Search

We present the calculation of the $K_{l3}$ form factors with $N_f = 2 + 1$ nonperturbatively $O(a)$-improved Wilson quark action and Iwasaki gauge action at the physical point on a large volume of (10.9 fm)$^3$ at one lattice spacing of $a = 0.085$ fm. We extract the form factors from 3-point functions with three different time separations between the source and sink operators to confirm suppression of excited state contributions. The form factors are calculated in very close to the zero momentum transfer, $q^2 = 0$, thanks to the large volume, so that stable interpolations to $q^2 = 0$ are carried out. Using our form factors, we obtain the form factor at $q^2 = 0$, $f_+(0) = 0.9603(16)(^{+14}_{\ -4})(44)(19)(1)$, where the first, second, and fifth errors are statistical, systematic errors from fit functions and the isospin breaking effect, respectively. The third and fourth errors denote the finite lattice spacing effects estimated from the renormalization factor and contribution beyond the leading order SU(3) chiral perturbation theory (ChPT). The result of $f_+(0)$ yields the Cabibbo-Kobayashi-Maskawa (CKM) matrix element, $|V_{us}| = 0.2255(13)(4)$, where the first error comes from our calculation and the second from the experiment. This value is consistent with the ones determined from the unitarity of the CKM matrix and the $K_{l2}$ decay within one standard deviation, while it is slightly larger than recent lattice calculations by at most 1.5 $\sigma$. Furthermore, we evaluate the shape of the form factors and the phase space integral from our results. We confirm that those results are consistent with the experiment, and also $|V_{us}|$ determined with our phase space integral agrees with the one in the above.

We investigate the finite size effect on the vector meson and the baryon sectors using a subset of the "PACS10" configurations which are generated, keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. Comparing the results on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices the ground states of octet baryons , which are stable on the lattice, show no finite size effect within less than 0.5% level of statistical errors. For those of vector mesons, which are unstable on the lattice, we observe that the effective masses are well below the experimental resonance levels both on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices. For the decuplet baryon sector we have found that the time dependence of the effective mass looks quite similar to that for the vector meson sector including the $\Omega$ baryon channel. We discuss its origin due to a possible mixing with the nearby multihadron states. Since the $\Xi$ baryon mass can be determined with the smallest ambiguity among the vector meson and the baryon masses, we use it together with the pion and kaon masses as the physical inputs to determine the physical point., Comment: 9 pages, 8 figures: published version

We present our preliminary result of the form factor of $ K→πlν$ semileptonic decays on the large volume configuration, $ L\approx10$ fm, with the physical $m_\pi$ and $m_K$ using the stout-smearing clover quark and Iwasaki gauge actions at $a^{−1}=2.333$ GeV. From an interpolation using the data in small momentum transfers, we determine the semileptonic decay form factors at zero momentum transfer. The result is compared with the previous lattice calculations. We also estimate the value of $|V_{us}|$ by combining our result with the experimental value of the kaon semileptonic decay.

We investigate the finite size effect on pseudoscalar meson masses and decay constants using a subset of the "PACS10" configurations which are generated keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. We have tried two kinds of analyses, fixing $\kappa$ values or measured axial Ward identity quark masses. Comparing the results on (5.4 fm$)^4$ and (10.8 fm$)^4$ lattices, we have found a sizable finite size effect on the pseudoscalar meson sector in the former analysis: a 2.1(8)%, 4.8(1.6)%, and 0.36(31)% finite size effect on $m_\pi$, $m_{\rm ud}$, and $f_\pi$, respectively, on the (5.4 fm$)^4$ lattice. For the latter analysis, the finite size effect on the pseudoscalar meson decay constants is 0.66(33)% for $f_\pi$, 0.26(13)% for $f_K$, and 0.40(32)% for $f_K/f_\pi$. These values with two-sigma error bars are consistent with the predictions from the full one-loop SU(3) chiral perturbation theory, which are 0.20% for $f_\pi$, 0.08% for $f_K$, and 0.13% for $f_K/f_\pi$. The finite size effect on the pseudoscalar meson masses is hardly detected under the current statistical precision., Comment: 7 pages, 10 figures, published version

We present our result for the $K\to\pi\pi$ decay amplitudes for both the $\Delta I=1/2$ and $3/2$ processes with the improved Wilson fermion action. In order to realize the physical kinematics, where the pions in the final state have finite momenta, we consider the decay process $K({\bf p}) \to \pi({\bf p}) + \pi({\bf 0})$ in the nonzero momentum frame with momentum ${\bf p}=(0,0,2\pi/L)$ on the lattice. Our calculations are carried out with $N_f=2+1$ gauge configurations generated with the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson fermion action at $a=0.091\,{\rm fm}$ ($1/a=2.176\,{\rm GeV}$), $m_\pi=260\,{\rm MeV}$, and $m_K=570\,{\rm MeV}$ on a $48^3\times 64$ ($La=4.4\,{\rm fm}$) lattice. For these parameters the energy of the $K$ meson is set at that of two-pion in the final state. We obtain ${\rm Re}A_2 = 2.431(19) \times10^{ -8}\,{\rm GeV}$, ${\rm Re}A_0 = 51(28) \times10^{ -8}\,{\rm GeV}$, and $\epsilon'/\epsilon = 1.9(5.7) \times10^{-3}$ for a matching scale $q^* =1/a$ where the errors are statistical. The dependence on the matching scale $q^*$ of these values is weak. The systematic error arising from the renormalization factors is expected to be around $1.3\%$ for ${\rm Re}A_2$ and $11 \%$ for ${\rm Re}A_0$. Prospects toward calculations with the physical quark mass are discussed.

We compute the electromagnetic form factor of the pion at the mass $m_\pi=0.145 $ GeV on the large volume of the spatial extent 8.1 fm, corresponding to $m_\pi L \approx 6$. We use $N_f = 2 + 1$ configurations generated with a non-perturbative improved Wilson quark action with the stout-smeared link and Iwasaki gauge action at $a^{-1}=2.333$ GeV. We obtain the form factor at small momentum transfer without the twisted boundary condition.Our preliminary results for the form factor and the mean-squared charge radius are reasonably consistent with the experiment.

We generate $2+1$ flavor QCD configurations near the physical point on a $96^4$ lattice employing the 6-APE stout smeared Wilson clover action with a nonperturbative $c_{\rm SW}$ and the Iwasaki gauge action at $\beta=1.82$. The physical point is estimated based on the chiral perturbation theory using several data points generated by the reweighting technique from the simulation point, wherer $m_\pi$,$m_K$ and $m_\Omega$ are used as physical inputs. The physics results include the quark masses, the hadron spectrum, the pseudoscalar meson decay constants and nucleon sigma terms, using the nonperturbative renormalization factors evaluated with the Schrodinger functional method., Comment: 7 pages, 10 figures. Proceedings of the 33rd International Symposium on Lattice Field Theory, July 14-18, 2015, Kobe, Japan

We present our result for the $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ decay amplitudes for both the $\mathrm{\ensuremath{\Delta}}I=1/2$ and $3/2$ processes with the improved Wilson fermion action. Expanding on the earlier works by Bernard et al. and by Donini et al., we show that mixings with four-fermion operators with wrong chirality are absent even for the Wilson fermion action for the parity odd process in both channels due to CPS symmetry. Therefore, after subtraction of an effect from the lower dimensional operator, a calculation of the decay amplitudes is possible without complications from operators with wrong chirality, as for the case with chirally symmetric lattice actions. As a first step to verify the possibility of calculations with the Wilson fermion action, we consider the decay amplitudes at an unphysical quark mass ${m}_{K}\ensuremath{\sim}2{m}_{\ensuremath{\pi}}$. Our calculations are carried out with ${N}_{f}=2+1$ gauge configurations generated with the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson fermion action at $a=0.091\text{ }\text{ }\mathrm{fm}$, ${m}_{\ensuremath{\pi}}=280\text{ }\text{ }\mathrm{MeV}$, and ${m}_{K}=580\text{ }\text{ }\mathrm{MeV}$ on a ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ ($La=2.9\text{ }\text{ }\mathrm{fm}$) lattice. For the quark loops in the penguin and disconnected contributions in the $I=0$ channel, the combined hopping parameter expansion and truncated solver method work very well for variance reduction. We obtain, for the first time with a Wilson-type fermion action, that $\mathrm{Re}{A}_{0}=60(36)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}8}\text{ }\text{ }\mathrm{GeV}$ and $\mathrm{Im}{A}_{0}=\ensuremath{-}67(56)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{GeV}$ for a matching scale ${q}^{*}=1/a$. The dependence on the matching scale ${q}^{*}$ for these values is weak.

We present results for the $K\to\pi\pi$ decay amplitudes for both the $\Delta I=1/2$ and $3/2$ channels. This calculation is carried out on 480 gauge configurations in $N_f=2+1$ QCD generated over 12,000 trajectories with the Iwasaki gauge action and non-perturbatively $O(a)$-improved Wilson fermion action at $a=0.091\,{\rm fm}$, $m_\pi=280\,{\rm MeV}$ and $m_K=580\,{\rm MeV}$ on a $32^3\times 64$ ($La=2.9\,{\rm fm}$) lattice. For the quark loops in the Penguin and disconnected contributions in the $I=0$ channel, the combined hopping parameter expansion and truncated solver techniques work very well for variance reduction. We obtain, for the first time with a Wilson-type fermion action, that ${\rm Re}A_0 = 60(36) \times10^{ -8}\,{\rm GeV}$ and ${\rm Im}A_0 =-67(56) \times10^{-12}\,{\rm GeV}$ for a matching scale $q^* =1/a$. The dependence on the matching scale is weak., Comment: 7 pages, 3 figures, Contribution to the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, Columbia University, New York, NY, USA

Recent theoretical and numerical progresses of the lattice calculations of $K\to\pi\pi$ decay amplitude are reviewed.

We present our recent results for the B-parameters, which parameterize the \Delta B=2 transition amplitudes. Calculations are made in quenched QCD at \beta=5.7, 5.9, and 6.1, using NRQCD for heavy quark and the $O(a)$-improved action for light quark. The operators are perturbatively renormalized including corrections of O(\alpha_s/am_Q). We examine scaling behavior of the B-parameters in detail, and discuss the systematic uncertainties using scatter of results with different analysis procedures adopted. As a result, we find B_{B_d}(m_b)=0.84(2)(8), B_{B_s}/B_{B_d}=1.017(10)(^{+4}_{-0}) and B_{S_s}(m_b)=0.87(1)(9)(^{+1}_{-0}) in the quenched approximation.

We present our results for the K+ → π+ π0 decay amplitude with the Wilson quark action in the quenched approximation at β = 6.1. The amplitude is extracted from the ratio of K → ππ 3-point function divided either by K and π meson 2-point functions or by K meson 2-point function and I = 2 ππ 4-point function, which yield results in good agreement. Finite size effects are examined with calculations made on 243 × 64 and 323 × 64 lattices. We convert the lattice amplitude into the continuum value employing a recent one-loop calculation of chiral perturbation theory by Golterman and Leung. The result is consistent with the experimental value if extrapolated to the chiral limit. Various uncertainties inherent in the present methods for calculating the decay amplitude are discussed.

We report on our effort toward a determination of the heavy-light decay constant in quenched QCD. Simulation results are analyzed in terms of the non-relativistic interpretation of relativistic fermions fully incorporating oneloop corrections in the mass and current renormalization factors for massive quark. For the Wilson action for which the analysis is completed, we obtain ƒ d = 192(30)MeV, ƒ d = 214(33)MeV, ƒ b = 171(29)MeV and ƒ b s =193(32)MeV in the continuum limit.

We study the scaling behavior of the step scaling function for SU(3) gauge theory, employing the Iwasaki gauge action and the Luescher-Weisz gauge action. In particular, we test the choice of boundary counter terms and apply a perturbative procedure for removal of lattice artifacts for the simulation results in the extrapolation procedure. We confirm the universality of the step scaling functions at both weak and strong coupling regions. We also measure the low energy scale ratio with the Iwasaki action, and confirm its universality.

We investigate the charmed baryon mass spectrum using the relativistic heavy quark action on 2+1 flavor PACS-CS configurations previously generated on $32^3 \times 64$ 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 becomes $L = 32 a = 2.88(1)$ 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., Comment: 12 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:1212.0073

Results for $f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$, and their ratios are presented. High statistics quenched runs at $\beta=5.7$, $5.85$, $6.0$, and $6.3$, plus a run still in progress at $\beta=6.52$ make possible a preliminary extrapolation to the continuum. The data allows good control of all systematic errors except for quenching, although not all of the error estimates have been finalized. Results from configurations which include effects of dynamical quarks show a significant deviation from the quenched results and make possible a crude estimate of the quenching error., Comment: 4 pages, compressed postscipt, presented at Lattice '95

The non-perturbative cSW determined by the Schrodinger functional (SF) method with the RG-improved gauge action in dynamical Nf = 3 QCD shows a finite volume effect when the numerical simulations are carried out at a constant lattice size L a . We remove the unwanted finite volume effect by keeping physical lattice extent L at a constant. The details of the method and the result obtained for non-perturbative cSW with a constant L are reported.

We report our calculation of the heavy-light decay constants f B and f D on a 20 3 × 48 lattice at β = 5.2 with n f = 2 sea quarks by the fully 0(a)-improved Wilson fermion and heavy quarks in Fermilab formalism. We find that the B meson decay constants are consistent with those obtained with the NRQCD formalism. It is shown that the quark mass dependence almost cancels in the B/D ratio of the decay constant so that the systematic errors in the chiral extrapolation can be reduced. Taking the Grinstein ratio, remaining uncertainties from the perturbation and discretization also cancel to give a precise prediction of ( f B s f B d ) ( f D s f D d ) of 1% accuracy.

We present a lattice QCD calculation of the parameters \alpha and \beta which are necessary in the theoretical estimation of the proton lifetime in grand unified theories (GUTs) using chiral lagrangian approach. The simulation is carried out using the Wilson quark action at three gauge coupling constants in the quenched approximation. We obtain |\alpha(2GeV)|=0.0091(08)(^{+10}_{-19})GeV^3 and |\beta(2GeV)|=0.0098(08)(^{+10}_{-20})GeV^3 in the continuum limit where the first error is statistical and the second one is due to scale setting., Comment: 3 pages, 2 figures, talk presented at Lattice2003(matrix)

We study the chiral behavior of the ratio of heavy-light decay constants on unquenched lattices with two flavor dynamical quarks using the plaquette gauge action and the nonperturbativelyO(a)-improved Wilson fermion action at β = 5.2. The heavy quarks are described by the clover action and the NRQCD action. We find that the sea quark mass dependence of the decay constants largely cancels in the double ratioR1 =fBs/fBd/fDs/fDd and the systematic error in the chiral limit can be drastically reduced. Our preliminary result with heavy clover isR1 = 1.018 ± 0.006 ± 0.010, where the first and the second errors are the statistical and the systematics errors.

We present results for the mass of the etaprime meson for two-flavor lattice QCD in the continuum limit, calculated on the CP-PACS computer, using an RG-improved gauge action and clover fermion action with tadpole-improved csw. Measurements are made at three couplings corresponding to a approx. 0.22, 0.16, 0.11 fm for four quark masses corresponding to mpi over mrho approx. 0.8, 0.75, 0.7, 0.6. Thw two-loop diagrams are evaluated using a noisy source method. Quark smearing for both one- and two- loop diagrams is successfully applied to obtain ground state signals in the etaprime channel. We obtain metaprime=0.960(87)+0.036-0.286GeV in the continuum limit, where the second error represents the systematic uncertainty coming from varying the functional form for chiral and continuum extrapolations.

We present the results of $1+1+1$ flavor $\mathrm{QCD}+\mathrm{QED}$ simulation at the physical point, in which the dynamical quark effects in QED and the up-down quark mass difference are incorporated by the reweighting technique. The physical quark masses together with the lattice spacing are determined with ${m}_{{\ensuremath{\pi}}^{+}}$, ${m}_{{K}^{+}}$, ${m}_{{K}^{0}}$ and ${m}_{{\ensuremath{\Omega}}^{\ensuremath{-}}}$ as physical inputs. Calculations are carried out using a set of $2+1$ flavor QCD configurations near the physical point generated by the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $\ensuremath{\beta}=1.9$ on a ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice. We evaluate the values of the up, down and strange quark masses individually with nonperturbative QCD renormalization.

We review the work of the PACS-CS Collaboration, which aimed to realize lattice quantum chromodynamics (QCD) calculations at the physical point, i.e., those with quark masses set at physical values. This has been a long-term goal of lattice QCD simulation since its inception in 1979. After reviewing the algorithmic progress, which played a key role in this development, we summarize the simulations that explored the quark mass dependence of hadron masses down to values close to the physical point. In addition to allowing a reliable determination of the light hadron mass spectrum, this work provided clues on the validity range of chiral perturbation theory, which is widely used in phenomenology.We then describe the application of the technique of quark determinant reweighting, which enables lattice QCD calculations exactly on the physical point. The physical quark masses and the strong coupling constants are fundamental constants of the strong interaction. We describe a non-perturbative Schrodinger functional approach to figure out the non-perturbative renormalization needed to calculate them. There are a number of physical applications that can benefit from lattice QCD calculations carried out either near or at the physical point. We take up three illustrative examples: calculation of the physical properties of the ρ meson as a resonance, the electromagnetic form factor and charge radius of the pion, and charmed meson spectroscopy. Bringing single hadron properties under control opens up a number of new areas for serious lattice QCD research. One such area is electromagnetic effects in hadronic properties.We discuss the combined QCD plus QED simulation strategy and present results on electromagnetic mass difference. Another area is multi-hadron states, or nuclei. We discuss the motivations and difficulties in this area, and describe our work for deuteron and helium as our initial playground. We conclude with a brief discussion on the future perspective of lattice QCD.

Renormalization factors for bilinear and four-quark operators with the Kogut-Susskind fermion action are perturbatively calculated to one-loop order in the general covariant gauge. Results are presented both for gauge invariant and non-invariant operators. For four-quark operators the full renormalization matrix for a complete set of operators with two types of color contraction structures are worked out and detailed numerical tables are given., Comment: 37 pages, LaTeX with epsf.sty, UTHEP-261/July 1993

Operator dependence of hadron masses for the Kogut-Susskind fermion action is studied with a quenched simulation at β = 6.0 on a 24 3 × 40 lattice at the quark mass m q a = 0.01 and 0.02. With an improved wall source masses are extracted for all 64 meson and 120 baryon operators local in time. For mesons hadron masses are separated into two levels corresponding to π and ϱ. The results confirm the spin-flavor assignment in the literature. At a finer level, however, the spectrum shows some fine structure for π whereas a good degeneracy is observed for ϱ. The spectrum of baryons is also basically divided into the nucleon and Δ. However, one set of operators theoretically assigned to the nucleon in fact couples to Δ. We also find a substantial operator dependence in the nucleon mass. This gives rise to a large uncertainty in m N m ϱ depending on which operators are used to extract hadron masses. A brief discussion is also made for the characteristic of the opposite parity states.

We perform a lattice QCD study of the $\ensuremath{\rho}$ meson decay from the ${N}_{f}=2+1$ full QCD configurations generated with a renormalization group improved gauge action and a nonperturbatively $O(a)$-improved Wilson fermion action. The resonance parameters, the effective $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ coupling constant and the resonance mass, are estimated from the $P$-wave scattering phase shift for the isospin $I=1$ two-pion system. The finite size formulas are employed to calculate the phase shift from the energy on the lattice. Our calculations are carried out at two quark masses, ${m}_{\ensuremath{\pi}}=410\text{ }\text{ }\mathrm{MeV}$ (${m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}}=0.46$) and ${m}_{\ensuremath{\pi}}=300\text{ }\text{ }\mathrm{MeV}$ (${m}_{\ensuremath{\pi}}/{m}_{\ensuremath{\rho}}=0.35$), on a ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ ($La=2.9\text{ }\text{ }\mathrm{fm}$) lattice at the lattice spacing $a=0.091\text{ }\text{ }\mathrm{fm}$. We compare our results at these two quark masses with those given in the previous works using ${N}_{f}=2$ full QCD configurations and the experiment.

We investigate the charm quark system using the relativistic heavy quark action on 2+1 flavor PACS-CS configurations previously generated on 323×64 lattice. The dynamical up, down, and strange quark masses are set to the physical values by using the technique of reweighting to shift the quark-hopping parameters from the values employed in the configuration generation. At the physical point, the lattice spacing equals a-1=2.194(10)??GeV and the spatial extent L=2.88(1)??fm. The charm quark mass is determined by the spin-averaged mass of the 1S charmonium state, from which we obtain mcharmMS? (μ=mcharmMS? )=1.260(1)(6)(35)??GeV, where the errors are due to our statistics, scale determination and renormalization factor. An additional systematic error from the heavy quark is of order αs2f(mQa)(aΛQCD), f(mQa)(aΛQCD)2, which are estimated to be a percent level if the factor f(mQa) analytic in mQa is of order unity. Our results for the charmed and charmed-strange meson decay constants are fD=226(6)(1)(5)??MeV, fDs=257(2)(1)(5)??MeV, again up to the heavy quark errors of order αs2f(mQa)(aΛQCD), f(mQa)(aΛQCD)2. Combined with the CLEO values for the leptonic decay widths, these values yield, Vcd, =0.205(6)(1)(5)(9), Vcs, =1.00(1)(1)(3)(3), where the last error is because of the experimental uncertainty of the decay widths.

The pion decay constant is calculated for full QCD on the lattice employing a variety of methods derived from current algebra and PCAC relations. The calculation is made at β=5.7 on a 204 lattice with two flavors of Kogut-Susskind quarks. Most of the calculation is made in the Landau gauge, for which various methods give results in a very good agreement, yielding ƒ π =97±9 ( statistical ) ± 4 ( systematic) MeV . In particular the results obtained with the gauge non-invariant axial-vector current perfectly agrees with those of the gauge invariant current, if corrected by the Z factor using the mean-field improvement of the gauge coupling constant and operators. Dependence of the results on the type of gauge fixing is also examined using the Coulomb gauge.

Pion decay constant and K meson B parameter are evaluated using non-local operators with and without gauge link variables addressing the question how the choice of operators affect the value of matrix elements. Calculation is made for both full and quenched QCD with Kogut-Susskind fermions. It is shown that the results obtained with the gauge non-invariant operators agree with those of the gauge invariant operators, if corrected by the Z factor using the mean-field improvement of the gauge coupling constant and operators.

I present derivation of L\"uscher's finite size formula for the elastic $N\pi$ and the $NN$ scattering system for several angular momenta from the relativistic quantum field theory., Comment: 8 pages, Poster at Lattice 2009(Hadron Spectroscopy), to be published in PoS(LAT2009)119

We report results on semileptonic B → πl v decay form factors near qmax2 using NRQCD heavy quark and clover light quark actions and currents improved through O(αa). An inconsistency with the soft pion relation f0 (qmax2 = fB / fπ found in a previous work is confirmed, and a possible solution with nonperturbative renormalization is discussed. We find that f+(q2) is well described by the B ∗ pole near qmax2, and its 1/MB scaling is also consistent with the prediction of the pole dominance model.

We investigate the quark mass dependence of baryon masses in 2+1 flavor lattice QCD using SU(3) heavy baryon chiral perturbation theory up to one-loop order. The baryon mass data used for the analyses are obtained for the degenerate up-down quark mass of 3 MeV to 24 MeV and two choices of the strange quark mass around the physical value. We find that the SU(3) chiral expansion fails to describe both the octet and the decuplet baryon data if phenomenological values are employed for the meson-baryon couplings. The SU(2) case is also examined for the nucleon. We observe that higher order terms are controlled only around the physical point. We also evaluate finite size effects using SU(3) heavy baryon chiralperturbation theory, finding small values of order 1% even at the physical point., Comment: 26 pages, 10 tables, 58 figures

We present the results of the physical point simulation in 2+1 flavor lattice QCD with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $\beta=1.9$ on a $32^3 \times 64$ lattice. The physical quark masses together with the lattice spacing is determined with $m_\pi$, $m_K$ and $m_\Omega$ as physical inputs. There are two key algorithmic ingredients to make possible the direct simulation at the physical point: One is the mass-preconditioned domain-decomposed HMC algorithm to reduce the computational cost. The other is the reweighting technique to adjust the hopping parameters exactly to the physical point. The physics results include the hadron spectrum, the quark masses and the pseudoscalar meson decay constants. The renormalization factors are nonperturbatively evaluated with the Schr{\"o}dinger functional method. The results are compared with the previous ones obtained by the chiral extrapolation method., Comment: 20 pages, 17 figures, version to appear in Phys. Rev. D

We calculate a two-pion wave function for the I=2 $S$-wave two-pion system with a finite scattering momentum and estimate the interaction range between two pions, which allows us to examine the validity of a necessary condition for the finite size formula presented by Rummukainen and Gottlieb. We work in the quenched approximation employing the plaquette gauge action for gluons and the improved Wilson action for quarks at $1/a=1.63 {\rm GeV}$ on $32^3\times 120$ lattice. The quark masses are chosen to give $m_\pi = 0.420$, 0.488 and $0.587 {\rm GeV}$. We find that the energy dependence of the interaction range is small and the necessary condition is satisfied for our range of the quark mass and the scattering momentum, $k \le 0.16 {\rm GeV}$. We also find that the scattering phase shift can be obtained with a smaller statistical error from the two-pion wave function than from the two-pion time correlator., Comment: 23 pages, 7 figures, added a reference (Phys.Rev.D73:054503,2006) in v2

We present the first results of the PACS-CS project which aims to simulate 2+1 flavor lattice QCD on the physical point with the nonperturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action. Numerical simulations are carried out at the lattice spacing of $a=0.0907(13)$fm on a $32^3\times 64$ lattice with the use of the DDHMC algorithm to reduce the up-down quark mass. Further algorithmic improvements make possible the simulation whose ud quark mass is as light as the physical value. The resulting PS meson masses range from 702MeV down to 156MeV, which clearly exhibit the presence of chiral logarithms. An analysis of the PS meson sector with SU(3) ChPT reveals that the NLO corrections are large at the physical strange quark mass. In order to estimate the physical ud quark mass, we employ the SU(2) chiral analysis expanding the strange quark contributions analytically around the physical strange quark mass. The SU(2) LECs ${\bar l}_3$ and ${\bar l}_4$ are comparable with the recent estimates by other lattice QCD calculations. We determine the physical point together with the lattice spacing employing $m_\pi$, $m_K$ and $m_\Omega$ as input. The hadron spectrum extrapolated to the physical point shows an agreement with the experimental values at a few % level of statistical errors, albeit there remain possible cutoff effects. We also find that our results of $f_\pi=134.0(4.2)$MeV, $f_K=159.4(3.1)$MeV and $f_K/f_\pi=1.189(20)$ with the perturbative renormalization factors are compatible with the experimental values. For the physical quark masses we obtain $m_{\rm ud}^\msbar=2.527(47)$MeV and $m_{\rm s}^\msbar=72.72(78)$MeV extracted from the axial-vector Ward-Takahashi identity with the perturbative renormalization factors., Comment: 43 pages, 48 figures

We present a lattice QCD calculation of the $\rho$ meson decay width via the $P$-wave scattering phase shift for the I=1 two-pion system. Our calculation uses full QCD gauge configurations for $N_f=2$ flavors generated using a renormalization group improved gauge action and an improved Wilson fermion action on a $12^3\times24$ lattice at $m_\pi/m_\rho=0.41$ and the lattice spacing $1/a=0.92 {\rm GeV}$. The phase shift calculated with the use of the finite size formula for the two-pion system in the moving frame shows a behavior consistent with the existence of a resonance at a mass close to the vector meson mass obtained in spectroscopy. The decay width estimated from the phase shift is consistent with the experiment, when the quark mass is scaled to the realistic value., Comment: LaTeX2e, 16 pages, 6 eps figures, uses revtex4 and graphicx