter at low and high temperatures, related to deconfining aspects of the QCD transition. Finally, we highlight the recent efforts towards understanding how lattice QCD calculation can provide input for our understanding of the matter created in heavy ion collisions and in particular on the freeze-out conditions met in the hydrodynamic evolution of this matter.

For many years chiral effective theory (ChEFT) has enabled and supported lattice QCD calculations of hadron observables by allowing systematic effects from unphysical lattice parameters to be controlled. In the modern era of precision lattice simulations approaching the physical point, ChEFT techniques remain valuable tools. In this review we discuss the modern uses of ChEFT applied to lattice studies of hadron structure in the context of recent determinations of important and topical quantities. We consider muon $g-2$, strangeness in the nucleon, the proton radius, nucleon polarizabilities, and sigma terms relevant to the prediction of dark-matter–hadron interaction cross-sections, among others.