The chiral susceptibility, or the first derivative of the chiral condensate with respect to the quark mass, is often used as a probe for the QCD phase transition since the chiral condensate is an order parameter of SU(2)L × SU(2)R symmetry breaking. However, the chiral condensate also breaks the axial U(1) symmetry, which is usually not paid attention to as it is already broken by anomaly. We investigate the susceptibilities in the scalar and pseudoscalar channels in order to quantify how much the axial U(1) anomaly contributes to the chiral phase transition. Employing a chirally symmetric lattice Dirac operator, and its eigenmode decomposition, we separate the axial U(1) breaking effects from others. Our result in two-flavor QCD indicates that the chiral susceptibility is dominated by the axial U(1) anomaly at temperatures T ∼ 190 MeV after the quadratically divergent constant is subtracted. 1 ar X iv :2 10 3. 05 95 4v 2 [ he pla t] 1 8 M ar 2 02

We investigate the axial U(1) anomaly of two-flavor QCD at temperatures 190--330 MeV. In order to preserve precise chiral symmetry on the lattice, we employ the Mobius domain-wall fermion action as well as overlap fermion action implemented with a stochastic reweighting technique. Compared to our previous studies, we reduce the lattice spacing to 0.07 fm, simulate larger multiple volumes to estimate finite size effect, and take more than four quark mass points, including one below physical point to investigate the chiral limit. We measure the topological susceptibility, axial U(1) susceptibility, and examine the degeneracy of U(1) partners in meson and baryon correlators. All the data above the critical temperature indicate that the axial U(1) violation is consistent with zero within statistical errors. The quark mass dependence suggests disappearance of the U(1) anomaly at a rate comparable to that of the SU(2)_L x SU(2)_R symmetry breaking.

We compute the topological susceptibility chi(t) of lattice QCD with 2+1 dynamical quark flavors described by the Mobius domain-wall fermion. Violation of chiral symmetry as measured by the residual mass is kept at similar to 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 byW. Bietenholz, P. de Forcrand, and U. Gerber, J. High Energy Phys. 12, 070 (2015) and W. Bietenholz, K. Cichy, P. de Forcrand, A. Dromard, and U. Gerber, PoS LATTICE 2016, 321 (2016). 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((MS) over bar)(2 GeV) = [274(13)(29) 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 F pi 2)-F-2 at the physical point.

Received 16 October 2017DOI:https://doi.org/10.1103/PhysRevD.96.079902© 2017 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasLattice QCDQCD phase transitionsQuantum chromodynamicsNuclear Physics

We calculate the form factors of the $K \to \pi l \nu$ semileptonic decays in three-flavor lattice QCD, and study their chiral behavior as a function of the momentum transfer and the Nambu-Goldstone boson masses. Chiral symmetry is exactly preserved by using the overlap quark action, which enables us to directly compare the lattice data with chiral perturbation theory (ChPT). We generate gauge ensembles at a lattice spacing of 0.11fm with four pion masses covering 290-540 MeV and a strange quark mass m_s close to its physical value. By using the all-to-all quark propagator, we calculate the vector and scalar form factors with high precision. Their dependence on m_s and the momentum transfer is studied by using the reweighting technique and the twisted boundary conditions for the quark fields. We compare the results for the semileptonic form factors with ChPT at next-to-next-to leading order in detail. While many low-energy constants appear at this order, we make use of our data of the light meson electromagnetic form factors in order to control the chiral extrapolation. We determine the normalization of the form factors as f_+(0) = 0.9636(36)(+57/-35), and observe reasonable agreement of their shape with experiment.

A Wolter-type 4-mirror system was designed and evaluated by ray-trace calculation. The design and fabrication process were developed. The master mandrel of oxygen-free copper was shaped by diamond turning. The Pyrex glass replica was made by a vacuum replication technique. A visible light image of a metal mesh could be obtained using this replica mirror.

We study the axial U(1) symmetry at a finite temperature in two-flavor lattice QCD. Employing the Mobius domain-wall fermions, we generate gauge configurations slightly above the critical temperature Tc with different lattice sizes L = 2-4 fm. Our action allows frequent topology tunneling while keeping good chiral symmetry close enough to that of overlap fermions. This allows us to recover full chiral symmetry by an overlap/domain-wall reweighting. Above the phase transition, a strong suppression of the low-lying modes is observed in both overlap and domain-wall Dirac spectra. We, however, find a sizable violation of the Ginsparg-Wilson relation in the Mobius domain-wall Dirac eigenmodes, which dominates the signals of the axial U(1) symmetry breaking near the chiral limit. We also find that the use of the overlap fermion only in the valence sector is dangerous since it suffers from the artifacts due to partial quenching. Reweighting the Mobius domain-wall fermion determinant to that of the overlap fermion, we observe the axial U(1) breaking to vanish in the chiral limit, which is stable against the changes of the lattice volume and lattice spacing.

We present a study of chiral behavior of light meson form factors in QCD with three flavors of overlap quarks. Gauge ensembles are generated at single lattice spacing 0.12 fm with pion masses down to 300 MeV. The pion and kaon electromagnetic form factors and the kaon semileptonic form factors are precisely calculated using the all-to-all quark propagator. We discuss their chiral behavior using the next-to-next-to-leading order chiral perturbation theory.

We study the chiral behavior of the electromagnetic (EM) form factors of pions and kaons in three-flavor lattice QCD. In order to make a direct comparison of the lattice data with chiral perturbation theory (ChPT), we employ the overlap quark action that has exact chiral symmetry. Gauge ensembles are generated at a lattice spacing of 0.11 fm with four pion masses ranging between M-pi similar or equal to 290 MeV and 540 MeV and with a strange quark mass m(s) close to its physical value. We utilize the all-to-all quark propagator technique to calculate the EM form factors with high precision. Their dependence on ms and on the momentum transfer is studied by using the reweighting technique and the twisted boundary conditions for the quark fields, respectively. A detailed comparison with SU(2) and SU(3) ChPT reveals that the next-to-next-to-leading order terms in the chiral expansion are important to describe the chiral behavior of the form factors in the pion mass range studied in this work. We estimate the relevant low-energy constants and the charge radii, and find reasonable agreement with phenomenological and experimental results.

Global topological charge decorrelates very slowly or even freezes in fine lattice simulations.On the other hand, its local fluctuations are expected to survive and lead to the correct physical results as long as the volume is large enough.We investigate this issue on recently generated configurations including dynamical domain-wall fermions at lattice spacings a = 0.08 fm and finer.We utilize the Yang-Mills gradient flow to define the topological charge density operator and calculate its long-distance correlation, through which we propose a new method for extracting the topological susceptibility in a sub-volume.This method takes care of the finite volume correction, which reduces the bias caused by the global topological charge.Our lattice data clearly show a shorter auto-correlation time than that of the naive definition using the whole lattice, and are less sensitive to the global topological history.Numerical results show a clear sea-quark mass dependence, which agrees well with the prediction of chiral perturbation theory.

The flavor-singlet component of the eta' meson is related to the topological structure of the SU(3) gauge field through the chiral anomaly. We perform a 2 + 1-flavor lattice QCD calculation and demonstrate that the two-point function of a gluonically defined topological charge density after a short Yang-Mills gradient flow contains the propagation of the eta' meson, by showing that its mass in the chiral and continuum limit is consistent with the experimental value. The gluonic correlator does not suffer from the contamination of the pion contribution, and the clean signal is obtained at significantly lower numerical cost compared to the conventional method with the quark bilinear operators.

We carry out a comparative study among five-dimensional formulations of chirally symmetric fermions about the algorithmic performance, chiral symmetry violation and topological tunneling to find a computationally inexpensive formulation with good chiral symmetry. With our choice of the lattice action, we have launched large-scale simulations on fine lattices aiming at a precision study of light and heavy quark physics. We report on the comparative study, current status of the large-scale simulations, and preliminary results on the residual quark mass and auto-correlation.

We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the eigenvalues are not significantly affected. We discuss the possibility of reweighting the gauge configurations generated with domain-wall fermions to those of exactly chiral lattice fermions.

We present a first attempt to determine nucleon–nucleon potentials in the parity-odd sector, which appear in the P11, P03, P13, P23–F23 channels, in Nf=2 lattice QCD simulations. These potentials are constructed from the Nambu–Bethe–Salpeter wave functions for JP=0−,1− and 2−, which correspond to the A1−, T1− and T2−⊕E− representation of the cubic group, respectively. We have found a large and attractive spin–orbit potential VLS(r) in the isospin-triplet channel, which is qualitatively consistent with the phenomenological determination from the experimental scattering phase shifts. The potentials obtained from lattice QCD are used to calculate the scattering phase shifts in the P11, P03, P13 and P23–F23 channels. The strong attractive spin–orbit force and a weak repulsive central force in spin-triplet P-wave channels lead to an attraction in the P23 channel, which is related to the P-wave neutron paring in neutron stars.

We calculate the electromagnetic pion form factor in lattice QCD with 2+1 flavors of the dynamical overlap quarks. Up and down quark masses are set below their physical values so that the system is in the so-called epsilon regime with the small size of our lattice ~ 1.8 fm. The finite volume corrections are generally expected to be ~ 100% in the epsilon regime. We, however, find a way to automatically cancel the dominant part of them. Inserting non-zero momenta and taking appropriate ratios of the two and three point functions, we can eliminate the contribution from the zero-momentum pion mode. Then the remaining finite volume effect is a small perturbation from the non-zero modes. Our lattice data agree with this theoretical prediction and the extracted pion charge radius is consistent with the experiment.

We investigate the charmed-baryon mass spectrum using the relativistic heavy-quark action on 2 + 1 flavor PACS-CS configurations previously generated on a 32(3) x 64 lattice. The dynamical up-down-and strange-quark masses are tuned to their physical values, reweighted from those employed in the configuration generation. At the physical point, the inverse lattice spacing determined from the Omega baryon mass gives a(-1) = 2.194(10) GeV, and thus the spatial extent equals L = 32a = 2.88(1) fm. Our results for the charmed-baryon masses are consistent with experimental values, except for the mass of Xi(cc), which has been measured by only one experimental group so far and has not been confirmed yet by others. In addition, we report values of other doubly and triply charmed baryon masses, which have never been measured experimentally.

We calculate the kaon semileptonic form factors in lattice QCD with three flavors of dynamical overlap quarks. Gauge ensembles are generated at pion masses as low as 290 MeV and at a strange quark mass near its physical value. We precisely calculate relevant meson correlators using the all-to-all quark propagator. Twisted boundary conditions and the reweighting technique are employed to vary the momentum transfer and the strange quark mass. We discuss the chiral behavior of the form factors by comparing with chiral perturbation theory and experiments.

We present our progress report on 1+1+1 flavor QCD+QED simulation at the physical point. Calculations are carried out with 2+1 flavor QCD gauge configurations generated by the PACS-CS Collaboration. The dynamical QED effect and the up-down quark mass difference are incorporated by the reweighting technique. We also discuss some physics results.

We study the equation of state in $2+1$ flavor QCD with nonperturbatively improved Wilson quarks coupled with the renormalization group-improved Iwasaki glue. We apply the $T$-integration method to nonperturbatively calculate the equation of state by the fixed-scale approach. With the fixed-scale approach, we can purely vary the temperature on a line of constant physics without changing the system size and renormalization constants. Unlike the conventional fixed-${N}_{t}$ approach, it is easy to keep scaling violations small at low temperature in the fixed-scale approach. We study $2+1$ flavor QCD at light quark mass corresponding to ${m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}}\ensuremath{\simeq}0.63$, while the strange quark mass is chosen around the physical point. Although the light quark masses are still heavier than the physical values, our equation of state is roughly consistent with recent results with highly improved staggered quarks at large ${N}_{t}$.

We study the phase structure of QCD at high temperature and density by lattice QCD simulations adopting a histogram method. We try to solve the problems which arise in the numerical study of the finite density QCD, focusing on the probability distribution function (histogram). As a first step, we investigate the quark mass dependence and the chemical potential dependence of the probability distribution function as a function of the Polyakov loop when all quark masses are sufficiently large, and study the properties of the distribution function. The effect from the complex phase of the quark determinant is estimated explicitly. The shape of the distribution function changes with the quark mass and the chemical potential. Through the shape of the distribution, the critical surface which separates the first order transition and crossover regions in the heavy quark region is determined for the 2+1-flavor case.