Clover Quark Action Research Articles

Kaon semileptonic form factors at the physical quark masses on large volumes in Nf = 2 + 1 lattice QCD

We present our results for the kaon semileptonic form factors calculated by using two sets of the PACS10 configuration, whose physical volumes are more than (10 fm)4 at the physical light and strange quark masses in the Nf = 2+1 lattice QCD. The configurations were generated using the Iwasaki gauge action and Nf = 2 + 1 stout-smeared clover quark action. The form factors near zero momentum transfer q 2 can be calculated thanks to the large volume. Using our data, a q 2 interpolation and continuum extrapolation are carried out simultaneously. The value of |Vus | is determined using the result of the form factors at q 2 = 0 in the continuum limit. Our result of |Vus| is compared with the one determined from the CKM matrix unitarity and with those determined using recent lattice results.

Electric Dipole Moment Results from lattice QCD

We utilize the gradient flow to define and calculate electric dipole moments induced by the strong QCD θ-term and the dimension-6 Weinberg operator. The gradient flow is a promising tool to simplify the renormalization pattern of local operators. The results of the nucleon electric dipole moments are calculated on PACS-CS gauge fields (available from the ILDG) using Nf = 2+1, of discrete size 323×64 and spacing a ≃ 0.09 fm. These gauge fields use a renormalization-group improved gauge action and a nonperturbatively O(a) improved clover quark action at β = 1.90, with cSW = 1.715. The calculation is performed at pion masses of mπ ≃ 411, 701 MeV.

Axial charges of N(1535) and N(1650) in two-flavor lattice QCD

We show the lattice QCD results on the axial charge gN*N*A of negative parity nucleon resonances, N* (1535) and N* (1650), which are key clues to the chiral structure in baryon sector. The measurements are performed with up and down dynamical quarks employing the renormalization-group improved gauge action at β = 1.95 and the O(a) improved clover quark action with the hopping parameters, κ = 0.1375, 0.1390 and 0.1400. In order to properly separate signals of N* (1535) and N* (1650), we construct 2×2 correlation matrices and diagonalize them. Wraparound contributions in the correlator, which can be another source of signal contaminations, are eliminated by imposing the Dirichlet boundary condition in the temporal direction. We find that the axial charge of N* (1535) takes small values as gN*N*A ∼O(0.1), whereas that of N* (1650) is about 0.5, which is found independent of quark masses and consistent with the predictions by the naive nonrelativistic quark model.

Two-flavor lattice QCD study of the axial charges of N(1535) and N(1650)

We show the first lattice QCD results on the axial charges $g_A^{N^*N^*}$ of $N^*(1535)$ and $N^*(1650)$. The measurements are performed with two flavors of dynamical quarks employing the renormalization-group improved gauge action at $\beta$=1.95 and the mean-field improved clover quark action with the hopping parameters, $\kappa$=0.1375, 0.1390 and 0.1400. We construct 2$\times$2 correlation matrices and diagonalize them so that the signals of $N^*(1535)$ and $N^*(1650)$ are properly separated. Wraparound contributions in the correlator, which can be another source of signal contaminations, are eliminated by imposing the Dirichlet boundary condition in the temporal direction. The axial charge of $N^*(1535)$ is found to take small values as $g_A^{N^*N^*}\sim {\mathcal O}(0.1)$, whereas that of $N^*(1650)$ is approximately 0.5, which is almost independent of quark masses and consistent with the predictions by the naive nonrelativistic quark model.

LATTICE QCD STUDY OF $g^{N^{\ast}N^{\ast}}_{A}$ WITH TWO FLAVORS OF DYNAMICAL QUARKS

We show the first lattice QCD result of the axial charge [Formula: see text] of N* (1535). We perform the measurements with two flavors of dynamical quarks employing the renormalization-group improved gauge action at β = 1.95 and the mean-field improved clover quark action with the hopping parameters, κ = 0.1375, 0.1390 and 0.1400. In order to avoid signal contaminations by N*(1650), we construct 2 × 2 correlation matrices and diagonalize them so that clear signal separation can be found. The wraparound contributions in the correlator, which can be another source of signal contamination, are eliminated by imposing the Dirichlet boundary condition in the temporal direction. We find that the axial charge of N*(1535) takes a small value, as [Formula: see text], which is almost independent of quark masses.

Axial charges ofN(1535)andN(1650)in lattice QCD with two flavors of dynamical quarks

We show the first lattice QCD results on the axial charge ${g}_{A}^{{N}^{*}{N}^{*}}$ of ${N}^{*}(1535)$ and ${N}^{*}(1650)$. The measurements are performed with two flavors of dynamical quarks employing the renormalization-group improved gauge action at $\ensuremath{\beta}=1.95$ and the mean-field improved clover quark action with the hopping parameters, $\ensuremath{\kappa}=0.1375$, 0.1390, and 0.1400. In order to properly separate signals of ${N}^{*}(1535)$ and ${N}^{*}(1650)$, we construct $2\ifmmode\times\else\texttimes\fi{}2$ correlation matrices and diagonalize them. Wraparound contributions in the correlator, which can be another source of signal contaminations, are eliminated by imposing the Dirichlet boundary condition in the temporal direction. We find that the axial charge of ${N}^{*}(1535)$ takes small values such as ${g}_{A}^{{N}^{*}{N}^{*}}\ensuremath{\sim}\mathcal{O}(0.1)$, whereas that of ${N}^{*}(1650)$ is about 0.5, which is found independent of quark masses and consistent with the predictions by the naive nonrelativistic quark model.

Electric polarizability of neutral hadrons from lattice QCD

By simulating a uniform electric field on a lattice and measuring the change in the rest mass, we calculate the electric polarizability of neutral mesons and baryons using the methods of quenched lattice QCD. Specifically, we measure the electric polarizability coefficient from the quadratic response to the electric field for 10 particles: the vector mesons ${\ensuremath{\rho}}^{0}$ and ${K}^{*0}$; the octet baryons n, ${\ensuremath{\Sigma}}^{0}$, ${\ensuremath{\Lambda}}^{0}$, and ${\ensuremath{\Xi}}^{0}$; and the decuplet baryons ${\ensuremath{\Delta}}^{0}$, ${\ensuremath{\Sigma}}^{*0}$, and ${\ensuremath{\Xi}}^{*0}$. Independent calculations using two fermion actions were done for consistency and comparison purposes. One calculation uses Wilson fermions with a lattice spacing of $a=0.10$ fm. The other uses tadpole-improved L\"uscher-Weisz gauge fields and clover quark action with a lattice spacing $a=0.17$ fm. Our results for neutron electric polarizability are compared to experiment.

Chiral extrapolations with small sea quark mass data in two-flavor lattice QCD

We present results on the light hadron spectrum and quark mass in two-flavor QCD calculated with small sea quark masses down to m P S / m V = 0.35 . The configurations are generated using the RG improved gauge and tadpole-improved clover quark action at β = 1.8 , where a −1 ≃ 1 GeV . Chiral extrapolations are made using not only polynomials and ChPT in the continuum but also formulae of Wilson chiral perturbation theory (WChPT) including O ( a 2 ) chiral breaking terms. We examine the viability of WChPT and its influence on quark masses.

Nonperturbative renormalization of meson decay constants in quenched QCD for a renormalization group improved gauge action

Renormalization constants ($Z$-factors) of vector and axial-vector currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schr\"odinger functional method. Non-perturbative values of $Z$-factors turn out to be smaller than one-loop perturbative values by $O(15%)$ at lattice spacing of $a^{-1}\approx$ 1 GeV. The pseudoscalar and vector meson decay constants calculated with the non-perturbative $Z$-factors show a much better scaling behavior compared to previous results obtained with tadpole improved one-loop $Z$-factors. In particular, the non-perturbative $Z$-factors normalized at infinite physical volume show that scaling violation of the decay constants are within about 10% up to the lattice spacing $a^{-1}\sim 1$ GeV. The continuum estimates obtained from data in the range $a^{-1}=$ 1 -- 2 GeV agree with those determined from finer lattices ($a^{-1}\sim 2-4$ GeV) with the standard action.

Light hadron spectroscopy in two-flavor QCD with small sea quark masses

We extend the study of the light hadron spectrum and the quark mass in two-flavor QCD to smaller sea quark mass, corresponding to $m_{PS}/m_{V}=0.60$--0.35. Numerical simulations are carried out using the RG-improved gauge action and the meanfield-improved clover quark action at $\beta=1.8$ ($a = 0.2$ fm from $\rho$ meson mass). We observe that the light hadron spectrum for small sea quark mass does not follow the expectation from chiral extrapolations with quadratic functions made from the region of $m_{PS}/m_{V}=0.80$--0.55. Whereas fits with either polynomial or continuum chiral perturbation theory (ChPT) fails, the Wilson ChPT (WChPT) that includes $a^2$ effects associated with explicit chiral symmetry breaking successfully fits the whole data: In particular, WChPT correctly predicts the light quark mass spectrum from simulations for medium heavy quark mass, such as $m_{PS}/m_V \simgt 0.5$. Reanalyzing the previous data %at $m_{PS}/m_{V}=0.80$--0.55 with the use of WChPT, we find the mean up and down quark mass being smaller than the previous result from quadratic chiral extrapolation by approximately 10%, $m_{ud}^{\bar{\rm MS}}(\mu=2 {GeV}) = 3.11(17)$ [MeV] in the continuum limit.

Discretization effects in the topological susceptibility in lattice QCD

We study the topological susceptibility $\ensuremath{\chi}$ in QCD with two quark flavors using lattice field configurations that have been produced with an $O(a)$-improved clover quark action. We find clear evidence for the expected suppression at a small quark mass ${m}_{q}$ and examine the variation of $\ensuremath{\chi}$ with this mass and the lattice spacing a. A joint continuum and chiral extrapolation yields good agreement with theoretical expectations as ${a,m}_{q}\ensuremath{\rightarrow}0.$ A moderate increase in autocorrelation is observed on the more chiral ensembles, but within large statistical errors. Finite volume effects are negligible for the Leutwyler-Smilga parameter ${x}_{\mathrm{LS}}\ensuremath{\gtrsim}10,$ and no evidence for a nearby phase transition is observed.

Non-perturbative renormalization of vector and axial vector currents in quenched QCD for a renormalization group improved gauge action

Renormalization constants of vector ($Z_V$) and axial-vector ($Z_A$) currents are determined non-perturbatively in quenched QCD for an RG-improved gauge action and a tadpole-improved clover quark action using the Schr\"odinger functional method. Meson decay constants $f_\rho$ and $f_\pi$ show much better scaling when $Z_V$ and $Z_A$ estimated for infinite physical volume are used instead of $Z$-factors from tadpole-improved one-loop perturbation theory.

Electric polarizability of hadrons

The electric polarizability of a hadron allows an external electric field to shift the hadron mass. We try to calculate the electric polarizability for several hadrons from their quadratic response to the field at a = 0.17 fm using an improved gauge field and the clover quark action. Results are compared to experiment where available.

Magnetic polarizability of hadrons from lattice QCD

We extract the magnetic polarizability from the quadratic response of a hadron's mass shift in progressively small static magnetic fields. The calculation is done on a 24 × 12 × 12 × 24 lattice at a = 0.17 fm with an improved gauge action and the clover quark action. The results are compared to those from experiments and models where available.

Exploring QCD at small sea quark masses with improved Wilson-type quarks

We explore the region of small sea quark masses below m ps/m v= 0.5 in two-flavor QCD using a mean-field improved clover quark action and an RG-improved gauge action at a ≅ 0.2 fm on 12 3 × 24 and 16 3 × 24 lattices. We find that instability of the standard BiCGStab algorithm at small quark masses can be mostly removed by the BiCGStab(DS- L) algorithm, which employs L-th minimal residual polynomials with a dynamical selection of L. We also find singular spikes of Δ H in the HMC algorithm at moderate values of Δτ. Nature of the spike is studied. We also study finite-size effects and chiral properties of meson masses.

Charmonium spectrum from quenched anisotropic lattice QCD

We present a detailed study of the charmonium spectrum using anisotropic lattice QCD. We first derive a tree-level improved clover quark action on the anisotropic lattice for arbitrary quark mass. The heavy quark mass dependences of the improvement coefficients, i.e. the ratio of the hopping parameters $\zeta=K_t/K_s$ and the clover coefficients $c_{s,t}$, are examined at the tree level. We then compute the charmonium spectrum in the quenched approximation employing $\xi = a_s/a_t = 3$ anisotropic lattices. Simulations are made with the standard anisotropic gauge action and the anisotropic clover quark action at four lattice spacings in the range $a_s$=0.07-0.2 fm. The clover coefficients $c_{s,t}$ are estimated from tree-level tadpole improvement. On the other hand, for the ratio of the hopping parameters $\zeta$, we adopt both the tree-level tadpole-improved value and a non-perturbative one. We calculate the spectrum of S- and P-states and their excitations. The results largely depend on the scale input even in the continuum limit, showing a quenching effect. When the lattice spacing is determined from the $1P-1S$ splitting, the deviation from the experimental value is estimated to be $\sim$30% for the S-state hyperfine splitting and $\sim$20% for the P-state fine structure. Our results are consistent with previous results at $\xi = 2$ obtained by Chen when the lattice spacing is determined from the Sommer scale $r_0$. We also address the problem with the hyperfine splitting that different choices of the clover coefficients lead to disagreeing results in the continuum limit.

Non-perturbative renormalization for a renormalization group improved gauge action

Renormalization constants of vector ( Z V ) and axial-vector ( Z A ) currents are determined non-perturbatively in quenched QCD for a renormalization group improved gauge action and a tadpole improved clover quark action using the Schrödinger functional method. Non-perturbative values of Z V and Z A turn out to be smaller than the one-loop perturbative values by O(10%) at a −1 ≈ 1 GeV. A sizable scaling violation of meson decay constants f π and f ρ observed with the one-loop renormalization factors remains even with non-perturbative renormalization.

Charmonium spectrum from quenched QCD on anisotropic lattices

We present our final results of the charmonium spectrum in quenched QCD on anisotropic lattices. Simulations are made with the plaquette gauge action and a tadpole improved clover quark action employing ξ = a s/a t = 3. We calculate the spectrum of S- and P-states and their excitation, and study the scaling behavior of mass splittings. Comparison is made with the experiment and previous lattice results. The issue of hyperfine splitting for different choices of the clover coefficients obtained by Klassen is discussed.

Light hadron spectroscopy with two flavors of dynamical quarks on the lattice

We present results of a numerical calculation of lattice QCD with two degenerate flavors of dynamical quarks, identified with up and down quarks, and with a strange quark treated in the quenched approximation. The lattice action and simulation parameters are chosen with a view to carrying out an extrapolation to the continuum limit as well as chiral extrapolations. Gauge configurations are generated with a renormalization-group improved gauge action and a mean field improved clover quark action at three values of $\beta$ and four sea quark masses. The sizes of lattice are chosen so that the physical spatial size is kept constant. Hadron masses, light quark masses and meson decay constants are measured at five valence quark masses. We also carry out complementary quenched simulations with the same improved actions. The quenched spectrum from this analysis agrees well in the continuum limit with the one of our earlier work using the standard action. We find the two-flavor full QCD meson masses in the continuum limit to be much closer to experimental meson masses than those from quenched QCD. We take these results as manifestations of sea quark effects in two-flavor full QCD. For baryon masses full QCD values for strange baryons are in agreement with experiment, while they differ increasingly with decreasing strange quark content, resulting in a nucleon mass higher than experiment. The pattern suggests finite size effects as a possible origin for this deviation. For light quark masses in the continuum limit we obtain values which are reduced by about 25% compared to the values in quenched QCD. We also present results for decay constants where large scaling violations obstruct a continuum extrapolation. Need for a non-perturbative estimate of renormalization factors is discussed.

Topological susceptibility in lattice QCD with two flavors of dynamical quarks

We present a study of the topological susceptibility in lattice QCD with two degenerate flavors of dynamical quarks. The topological charge is measured on gauge configurations generated with a renormalization group improved gauge action and a mean field improved clover quark action at three values of $\beta=6/g^2$, corresponding to lattice spacings of $a \approx 0.22$, 0.16 and 0.11 fm, with four sea quark masses at each $\beta$. The study is supplemented by simulations of pure SU(3) gauge theory with the same gauge action at 5 values of $\beta$ with lattice spacings 0.09 fm$\simlt a \simlt$0.27 fm. We employ a field theoretic definition of the topological charge together with cooling. For the topological susceptibility in the continuum limit of pure SU(3) gauge theory we obtain $\chi_t^{1/4} = 197^{+13}_{-16}$ MeV where the error shows statistical and systematic ones added in quadrature. In full QCD $\chi_t$ at heavy sea quark masses is consistent with that of pure SU(3) gauge theory. A decrease of $\chi_t$ toward light quark masses, as predicted by the anomalous Ward-Takahashi identity for U(1) chiral symmetry, becomes clearer for smaller lattice spacings. The cross-over in the behavior of $\chi_t$ from heavy to light sea quark masses is discussed.