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Register a new userPrecise determination of $B_K$ and light quark masses in quenched domain-wall QCD
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We calculate non-perturbative renormalization factors at hadronic scale for $Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schr{o}dinger functional method. Combining them with the non-perturbative renormalization group running by the Alpha collaboration, our result yields the fully non-perturbative renormalization factor, which converts the lattice bare $B_K$ to the renormalization group invariant (RGI) $hat{B}_K$. Applying this to the bare $B_K$ previously obtained by the CP-PACS collaboration at $a^{-1}simeq 2, 3, 4$ GeV, we obtain $hat{B}_K=0.782(5)(7)$ (equivalent to $B_K^{bar{rm MS}}({rm NDR}, 2 {rm GeV}) = 0.565(4)(5)$ by 2-loop running) in the continuum limit, where the first error is statistical and the second is systematic due to the continuum extrapolation. Except the quenching error, the total error we have achieved is less than 2%, which is much smaller than the previous ones. Taking the same procedure, we obtain $m_{u,d}^{rm RGI}=5.613(66)$ MeV and $m_s^{rm RGI}=147.1(17)$ MeV (equivalent to $m_{u,d}^{bar{rm MS}}(2 {rm GeV})=4.026(48)$ MeV and $m_{s}^{bar{rm MS}}(2 {rm GeV})=105.6(12)$ MeV by 4-loop running) in the continuum limit.
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We present non-perturbative renormalization factors for $Delta S=2$ four-quark operators in quenched domain-wall QCD using the Schroedinger functional method. Non-perturbative renormalization factor for $B_K$ is evaluated at hadronic scale. Combined with the non-perturbative RG running obtained by the Alpha collaboration, our result yields renormalization factor which converts lattice bare $B_K$ to the renormalization group invariant one. We apply the renormalization factor to bare $B_K$ previously obtained by the CP-PACS collaboration with the quenched domain-wall QCD(DWQCD). We compare our result with previous ones obtained by perturbative renormalization factors, different renormalization schemes or different quark actions. We also show that chiral symmetry breaking effects in the renormalization factor are numerically small.
We present results for several light hadronic quantities ($f_pi$, $f_K$, $B_K$, $m_{ud}$, $m_s$, $t_0^{1/2}$, $w_0$) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly-physical pion masses at two lattice spacings. We perform a short, O(3)%, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum `global fit with a number of other ensembles with heavier pion masses. We use the physical values of $m_pi$, $m_K$ and $m_Omega$ to determine the two quark masses and the scale - all other quantities are outputs from our simulations. We obtain results with sub-percent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including: $f_pi$ = 130.2(9) MeV; $f_K$ = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the $bar {rm MS}$ scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, $B_K$, in the RGI scheme, 0.750(15) and the $bar{rm MS}$ scheme at 3 GeV, 0.530(11).
We present details of simulations for the light hadron spectrum in quenched QCD carried out on the CP-PACS parallel computer. Simulations are made with the Wilson quark action and the plaquette gauge action on 32^3x56 - 64^3x112 lattices at four lattice spacings (a approx 0.1-0.05 fm) and the spatial extent of 3 fm. Hadronic observables are calculated at five quark masses (m_{PS}/m_V approx 0.75 - 0.4), assuming the u and d quarks being degenerate but treating the s quark separately. We find that the presence of quenched chiral singularities is supported from an analysis of the pseudoscalar meson data. We take m_pi, m_rho and m_K (or m_phi) as input. After chiral and continuum extrapolations, the agreement of the calculated mass spectrum with experiment is at a 10% level. In comparison with the statistical accuracy of 1-3% and systematic errors of at most 1.7% we have achieved, this demonstrates a failure of the quenched approximation for the hadron spectrum: the meson hyperfine splitting is too small, and the octet masses and the decuplet mass splittings are both smaller than experiment. Light quark masses are calculated using two definitions: the conventional one and the one based on the axial-vector Ward identity. The two results converge toward the continuum limit, yielding m_{ud}=4.29(14)^{+0.51}_{-0.79} MeV. The s quark mass depends on the strange hadron mass chosen for input: m_s = 113.8(2.3)^{+5.8}_{-2.9} MeV from m_K and m_s = 142.3(5.8)^{+22.0}_{-0} MeV from m_phi, indicating again a failure of the quenched approximation. We obtain Lambda_{bar{MS}}^{(0)}= 219.5(5.4) MeV. An O(10%) deviation from experiment is observed in the pseudoscalar meson decay constants.
We present a calculation of the renormalization coefficients of the quark bilinear operators and the K-Kbar mixing parameter B_K. The coefficients relating the bare lattice operators to those in the RI/MOM scheme are computed non-perturbatively and then matched perturbatively to the MSbar scheme. The coefficients are calculated on the RBC/UKQCD 2+1 flavor dynamical lattice configurations. Specifically we use a 16^3 x 32 lattice volume, the Iwasaki gauge action at beta=2.13 and domain wall fermions with L_s=16.
We investigate the chiral properties of quenched domain-wall QCD (DWQCD) at the lattice spacings $a^{-1} simeq 1$ and 2 GeV for both plaquette and renormalization-group (RG) improved gauge actions. In the case of the plaquette action we find that the quark mass defined through the axial Ward-Takahashi identity remains non-vanishing in the DWQCD chiral limit that the bare quark mass $m_fto 0$ and the length of the fifth dimension $N_stoinfty$, indicating that chiral symmetry is not realized with quenched DWQCD up to $a^{-1} simeq 2$ GeV. The behavior is much improved for the RG-improved gauge action: while a non-vanishing quark mass remains in the chiral limit at $a^{-1}simeq 1$ GeV, the result at $a^{-1}simeq 2$ GeV is consistent with an exponentially vanishing quark mass in the DWQCD chiral limit, indicating the realization of exact chiral symmetry. An interpretation and implications are briefly discussed.
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