Topological fluctuations in Two flavors Lattice QCD

Light quark masses, chiral condensate and quark–gluon condensate in quenched lattice QCD with exact chiral symmetry

We calculate pion mass, pion decay constant, PCAC quark mass and nucleon mass in two flavour lattice QCD with unimproved Wilson fermion and gauge actions. Simulations are performed using DD-HMC algorithm at two lattice spacings and two volumes for several values of the quark mass. The cutoff effects in pion mass and nucleon mass for the explored region of parameter space are found to be negligible. We extract the average value of the up–down quark mass in the MS¯ scheme at 2 GeV, which is in good agreement with the world data. The chiral behaviours of pion mass, pion decay constant and quark condensate are found to be qualitatively consistent with NLO chiral perturbation theory. The extracted values of the pion decay constant and the chiral condensate are in reasonable agreement with the world data.

We solve the coupled system of Dyson-Schwinger and Bethe-Salpeter equations for the quark propagator and the pion Bethe-Salpeter amplitude on a finite volume. To this end we use a truncation scheme that includes pion cloud effects in the quark propagator and light mesons. We study volume effects in the quark condensate, the pion mass and the pion decay constant and compare to corresponding results in other approaches. In general we find large effects for volumes below V=(1.8 fm)^4.

Chiral and topological properties of the QCD vacuum are studied on a lattice for the confinement and the quark‐gluon plasma phase. We observe in both phases a suppression of chiral and topological fluctuations in the vicinity of static mesons. The formation of a flux tube between the static quark‐antiquark pair is clearly visible in the confinement phase. In the plasma phase a global decrease of the quark condensate and the topological susceptibility takes place.

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We present lattice QCD results for masses and magnetic polarizabilities of light and strange pseudoscalar mesons, chiral condensates, decay constants of neutral pion, and neutral kaon in the presence of background magnetic fields with $eB$ ranging up to around $3.35\text{ }\text{ }{\mathrm{GeV}}^{2}$ ($\ensuremath{\sim}70{M}_{\ensuremath{\pi}}^{2}$) in the vacuum. The computations were carried out in ($2+1$)-flavor QCD mostly on ${32}^{3}\ifmmode\times\else\texttimes\fi{}96$ lattices using the highly improved staggered quark action with ${M}_{\ensuremath{\pi}}\ensuremath{\approx}220\text{ }\text{ }\mathrm{MeV}$ at zero temperature. We find that the masses of neutral pseudoscalar mesons monotonously decrease as the magnetic field strength grows and then saturate at a nonzero value, while there exists a nonmonotonous behavior of charged pion and kaon masses in the magnetic field. We observe a $qB$ scaling of the up and down quark flavor components of neutral pion mass, neutral pion decay constant as well as the quark chiral condensates at $0.05\ensuremath{\lesssim}eB\ensuremath{\lesssim}3.35\text{ }\text{ }{\mathrm{GeV}}^{2}$. We show that the correction to the Gell-Mann-Oakes-Renner relation involving the neutral pion is less than 6% and the correction for the relation involving neutral kaon is less than 30% at $eB\ensuremath{\lesssim}3.35\text{ }\text{ }{\mathrm{GeV}}^{2}$. We also derive the Ward-Takahashi identities for QCD in the magnetic field in the continuum formulation including the relation between integrated neutral pseudoscalar meson correlators and chiral condensates.

The influence of temperature on the pion decay constant and the two-photon decay of π0 is considered near the chiral symmetry restoration point. We analyze how the mass and decay width relate to each other and find that the π0 decay width in hot matter is suppressed, provided that the pion mass vanishes at the critical point; it diverges if pion mass remains finite while quark condensate is dissolved at T c .

We measure the topological charge of the gauge configurations generated by lattice simulations of 2 flavors QCD on a $ 16^3 \times 32 $ lattice, with Optimal Domain-Wall Fermion (ODWF) at $ N_s = 16 $ and plaquette gauge action at $ \beta = 5.90 $. Using the Adaptive Thick-Restart Lanczos algorithm, we project the low-lying modes of the 4D effective Dirac operator of ODWF, and obtain the topological charge and topological susceptibility. Our result of topological susceptibility agrees with the sea-quark mass dependence predicted by the chiral perturbation theory, and provides a determination of the chiral condensate.

We present a systematic study of the effectiveness of light quark mass reweighting. This method allows a single lattice QCD ensemble, generated with a specific value of the dynamical light quark mass, to be used to determine results for other, nearby light dynamical quark masses. We study two gauge field ensembles generated with 2+1 flavors of dynamical domain wall fermions with light quark masses m_l=0.02 (m_\pi=620 MeV) and m_l=0.01 (m_\pi=420 MeV). We reweight each ensemble to determine results which could be computed directly from the other and check the consistency of the reweighted results with the direct results. The large difference between the 0.02 and 0.01 light quark masses suggests that this is an aggressive application of reweighting as can be seen from fluctuations in the magnitude of the reweighting factor by four orders of magnitude. Never-the-less, a comparison of the reweighed topological charge, average plaquette, residual mass, pion mass, pion decay constant, and scalar correlator between these two ensembles shows agreement well described by the statistical errors. The issues of the effective number of configurations and finite sample size bias are discussed. An examination of the topological charge distribution implies that it is more favorable to reweight from heavier mass to lighter quark mass.

We study the θ-vacuum of QCD using two-flavor chiral perturbation theory (χPT) in the presence of a uniform, background magnetic field calculating the magnetic field-dependent free energy density, the topological density, the topological susceptibility and the fourth cumulant at one-loop order. We find that the topological susceptibility is enhanced by the magnetic field while the fourth topological cumulant is diminished at weak fields and enhanced at larger fields when θ=0. However, in the QCD vacuum with θ≠0, the topological susceptibility can be either monotonically enhanced or diminished relative to their θ-vacuum values. The fourth cumulant also exhibits monotonic enhancement or suppression except for regions of θ near 0 and 2π, where it is both diminished and enhanced. Finally, the topological density is enhanced for all magnetic fields with its relative shift being identical to the relative shift of the up and down quark condensates in the θ-vacuum.

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson bound state amplitudes and the dressed quark-W vertex in a manifestly covariant calculation of the K_{l3} transition form factors and decay width in impulse approximation. With model gluon parameters previously fixed by the chiral condensate, the pion mass and decay constant, and the kaon mass, our results for the K_{l3} form factors and the kaon semileptonic decay width are in good agreement with the experimental data.

The topological susceptibility is one of the quantities that has a large discretization error, and the error can be sensitive to the choice of fermion action. We report on our results from physical point simulations with 2+1 flavor Möbius domain wall fermion at finite temperature. We also present the chiral condensate and disconnected susceptibility. The temporal lattice size is Nt=12 and 16, and the temperature range is around 140 MeV to 250 MeV for the chiral condensate and susceptibility. A coarse lattice with Nt=10 covers up to 500 MeV to measure the topological susceptibility.

We investigate topology in lattice simulations of QCD with two flavors of dynamical Wilson fermions. At various sea quark masses we find reasonable agreement between results for the topological charge from fermionic and gluonic definitions, the latter with cooling. We study correlations of the topological charge with light hadronic observables and find effects in the flavor singlet pseudoscalar channel. The quark mass dependence of the topological susceptibility $\ensuremath{\chi}$ is consistent with the leading order small ${m}_{\ensuremath{\pi}}$ expectation, $\ensuremath{\chi}{=f}_{\ensuremath{\pi}}^{2}{m}_{\ensuremath{\pi}}^{2}/4.$

We calculate the pion mass from Goldstone modes in the Higgs mechanism related to the neutron decay. The Goldstone pion modes acquire mass by a vacuum misalignment of the Higgs field. The size of the misalignment is controlled by the ratio between the electronic and the nucleonic energy scales. The nucleonic energy scale is involved in the neutron to proton transformation and the electronic scale is involved in the related creation of the electronic state in the course of the electroweak neutron decay. The respective scales influence the mapping of the intrinsic configuration spaces used in our description. The configuration spaces are the Lie groups U(3) for the nucleonic sector and U(2) for the electronic sector. These spaces are both compact and lead to periodic potentials in the Hamiltonians in coordinate space. The periodicity and strengths of these potentials control the vacuum misalignment and lead to a pion mass of 135.2(1.5) MeV with an uncertainty mainly from the fine structure coupling at pionic energies. The pion decay constant 92 MeV results from comparing the fourth-order self-coupling in an effective pion field theory with the corresponding fourth-order term in the Higgs potential. We suggest analogies with the Goldberger-Treiman relation.

We compute the topological susceptibility $\chi_t$ of lattice QCD with $2+1$ dynamical quark flavors described by the M\"obius domain wall fermion. Violation of chiral symmetry as measured by the residual mass is kept at $\sim$1 MeV or smaller. We measure the fluctuation of the topological charge density in a `slab' sub-volume of the simulated lattice using the method proposed by Bietenholz {\it et al.} The quark mass dependence of $\chi_t$ is consistent with the prediction of chiral perturbation theory, from which the chiral condensate is extracted as $\Sigma^{\overline{\rm MS}} (\mbox{2GeV}) = [274(13)(29)\mbox{MeV}]^3$, where the first error is statistical and the second one is systematic. Combining the results for the pion mass $M_\pi$ and decay constant $F_\pi$, we obtain $\chi_t = 0.229(03)(13)M_\pi^2F_\pi^2$ at the physical point.