Search

We investigate relations between the chiral susceptibility and axial $U(1)$ anomaly in lattice QCD at high temperatures. Employing the exactly chiral symmetric Dirac operator, we separate the purely axial $U(1)$ breaking effect in the connected and disconnected chiral susceptibilites in a theoretically clean manner. Preliminary results for two-flavor lattice QCD near the critical temperature are presented., Comment: 9 pages, 3 figures, LATTICE2023, minor corrections

We calculate the form factors for the $B \to D^*\ell\nu_\ell$ decay in 2+1 flavor lattice QCD. For all quark flavors, we employ the M\"obius domain-wall action, which preserves chiral symmetry to a good precision. Our gauge ensembles are generated at three lattice cutoffs $a^{-1} \sim 2.5$, 3.6 and 4.5 GeV with pion masses as low as $M_\pi \sim 230$ MeV. The physical lattice size $L$ satisfies the condition $M_\pi L \geq 4$ to control finite volume effects (FVEs), while we simulate a smaller size at the smallest $M_\pi$ to directly examine FVEs. The bottom quark masses are chosen in a range from the physical charm quark mass to $0.7 a^{-1}$ to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses based on heavy meson chiral perturbation theory at next-to-leading order. Then the recoil parameter dependence is parametrized using a model independent form leading to our estimate of the decay rate ratio between the tau ($\ell = \tau$) and light lepton ($\ell = e,\mu$) channels $R(D^*) = 0.252(22)$ in the Standard Model. A simultaneous fit with recent data from the Belle experiment yields $|V_{cb}| = 39.19(91)\times 10^{-3}$, which is consistent with previous exclusive determinations, and shows good consistency in the kinematical distribution of the differential decay rate between the lattice and experimental data., Comment: 45 pages, 19 figures; v2: version published in PRD

We calculate the $B \to D^{(*)} \ell \nu$ form factors in 2+1 flavor relativistic lattice QCD by employing the M\"obius domain-wall action for all quark flavors. Our simulations are carried out at lattice cut-offs $a^{-1} \sim 2.5$, 3.6 and 4.5 GeV with the bottom quark masses up to 0.7 $a^{-1}$ to control discretization effects. We extrapolate the form factors to the continuum limit and physical quark masses, and discuss systematic uncertainties of the form factors., Comment: 9 pages, 4 figures, talk presented at the 38th International Symposium on Lattice Field Theory (LATTICE2021), 26th-30th July, 2021, Zoom/Gather@MIT, USA

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. We consider nucleon matrix elements, and review the determinations of the axial, scalar and tensor bilinears, both isovector and flavor diagonal. Finally, in this review we have added a new section reviewing determinations of scale-setting quantities., Comment: 418 pages, 53 figures, 200 tables, 1056 references. Minor changes, version as published in EPJC. arXiv admin note: substantial text overlap with arXiv:1902.08191, arXiv:1607.00299, arXiv:1310.8555

In the early days of QCD, the axial $U(1)$ anomaly was considered as a trigger for the breaking of the $SU(2)_L\times SU(2)_R$ symmetry through topological excitations of gluon fields. However, it has been a challenge for lattice QCD to quantify the effect. In this work, we simulate QCD at high temperatures with chiral fermions. The exact chiral symmetry enables us to separate the contribution from the axial $U(1)$ breaking from others among the susceptibilities in the scalar and pseudoscalar channels. Our result in two-flavor QCD indicates that the chiral susceptibility, which is conventionally used as a probe for $SU(2)_L\times SU(2)_R$ breaking, is actually dominated by the axial $U(1)$ breaking at temperatures $T\ge 165$ MeV., Comment: 9 pages, 3 figures, contribution to LATTICE 2021, published version

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 $SU(2)_L \times SU(2)_R$ 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 and apparently gives little impact on the transition. We investigate the susceptibilities in the scalar and pseudoscalar channels in order to quantify how much the axial $U(1)$ breaking 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 both of the connected and disconnected chiral susceptibilities are dominated by the axial $U(1)$ breaking at temperatures $T\gtrsim 190$ MeV after the quadratically divergent constant is subtracted., Comment: 16 pages, 6 figures, to appear in PTEP

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., Comment: 40 pages, 19 figures, the version published in PRD

We report on our calculation of the B \to D^(*) \ell \nu form factors in 2+1 flavor lattice QCD. The M\"obius domain-wall action is employed for light, strange, charm and bottom quarks. At lattice cutoffs 1/a \sim 2.4, 3.6 and 4.5 GeV, we simulate bottom quark masses up to 0.7/a to control discretization errors. The pion mass is as low as 230 MeV. We extrapolate the form factors to the continuum limit and physical quark masses, and make a comparison with recent phenomenological analyses., Comment: 7 pages, 4 figures, talk presented at the 37th International Symposium on Lattice Field Theory (Lattice2019), 16-22 June 2019, Wuhan, China

Properties of QCD matter change significantly around the chiral crossover temperature, and the effects on $U(1)_A$ and topological susceptibilities, as well as the meson spectrum have been studied with much care. Baryons and the effect of parity doubling in this temperature range have been analyzed previously by various other groups employing different setups. Here we construct suitable operators to investigate chiral and axial $U(1)_A$ symmetries in the baryon spectrum. Measurements for different volumes and quark-masses are done with two flavors of chirally symmetric domain-wall fermions at temperatures above the critical one. The possibility of emergent $SU(4)$ and $SU(2)_{CS}$ symmetries is discussed., Comment: 7 pages, 4 figures, talk presented at the 37th International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China. Updated numerical data in Fig. 1 and Fig. 2

We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $SU(2)_L\times SU(2)_R$ and $SU(3)_L\times SU(3)_R$ Chiral Perturbation Theory. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for $D$- and $B$-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal., Comment: 458 pages, 46 figures, 209 tables, 1146 references. Minor changes, version as published in EPJC. arXiv admin note: substantial text overlap with arXiv:1607.00299, arXiv:1310.8555

Based on a complete set of $J = 0$ and $J=1$ spatial isovector correlation functions calculated with $N_F = 2$ domain wall fermions we identify an intermediate temperature regime of $T \sim 220 - 500$ MeV ($1.2T_c$--$2.8T_c$), where chiral symmetry is restored but the correlators are not yet compatible with a simple free quark behavior. More specifically, in the temperature range $T \sim 220 - 500$ MeV we identify a multiplet structure of spatial correlators that suggests emergent $SU(2)_{CS}$ and $SU(4)$ symmetries, which are not symmetries of the free Dirac action. The symmetry breaking effects in this temperature range are less than 5%. Our results indicate that at these temperatures the chromo-magnetic interaction is suppressed and the elementary degrees of freedom are chirally symmetric quarks bound into color-singlet objects by the chromo-electric component of the gluon field. At temperatures between 500 and 660 MeV the emergent $SU(2)_{CS}$ and $SU(4)$ symmetries disappear and one observes a smooth transition to the regime above $T \sim 1$ GeV where only chiral symmetries survive, which are finally compatible with quasi-free quarks., Comment: A new figure and discussion added. Accepted for publication in PRD

We study the topological charge in $N_f=2$ QCD at finite temperature using M\"obius domain-wall fermions. The susceptibility $\chi_t$ of the topological charge defined either by the index of overlap Dirac operator or a gluonic operator is investigated at several values of temperature $T\ (>T_c)$ varying the quark mass. A strong suppression of the susceptibility is observed below a certain value of the quark mass. The relation with the restoration of $U_A(1)$ is discussed., Comment: 8 pages, 8 figures, Proceedings of the 35th International Symposium on Lattice Field Theory, June 18-24, 2017, Granada, Spain

We study spatial isovector meson correlators in $N_f=2$ QCD with dynamical domain-wall fermions on $32^3\times 8$ lattices at temperatures $T=220-380$ MeV. We measure the correlators of spin-one ($J=1$) operators including vector, axial-vector, tensor and axial-tensor. Restoration of chiral $U(1)_A$ and $SU(2)_L \times SU(2)_R$ symmetries of QCD implies degeneracies in vector--axial-vector ($SU(2)_L \times SU(2)_R$) and tensor--axial-tensor ($U(1)_A$) pairs, which are indeed observed at temperatures above $T_c$. Moreover, we observe an approximate degeneracy of all $J=1$ correlators with increasing temperature. This approximate degeneracy suggests emergent $SU(2)_{CS}$ and $SU(4)$ symmeries at high temperatures, that mix left- and right-handed quarks., Comment: This revised version contains all corrections that will appear in the forthcoming erratum

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., Comment: 23pages, 10figures, metadata abstract corrected

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., Comment: 34 pages, 13 figures

We study the vector and axial-vector current correlators in perturbative and non-perturbative regimes of QCD. The correlators in Euclidean coordinate space are calculated on the lattice using the M\"obius domain-wall fermion formulation at three lattice spacings covering 0.044--0.080~fm. The dynamical quark effects of $2+1$ light flavors are included. The sum $V+A$ and the difference $V-A$ of the vector ($V$) and axial-vector ($A$) current correlators calculated on the lattice after extrapolating to the physical point agree with those converted from the ALEPH experimental data of hadronic $\tau$ decays. The level of the agreement in the $V+A$ channel is about $1.3\sigma$ or smaller in the region of $|x|\ge0.4$~fm, while that in the $V-A$ channel is about $1.8\sigma$ at $|x|=0.74$~fm and smaller at other distances. We also extract the hiral condensate from the short-distance correlators on the lattice using the PCAC relation. Its result extrapolated to the chiral and continuum limit is compatible with other estimates at low energies., Comment: 32 pages, 19 figures

We report on our study of the D meson semileptonic decays in 2+1 flavor lattice QCD. Gauge ensembles are generated at three lattice cutoffs up to 4.5 GeV and with pion masses as low as 300 MeV. We employ the Moebius domain-wall fermion action for both light and charm quarks. We report our preliminary results for the vector and scalar form factors and discuss their dependence on the momentum transfer, quark masses and lattice spacing., Comment: 7 pages, 4 figures, talk presented at the 34th International Symposium on Lattice Field Theory (Lattice 2016), 24-30 July 2016, University of Southampton, UK

We study the axial U(1) symmetry at 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 of 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 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., Comment: 29 pages, 14 figures, references are updated

We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in the semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory. We review the determination of the BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. The latter quantities are an addition compared to the previous review. For the heavy-quark sector, we provide results for mc and mb (also new compared to the previous review), as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. Finally, we review the status of lattice determinations of the strong coupling constant alpha_s., Comment: 383 pages, 32 figures, 160 tables, 795 references

We determine the renormalization constants for flavor non-singlet fermion bilinear operators of M\"obius domain-wall fermions. The renormalization condition is imposed on the correlation functions in the coordinate space, such that the non-perturbative lattice calculation reproduces the perturbatively calculated counterpart at short distances. The perturbative expansion is precise as the coefficients are available up to $O(\alpha_s^4)$. We employ $2+1$-flavor lattice ensembles at three lattice spacings in the range 0.044--0.080~fm., Comment: 36 pages, 20 figures

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., Comment: 7 pages, 4 figures, Proceedings of the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japan

We calculate the spectral function of the QCD Dirac operator using the four-dimensional effective operator constructed from the Mobius domain-wall implementation. We utilize the eigenvalue filtering technique combined with the stochastic estimate of the mode number. The spectrum in the entire eigenvalue range is obtained with a single set of measurements. Results on 2+1-flavor ensembles with Mobius domain-wall sea quarks at lattice spacing ~ 0.08 fm are shown., Comment: 7 pages, 4 figures, presented at the 33rd International Symposium on Lattice Field Theory, 14 -18 July 2015, Kobe, Japan

We investigate the correlators of flavor non-singlet bilinear operators calculated on the lattice at short distances. In the continuum theory, non-perturbative effects are encoded in the form of the operator product expansion (OPE). We test the prediction of OPE by comparing lattice results with those in the continuum theory. We also determine the renormalization factors of quark currents.

Calculation of the eta-prime meson mass is a notoriously difficult problem, as it requires evaluation of the disconnected diagram which is costly and noisy. In this work, we use a gluonic operator to extract the eta-prime state after smearing the link variables through the Wilson flow. With this choice, one can avoid a large cancellation of pion contribution between the connected and disconnected diagrams. We obtain the eta-prime meson mass on lattices with three different lattice spacings and two physical volumes, which allow us to estimate its continuum and large volume limits., Comment: 7 pages, 3 figures, Proceedings of the 33rd International Symposium on Lattice Field Theory, 14-18 July 2015, Kobe, Japan

The flavor-singlet component of the eta prime 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 prime 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., Comment: 11pages, 5figures, minor corrections, to appear in PRD

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., Comment: 7 pages, 4 figures, presented at the 32nd International Symposium on Lattice Field Theory (Lattice 2014), June 23-28 2014, New York, USA, references added

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., Comment: 16pages, 5 figures, minor corrections, references added, published by PRD

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., Comment: 7 pages, talk presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, Germany

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., Comment: 7 pages, 3 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July-3 August 2013, Mainz, Germany

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., Comment: 7 pages, 8 pdf figures, talk presented at the 30th International Symposium on Lattice Field Theory (Lattice2012), Cairns, Australia, 24-29 June 2012

We consider how to extract the pion form factors in the epsilon regime. Using the correlators with non-zero momenta and taking appropriate ratios of them, we eliminate the dominant finite volume effect from the zero-momentum pion mode. Our preliminary lattice result for the pion charge radius is consistent with the experiment., Comment: 7 pages, 3 figures, Presented at Lattice 2012, June 24-29, 2012, Cairns, Australia. To be published as PoS(Lattice2012)198

We report on our calculation of the kaon semileptonic form factors in Nf=2+1 lattice QCD. Chiral symmetry is exactly preserved by using the overlap quark action for a straightforward comparison with chiral perturbation theory (ChPT). We simulate three pion masses down to 290 MeV at a single lattice spacing of 0.11 fm and at a strange quark mass very close to its physical value. The form factors near zero momentum transfer are precisely calculated by using the all-to-all propagator and twisted boundary conditions. We compare the normalizations and slopes of the form factors with ChPT and experiments., Comment: 7 pages, talk presented at the XXIX International Symposium on Lattice Field Theory (Lattice 2011), Squaw Valley, Lake Tahoe, California, July 10-16, 2011

We report on a lattice simulation result for four-dimensional {\cal N}=1 SU(2) super Yang-Mills theory with the dynamical overlap gluino. We study the spectrum of the overlap Dirac operator at three different gluino masses m=0.2, 0.1 and 0.05 with the Iwasaki action on a 8^3 \times 16 lattice. We find that the lowest eigenvalue distributions are in good agreement with the prediction from the random matrix theory. Moreover the mass dependence of the condensate is almost constant, which gives a clean chiral limit. Our results for the gluino condensate in the chiral limit is < \bar{\psi} \psi > r_0^3 = 0.63(12), where r_0 is the Sommer scale., Comment: 7 pages, 3 figures. Talk presented at The XXIX International Symposium on Lattice Field Theory - Lattice 2011, July 10-16, 2011, Squaw Valley, Lake Tahoe, California

A simulation of lattice QCD at (or even below) the physical pion mass is feasible on a small lattice size of \sim 2 fm. The results are, however, subject to large finite volume effects. In order to precisely understand the chiral behavior in a finite volume, we develop a new computational scheme to interpolate the conventional epsilon and p regimes within chiral perturbation theory. In this new scheme, we calculate the two-point function in the pseudoscalar channel, which is described by a set of Bessel functions in an infra-red finite way as in the epsilon regime, while chiral logarithmic effects are kept manifest as in the p regime. The new ChPT formula is compared to our 2+1- flavor lattice QCD data near the physical up and down quark mass, mud \sim 3 MeV on an L \sim 1.8 fm lattice. We extract the pion mass = 99(4) MeV, from which we attempt a chiral "interpolation" of the observables to the physical point., Comment: 7 pages, 2 figures. Talk presented at the XXIX International Symposium on Lattice Field Theory (Lattice 2011), July 10-16, 2011, Squaw Valley, Lake Tahoe, California

We calculate the chiral condensate of QCD with 2, 2+1 and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up and down quark masses covering a range between 3 and 100 MeV. On L ~ 1.8-1.9 fm lattices at a lattice spacing ~ 0.11 fm, we calculate the eigenvalue spectrum of the overlap-Dirac operator. By matching the lattice data with the analytical prediction from chiral perturbation theory at the next-to-leading order, the chiral condensate in the massless limit of up and down quarks is determined., Comment: 38 pages, 11 figures, minor corrections, version appearing in PRD

We report on our calculation of pion and kaon form factors in three-flavor QCD using the overlap quark action. Gauge ensembles are generated on a 16^3 \times 48 lattice at a lattice spacing of 0.11 fm with pion masses down to 310 MeV. Connected and disconnected meson correaltors are calculated using the all-to-all quark propagator. We present our preliminary analysis on the chiral behavior of the electromagnetic and scalar form factors as well as a comparison of the shape of the K to pi form factors with experiment., Comment: 7pages, talk presented at The XXVIII International Symposium on Lattice Field Theory, Lattice2010

We determine the strong coupling constant $\alpha_s$ from a lattice calculation of vacuum polarization functions (VPF) in three-flavor QCD with dynamical overlap fermions. Fitting lattice data of VPF to the continuum perturbative formula including the operator product expansion, we extract the QCD scale parameter $\Lambda_{\overline{MS}}^{(3)}$. At the $Z$ boson mass scale, we obtain $\alpha_s^{(5)}(M_Z)=0.1181(3)(^{+14}_{-12})$, where the first error is statistical and the second is our estimate of various systematic uncertainties., Comment: 15 pages, 7 figures, references updated. After correction of error in code, final value is changed, see Erratum Phys.Rev.D89,099903 (2014)

We perform a precise calculation of the chiral condensate in QCD using lattice QCD with 2+1 flavors of dynamical overlap quarks. Up and down quark masses cover a range between 3 and 100 MeV on a 16^3x48 lattice at a lattice spacing around 0.11 fm. At the lightest sea quark mass, the finite volume system on the lattice is in the epsilon-regime. By matching the low-lying eigenvalue spectrum of the Dirac operator with the prediction of chiral perturbation theory at the next-to-leading order, we determine the chiral condensate in 2+1-flavor QCD with strange quark mass fixed at its physical value as Sigma (MS-bar at 2 GeV) = [242(04)(^+19_-18}) MeV}]^3, where the errors are statistical and systematic, respectively., Comment: 4 pages, 3 figures, errors in table 1 and fig.3 corrected. Published in PRL

We present an update of the light meson spectrum with $N_f$=2+1 overlap fermions on a $16^3\times 48$ lattice at five different up and down quark masses and two strange quark masses. Based on our experience with the previous simulation with $N_f=2$, we carry out the chiral extrapolation with the prediction of the chiral perturbation theory at the next-to-next-to leading order. We also check the consistency of our analysis by using alternative chiral extrapolation with a reduced theory in which the strange quark mass is integrated out., Comment: 7 pages, 6 figures, talk presented at The XXVII International Symposium on Lattice Field Theory - LAT2009, July 26-31 2009, Peking University, Beijing, China

We report on our study of flavor-singlet mesons in three-flavor QCD with dynamical overlap quarks. Gauge ensembles are generated on a 16^3 x 48 lattice at a lattice spacing of 0.10 fm with the strange quark masses around its physical value m_s,phys and up and down quark masses down to m_s,phys/5. Connected and disconnected meson correlators are calculated using the all-to-all quark propagator. We present our preliminary results on the spectrum of flavor-singlet pseudoscalar and vector mesons., Comment: 7 pages, talk presented at The XXVII International Symposium on Lattice Field Theory - LAT2009, July 26-31 2009, Peking University, Beijing, China

We study the sigma term and the strange quark content of nucleon in 2+1-flavor QCD with dynamical overlap fermions. We analyze the lattice data of nucleon mass taken at two different strange quark masses with five values of up and down quark masses each. Using the reweighting technique, we study the strange quark mass dependence of the nucleon and extract the strange quark content., Comment: 7 pages, 4 figures, talk given at the XXVII International Symposium on Lattice Field Theory, July 26-31 2009, Peking University, Beijing, China

Using the non-perturbative renormalization technique, we calculate the renormalization factors for quark bilinear operators made of overlap fermions on the lattice. The background gauge field is generated by the JLQCD and TWQCD collaborations including dynamical effects of two or 2+1 flavors of light quarks on a 16$^3\times$32 or 16$^3\times$48 lattice at lattice spacing around 0.1 fm. By reducing the quark mass close to the chiral limit, where the finite volume system enters the so-called $\epsilon$-regime, the unwanted effect of spontaneous chiral symmetry breaking on the renormalization factors is suppressed. On the lattices in the conventional $p$-regime, this effect is precisely subtracted by separately calculating the contributions from the chiral condensate., Comment: 36 pages, 41 figure files

We calculate pion vector and scalar form factors in two-flavor lattice QCD and study the chiral behavior of the vector and scalar radii _{V,S}. Numerical simulations are carried out on a 16^3 x 32 lattice at a lattice spacing of 0.12 fm with quark masses down to \sim m_s/6, where m_s is the physical strange quark mass. Chiral symmetry, which is essential for a direct comparison with chiral perturbation theory (ChPT), is exactly preserved in our calculation at finite lattice spacing by employing the overlap quark action. We utilize the so-called all-to-all quark propagator in order to calculate the scalar form factor including the contributions of disconnected diagrams and to improve statistical accuracy of the form factors. A detailed comparison with ChPT reveals that the next-to-next-to-leading-order contributions to the radii are essential to describe their chiral behavior in the region of quark mass from m_s/6 to m_s/2. Chiral extrapolation based on two-loop ChPT yields _V=0.409(23)(37)fm and _S=0.617(79)(66)fm, which are consistent with phenomenological analysis. We also present our estimates of relevant low-energy constants., Comment: 32 pages, 18 figures, typos corrected

We present a calculation of the nucleon sigma term on two-flavor QCD configurations with dynamical overlap fermions. We analyse the lattice data for the nucleon mass using the baryon chiral perturbation theory. Using partially quenched data sets, we extract the connected and disconnected contributions to the nucleon sigma term separately. Chiral symmetry on the lattice simplifies the determination of the disconnected contribution. We find that the strange quark content, which determines the neutralino dark matter reaction rate with nucleon through the Higgs boson exchange, is much smaller than the previous lattice results., Comment: 7 pages, 6 figures, Talk given at 26th International Symposium on Lattice Field Theory (Lattice 2008), Williamsburg, Virginia, 14-20 Jul 2008

We calculate the pion vector and scalar form factors in two-flavor QCD. Gauge configurations are generated with dynamical overlap quarks on a 16^3 x 32 lattice at a lattice spacing of 0.12 fm with sea quark masses down to a sixth of the physical strange quark mass. Contributions of disconnected diagrams to the scalar form factor is calculated employing the all-to-all quark propagators. We present a detailed comparison of the vector and scalar radii with chiral perturbation theory to two loops., Comment: 7 pages; Talk presented at the XXVI International Symposium on Lattice Field Theory, July 14 - 19 2008, Williamsburg, Virginia, USA; v2: a reference added

We report on a numerical simulation with 2+1 dynamical flavors of overlap fermions. We calculate pseudo-scalar masses and decay constants on a $16^3\times 48 \times (0.11 {\rm fm})^4$ lattice at five different up and down quark masses and two strange quark masses. The lightest pion mass corresponds to $\approx 310$ MeV. We also study the validity of the chiral perturbation theory using the results of the numerical simulation with two dynamical flavors and conclude that the one-loop formulae cannot be directly applied in the strange quark mass region. We therefore extrapolate our 2+1-flavor results to the chiral limit by fitting the data to the two-loop formulae of the chiral perturbation theory., Comment: 7 pages, 7 figure files. Talk given at the XXVI International Symposium on Lattice Field Theory, July 14 - 19 2008, Williamsburg, Virginia, USA

We consider chiral perturbation theory in a finite volume and in a mixed regime of quark masses. We take N_l light quarks near the chiral limit, in the so-called epsilon-regime, while the remaining N_h quarks are heavier and in the standard p-regime. We compute in this new mixed regime the finite-size scaling of the light meson correlators in the scalar, pseudoscalar, vector and axial vector channels.Using the replica method, we easily extend our results to the partially quenched theory. With the help of our results, lattice QCD simulations with 2+1 flavors can safely investigate pion physics with very light up and down quark masses even in the region where the pion's correlation length overcomes the size of the space-time lattice., Comment: 32 pages, 6 figures, published version

We calculate the nucleon sigma term in two-flavor lattice QCD utilizing the Feynman-Hellman theorem. Both sea and valence quarks are described by the overlap fermion formulation, which preserves exact chiral and flavor symmetries on the lattice. We analyse the lattice data for the nucleon mass using the analytical formulae derived from the baryon chiral perturbation theory. From the data at valence quark mass set different from sea quark mass, we may extract the sea quark contribution to the sigma term, which corresponds to the strange quark content. We find that the strange quark content is much smaller than the previous lattice calculations and phenomenological estimates., Comment: 27 pages

We present a lattice calculation of $L_{10}$, one of the low energy constants in Chiral Perturbation Theory, and the charged-neutral pion squared mass splitting, using dynamical overlap fermion. Exact chiral symmetry of the overlap fermion allows us to reliably extract these quantities from the difference of the vacuum polarization functions for vector and axial-vector currents. In the context of the technicolor models, these two quantities are read as the $S$-parameter and the pseudo-Nambu-Goldstone boson mass respectively, and play an important role in discriminating the models from others. This calculation can serve as a feasibility study of the lattice techniques for more general technicolor gauge theories., Comment: 9 pages, 3 figures, references added, minor corrections made, version to appear in PRL

We determine the topological susceptibility $ \chi_t $ in the trivial topological sector generated by lattice simulations of two-flavor QCD with overlap Dirac fermion, on a $16^3 \times 32$ lattice with lattice spacing $\sim$ 0.12 fm, at six sea quark masses $m_q$ ranging from $m_s/6$ to $m_s$ (where $m_s$ is the physical strange quark mass). The $ \chi_t $ is extracted from the plateau (at large time separation) of the time-correlation function of the flavor-singlet pseudoscalar meson ($\eta'$), which arises from the finite size effect due to fixed topology. In the small $m_q$ regime, our result of $\chi_t$ is proportional to $m_q$ as expected from chiral effective theory. Using the formula $\chi_t=m_q\Sigma/N_f$ by Leutwyler-Smilga, we obtain the chiral condensate in $N_f=2$ QCD as $\Sigma^{\bar{\mathrm{MS}}}(\mathrm{2 GeV})=[252(5)(10) \mathrm{MeV}]^3 $, in good agreement with our previous result obtained in the $\epsilon$-regime., Comment: 7 pages, 3 figures, talk presented at the 25th International Symposium on Lattice Field Theory, Regensburg, Germany, 30 Jul - 4 Aug 2007