We calculate non-perturbative renormalization factors at hadronic scale for $ΔS=2$ four-quark operators in quenched domain-wall QCD using the Schrödinger 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.
We investigate basic physical quantities for quenched simulation with domain-wall fermions and the DBW2 gauge action. Masses and decay constant of pseudoscalar mesons are measured. Scaling properties are tested.
We examine the chiral limit of domain wall fermions in quenched QCD. One expects that in a quenched simulation, exact fermion zero modes will give a divergent, 1/m behavior in the chiral condensate for sufficiently small valence quark masses. Unlike other fermion formulations, domain wall fermions clearly demonstrate this behavior.
We give a progress report of our new $a^{-1}\approx 3$ GeV quenched calculation of kaon matrix elements with domain-wall fermion and DBW2 gauge action. Our smaller lattice spacing allows us to address the effect of charmed quark on the lattice. We show preliminary results of $B_K$ renormalized non-perturbatively and $K\toπ$ matrix elements.
We study the singlet and non-singlet scalar-meson masses using domain wall fermions and the quenched approximation. The singlet mass is found to be smaller than the non-singlet mass and indicates that the lowest singlet meson state could be lighter than 1 GeV. The two-point functions for very small quark masses are compared with expectations from the small-volume chiral perturbation theory and the presence of fermionic zero modes.
We present preliminary results for the mass spectrum of the nucleon and its low-lying excited states from quenched lattice QCD using the domain wall fermion method which preserves the chiral symmetry at finite lattice cutoff. Definite mass splitting is observed between the nucleon and its parity partner. This splitting grows with decreasing valence quark mass. We also present preliminary data regarding the first positive-parity excited state.
The domain wall fermion formulation exhibits full chiral symmetry for finite lattice spacing except for the effects of mixing between the domain walls. Close to the continuum limit these symmetry breaking effects should be described by a single residual mass. We determine this mass from the conservation law obeyed by the conserved axial current in quenched simulations with beta=5.7 and 6.0 and domain wall separations varying between 12 and 48 on 8^3x32 and 16^3x32 lattices. Using the resulting values for the residual mass we perform two complete and independent calculations of the pion decay c…
We report on simulations of quenched QCD using domain wall fermions, where we focus on basic questions about the formalism and its ability to produce expected low energy hadronic physics for light quarks. The work reported here is on quenched $8^3 \times 32$ lattices at $β= 5.7$ and 5.85, using values for the length of the fifth dimension between 10 and 48. We report results for parameter choices which lead to the desired number of flavors, a study of undamped modes in the extra dimension and hadron masses.
By considering the local vector current between nucleon states and imposing charge conservation we determine, for $O(a)$ improved Wilson fermions, its renormalisation constant and quark mass improvement coefficient. The computation is performed for both quenched and two flavour unquenched fermions.
We non-perturbatively calculate the renormalization factor of the static axial vector current in O(a) improved quenched lattice QCD. Its scale dependence is mapped out in the Schroedinger functional scheme by means of a recursive finite-size scaling technique, taking the continuum limit in each step. We also obtain Z_A^{stat} for Wilson fermions in order to renormalize existing unimproved data on F_B^{bare} non-perturbatively.
We present non-perturbative renormalization factors for $ΔS=2$ 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…
We present numerical results for the kaon B-parameter, B_K, determined in the quenched approximation of lattice QCD. Our simulations are performed using domain-wall fermions and the renormalization group improved, DBW2 gauge action which combine to give quarks with good chiral symmetry at finite lattice spacing. Operators are renormalized non-perturbatively using the RI/MOM scheme. We study scaling by performing the simulation on two different lattices with a^{-1} = 1.982(30) and 2.914(54) GeV. We combine this quenched scaling study with an earlier calculation of B_K using two flavors of dynam…
We investigate the existence of chiral zero modes at a^{-1} \simeq 1 GeV in quenched domain-wall QCD. Simulations are carried out for the plaquette and an RG-improved gauge actions on a 12^3x24xN_s lattice with N_s=10-50. We find that the pion mass in the chiral limit remains non-vanishing as N_s\to\infty for both gauge actions. Possible origins of this non-vanishing pion mass are discussed.
We present a precise determination of the leptonic decay constant F_D(s) of the D(s)-meson in quenched lattice QCD. This work is particularly focused on the analysis and discussion of all sources of systematic errors. We simulate directly at the physical quark masses for five different lattice spacings between 0.1fm and 0.03fm using O(a)-improvement. The finest lattice is still work in progress. After taking the continuum limit and setting the scale with the Kaon decay constant F_K=160MeV we arrive at a value of F_D(s)=252(9)MeV. Setting the scale with the nucleon mass instead leads to a decre…
The domain wall fermion (DWF) method, with its almost perfectly preserved chiral symmetry on the lattice, makes the calculation of the nucleon axial charge particularly easy. By maintaining chiral symmetry and using the Ward-Takahashi (WT) identity, one has Z_A = Z_V and the bare lattice calculation yields the physical value without explicit renormalization. The DBW2 improved gauge action provides further enhancement of the symmetry and hence a more accurate WT identity at coarse lattice spacing. Taking advantage of these methods, we confirmed a significant volume dependence of the nucleon axi…
We present a calculation of the $K\toππ$ decay amplitudes from the $K\toπ$ matrix elements using leading order relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD with the domain-wall fermion action and the renormalization group improved gluon action. Our results show that the I=2 amplitude is reasonably consistent with experiment whereas the I=0 amplitude is sizably smaller. Consequently the $ΔI=1/2$ enhancement is only half of the experimental value, and $ε'/ε$ is negative.
We present a study of $B$-parameters for generic $ΔS=2$ four-quark operators in domain wall QCD. Our calculation covers all the $B$-parameters required to study the neutral kaon mixing in the standard model (SM) and beyond it. We evaluate one-loop renormalization factors of the operators employing the plaquette and Iwasaki gauge actions. Numerical simulations are carried out in quenched QCD with both gauge actions on $16^3\times 32\times 16$ and $24^3\times 32\times 16$ at the lattice spacing $1/a\approx 2$GeV. We investigate the relative magnitudes of the non-SM $B$-parameters to the SM one, …
A serious difficulty in conventional lattice field theory calculations is the coupling between the chiral and continuum limits. With both staggered and Wilson fermions, the chiral limit cannot be realized without first taking the limit of vanishing lattice spacing. In this talk, we report on extensive studies of the domain wall formulation of lattice fermions, which avoids this difficulty at the expense of requiring that fermion propagators be computed in five dimensions. A variety of results will be described for quenched and dynamical simulations at both zero and finite temperature. Conclusi…
We study the chiral properties and the validity of perturbation theory for domain wall fermions in quenched lattice QCD at beta=6.0. The explicit chiral symmetry breaking term in the axial Ward-Takahashi identity is found to be very small already at Ns=10, where Ns is the size of the fifth dimension, and its behavior seems consistent with an exponential decay in Ns within the limited range of Ns we explore. From the fact that the critical quark mass, at which the pion mass vanishes as in the case of the ordinary Wilson-type fermion, exists at finite Ns, we point out that this may be a signal o…
We investigate the ground state energies of vector $ρ^{\pm}$ and $K^{\pm *}$ mesons depending on the magnetic field value in the $SU(3)$ lattice gauge theory. It has been shown that the energy of a vector particle depends on its spin projection on the field axis. The magnetic dipole polarizability and hyperpolarizabilities give significant contributions to the energy value which prevents the formation of the charged vector meson condensate at high magnetic fields. We calculate the g-factor of $ρ^{\pm}$ and $K^{\pm*}$ mesons and the dipole magnetic polarizability of $ρ^{\pm}$ mesons.
We explore the possibility for an evaluation of non-leptonic $ΔS=1$ $K$ decay amplitudes through the calculation of $K\toπ$ matrix elements using domain-wall QCD. The relation between the physical $K\toππ$ matrix elements and $K\toπ$ matrix elements deduced from chiral perturbation theory is recapitulated. Quenched numerical simulations are performed on an $16^3\times 32\times 16$ lattice at a lattice spacing $a^{-1}\approx 2$GeV for both the standard plaquette gauge action and a renormalization-group improved gauge action, and reasonable signals for $K\toπ$ matrix elements are obtained. Preli…
Quenched QCD simulations on three volumes, $8^3 \times$, $12^3 \times$ and $16^3 \times 32$ and three couplings, $β=5.7$, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass ($\mres$) whose size decreases as the separation between the domain walls ($L_s$) is increased. However, at stronger couplings much larger values of $L_s$ are required to achieve a given physical value of $\mres$. For $β=6.0$ and $L_s=16$, we find $\mre…
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 $m_f\to 0$ and the length of the fifth dimension $N_s\to\infty$, 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 ga…
Values for the strange quark mass and average up/down mass have been obtained from quenched lattice QCD simulations using the domain wall fermion action. This discretization preserves the properties of flavor and chiral symmetry at nonzero lattice spacing. Results are shown for two values of the lattice spacing. The mass renormalization constant is computed nonperturbatively.
We report on a calculation of $B_K$ with domain wall fermion action in quenched QCD. Simulations are made with a renormalization group improved gauge action at $β=2.6$ and 2.9 corresponding to $a^{-1}\approx 2$GeV and 3GeV. Effects due to finite fifth dimensional size $N_5$ and finite spatial size $N_σ$ are examined in detail. Matching to the continuum operator is made perturbatively at one loop order. We obtain $B_K(μ= 2 {GeV})= 0.5746(61)$, where the error is statistical only, as an estimate of the continuum value in the $\msbar$ scheme with naive dimensional regularization. This value is sm…
We report the status of RBCK calculations on nucleon structure with quenched and dynamical domain wall fermions. The quenched results for the moments of structure functions (< x >_q), (< x>_{Δu - Δd}), and (< 1 >_{δq}) from 1.3 GeV cutoff lattices are complete with non perturbative renormalization (NPR). The dynamical results with two degenerate dynamical quark flavors from 1.7 GeV cutoff lattices are without NPR while the axial charge result is naturally renormalized.
We report on a calculation of $B_K$ with domain wall fermion action in quenched QCD. Simulations are made with a renormalization group improved gauge action at $β=2.6$ and 2.9 corresponding to $a^{-1}\approx 2$GeV and 3GeV. Effects due to finite fifth dimensional size $N_5$ and finite spatial size $N_σ$ are examined in detail. Matching to the continuum operator is made perturbatively at one loop order. We obtain $B_K(μ= 2 GeV)= 0.5746(61)(191)$, where the first error is statistical and the second error represents an estimate of scaling violation and ${\cal O}(α^2)$ errors in the renormalizatio…
We report results of quark masses in quenched lattice QCD with the Kogut-Susskind fermion action, employing the Reguralization Independent scheme (RI) of Martinelli et al. to non-perturbatively evaluate the renormalization factor relating the bare quark mass on the lattice to that in the continuum. Calculations are carried out at β=6.0, 6.2, and 6.4, from which we find $m^{\bar{MS}}_{ud} (2 GeV)= 4.23(29) MeV$ for the average up and down quark mass and, with the $ϕ$ meson mass as input, $m^{\bar{MS}}_{s} (2 GeV)= 129(12) MeV$ for the strange mass in the continuum limit. These values are about …
Preliminary results of a study of quenched chiral logarithms at beta=5.7 are presented. Four independent determinations of the quenched chiral log parameter delta are obtained. Two of these are from estimates of the eta-prime mass, one from the residue of the hairpin diagram and the other from the topological susceptibility combined with the Witten-Veneziano formula. The other two determinations of delta are from measurement of virtual eta-prime loop effects in mpi^2 vs. quark mass and in the chiral behavior of the pseudoscalar decay constant. All results are consistent with delta=.080(15). Th…
We calculate the static quark and anti-quark potential both in quenched and two-flavor dynamical quark lattice QCD using DBW2 gauge and domain-wall quark actions. Lattice spacings from Sommer scale are determined. We find (i) mixing of excited states is different in between quenched and dynamical, (ii) lattice spacing $a_{r_0}\sim a_{m_ρ}$ in dynamical and (iii) coefficient of Coulomb term being $α_{N_f=0}<α_{N_f=2}$ at $a^{-1}\sim$ 2 GeV.
We argue that quenched QCD has non-trivial phase structure for negative quark mass, including the possibility of a parity-flavor breaking Aoki phase. This has implications for simulations with domain-wall or overlap fermions.
We present a lattice determination of the leptonic decay constant F_Ds of the Ds-meson using its mass and F_K as experimental input. Setting the scale with F_K=160 MeV, our final result is F_Ds = 252(9) MeV. The error contains all uncertainties apart from the quenched approximation. Setting the scale with the nucleon mass instead leads to an increase of 3(1) MeV of the leptonic decay constant which might indicate a small quenching error.
In our previous DWF calculation with the Wilson gauge action at $β=6.0$ ($a^{-1}\simeq$ 1.9 GeV) on a $16^3 \times 32 \times 16$ lattice, we found that $\Ga$ had a fairly strong dependence on the quark mass. A simple linear extrapolation of $\Ga$ to the chiral limit yielded a value that was almost a factor of two smaller than the experimental one. Here we report our recent study of this issue. In particular, we investigate possible errors arising from finite lattice volume, especially in the lighter quark mass region. We employ a RG-improved gauge action (DBW2), which maintains very good chira…
We present an update on our previous determination of the Lambda parameter in QCD. The main emphasis is on results for two flavours of light dynamical quarks, where we can now almost double the amount of data used, including values at smaller lattice spacings. The calculations are performed using $O(a)$ improved Wilson fermions. Little change is found to previous numerical values.
The scale parameter $Λ_{\overline{MS}}$ is computed on the lattice in the quenched approximation and for $N_f = 2$ flavors of light dynamical quarks. The dynamical calculation is done with non-perturbatively $O(a)$ improved Wilson fermions. In the continuum limit we obtain $Λ_{\overline{MS}}^{N_f=0} = 243(1)(10)$ MeV and $Λ_{\overline{MS}}^{N_f=2} = 217(16)(11)$ MeV, respectively.
We study the effective monopole action obtained in the Maximal Abelian projection of quenched SU(2) lattice QCD. We determine the quadratic part of the lattice action using analytical blocking from continuum dual superconductor model to the lattice model. The leading contribution to the quadratic action depends explicitly on value of the monopole condensate. We show that the analytical monopole action matches the numerically obtained action in quenched SU(2) QCD with a good accuracy. The comparison of numerical and analytical results gives us the value of the monopole condensate in quenched SU…
In the past year domain wall fermion simulations have moved from exploratory stages to the point where systematic effects can be studied with different gauge couplings, volumes, and lengths in the fifth dimension. Results are presented here for the chiral condensate, the light hadron spectrum, and the strange quark mass. We focus especially on the pseudoscalar meson mass and show that, in small volume, the correlators used to compute it can be contaminated to different degrees by topological zero modes. In large volume a nonlinear extrapolation to the chiral limit, e.g. as expected from quench…
We compute the strange and the average up/down quark masses in the quenched approximation of lattice QCD, by using the O(a)-improved Wilson action and operators and by implementing the non-perturbative renormalization. Our computation is performed at four values of the lattice spacing, from which we could extrapolate to the continuum limit. Our final result for the strange quark mass (in the MSbar scheme) is ms(2 GeV) = (106 +/- 2 +/- 8) MeV. For the average up/down quark mass we have ml(2 GeV) = (4.4 +/- 0.1 +/- 0.4) MeV. The ratio ms/ml = (24.3 +/- 0.2 +/- 0.6).
We present recent results for the prediction of the Bs lifetime difference from lattice Heavy Quark Effective Theory simulations. In order to get a next-to-leading order result we have calculated the matching between QCD and HQET and the two-loop anomalous dimensions in the HQET for all the ΔB=2 operators, in particular for the operators which enter the width difference. We present results from quenched and, for the first time, from unquenched simulations. We obtain for the Bs lifetime difference, (ΔΓ_Bs/Γ_Bs)^{(que.)}=(5.1+/- 1.9+/- 1.7)10^(-2) and (ΔΓ_Bs/Γ_Bs)^{(unq.)}=(4.3+/- 2.0+/- 1.9)10^…
This paper summarizes the recent calculations of the masses and decay constants of the pseudoscalar mesons at the two-loop level, or NNLO, in Partially Quenched Chiral Perturbation Theory (PQxPT). Possible applications include chiral extrapolations of Lattice QCD, as well as the determination of the low-energy constants (LEC:s) of QCD.
We present a lattice determination of the charm quark's mass, using the mass of the D_s meson as experimental input. All errors are under control with the exception of the quenched approximation. Setting the scale with F_K=160 MeV, our final result for the renormalization group invariant (RGI) quark mass is M_c = 1.654(45) GeV, which translates to m_c(m_c) =1.301(34) GeV for the running mass in the MSbar scheme. A 6 percent increase of the RGI quark mass is observed when the scale is set by the nucleon mass. This is a typical quenched scale ambiguity, which is reduced to about 3 percent for m_…
In view of the recent excitement about a tension between determinations of f_Ds from experiment and from simulations of lattice QCD with dynamical quarks, we try to clear up the picture of lattice determinations in the continuum limit of the quenched approximation. For O(a) improved Wilson quarks we see linear scaling in the squared lattice spacing a^2 only for a<~0.08fm. For coarser lattices we observe significant contaminations from higher order cutoff effects. As an aside we also study the scaling of the charm quark mass and the ratio of the vector to the pseudo-scalar decay constant and th…
In this contribution the costs of simulations employing domain wall and overlap fermions are estimated. In the discussion we will stay within the quenched approximation.
We present the status of our calculation of the first few moments of the nucleon structure functions. Our calculations are done using domain wall fermions in the quenched approximation with the DBW2 gauge action at 1.3GeV inverse lattice spacing.
We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due…
We make a comparison between our quenched-hadron-spectroscopy results for the non-perturbatively-improved Wilson action and the corresponding unimproved case, at beta=6.2 on the same set of gauge configurations. Within our statistics, we find a sizeable improvement for the baryon spectrum and for the determination of the strange-quark mass.
A numerical study of quenched QCD for light quarks is presented using O(a) improved fermions. Particular attention is paid to the possible existence and determination of quenched chiral logarithms. A `safe' region to use for chiral extrapolations appears to be at and above the strange quark mass.
Motivated by recent measurements at J-Lab, the pion electromagnetic form-factor is investigated with quenched domain wall fermions and a renormalization group improved gauge action called DBW2. We see that quark mass dependence of the form-factor with finite momentum transfers is rather small.
The mass splittings in the pseudoscalar mesons are studied by combining 2+1 flavor domain wall fermion gauge configurations, generated by the RBC/UKQCD collaborations, and quenched, non-compact, lattice QED configurations. We extract the QED low energy constants in SU(3) partially quenched chiral perturbation theory, up to next-to-leading order, and determine the non-degenerate u, d and s quark masses. Systematic uncertainties due to chiral extrapolations are discussed. The chiral symmetry breaking of domain wall fermions on the lattice and its effect in partially quenched chiral perturbation …
We study the chiral condensate, $<\barψψ>$, and various quark bilinear vertex functions for domain wall fermions at different lattice scales, with both the Wilson and DBW2 gauge actions, in both quenched and dynamical fermion simulations. We use the vertex functions to calculate renormalization factors within a non-perturbative scheme.
We report the current status of RBCK calculations on nucleon structure with both quenched and unquenched lattice QCD. The combination of domain wall fermions and DBW2 gauge action works well for isovector vector and axial charges, and moments of structure functions <x>_q, d_1, and <1>_{δq}.
Gauge fixed domain wall fermions are investigated in the reduced model at small Yukawa couplings. We present chiral propagators at the waveguide boundaries using quenched numerical simulations and analytic methods. There is no evidence of mirror chiral modes at the waveguide boundaries.
We report a study describing the charm quark by a domain-wall fermion (DWF) in lattice quantum chromodynamics (QCD). Our study uses a quenched gauge ensemble with the DBW2 rectangle-improved gauge action at a lattice cutoff of $a^{-1} \sim 3$ GeV. We calculate masses of heavy-light (charmed) and heavy-heavy (charmonium) mesons with spin-parity $J^P = 0^\mp$ and $1^\mp$, leptonic decay constants of the charmed pseudoscalar mesons ($D$ and $D_s$), and the $D^0$-$\bar{D^0}$ mixing parameter. The charm quark mass is found to be $m^{\bar{\rm MS}}_{c}(m_{c})=1.24(1)(18)$ GeV. The mass splittings in …
We present calculations of the decay constants and kaon B-parameter $B_K$ as the first stage of RBC Collaboration's quenched numerical simulations using DBW2 gauge action and domain-wall fermions. Some of potential systematic errors and consistency to previous works are discussed.
We study the lattice spacing dependence of meson spectral functions calculated in quenched QCD with domain wall fermions as well as clover Wilson fermions in quenched and partially-quenched QCD. We conclude that for lattice spacing $a \le 3$ GeV all excited states appearing in the spectral functions are lattice artifacts.
We present the one-loop results of the mass dependent $O(a)$ improvement coefficients for the heavy-light vector and axial-vector currents consisting of the relativistic heavy and the domain-wall light quarks. The calculations are performed with the plaquette, Iwasaki and DBW2 gauge actions. The heavy quark mass and domain-wall height dependence is investigated. We point out that the exact chiral symmetry held by the lattice light quark action leads to an exact relation between the improvement coefficients for the vector and axial-vector currents without regard to the lattice heavy quark actio…
We present a quenched lattice calculation of the nucleon isovector vector and axial-vector charges gV and gA. The chiral symmetry of domain wall fermions makes the calculation of the nucleon axial charge particularly easy since the Ward-Takahashi identity requires the vector and axial-vector currents to have the same renormalization, up to lattice spacing errors of order O(a^2). The DBW2 gauge action provides enhancement of the good chiral symmetry properties of domain wall fermions at larger lattice spacing than the conventional Wilson gauge action. Taking advantage of these methods and perfo…
We explore application of the domain wall fermion formalism of lattice QCD to calculate the $K\toππ$ decay amplitudes in terms of the $K\toπ$ and $K\to 0$ hadronic matrix elements through relations derived in chiral perturbation theory. Numerical simulations are carried out in quenched QCD using domain-wall fermion action for quarks and an RG-improved gauge action for gluons on a $16^3\times 32\times 16$ and $24^3\times 32\times 16$ lattice at $β=2.6$ corresponding to the lattice spacing $1/a\approx 2$GeV. Quark loop contractions which appear in Penguin diagrams are calculated by the random no…
We report on the nucleon decay matrix elements with domain-wall fermions in quenched approximation. Results from direct and indirect method are compared with a focus on the process of a proton decaying to a pion and a lepton. We discuss the renormalization necessary for the matching to the continuum theory. Preliminary results for the renormalized chiral lagrangian parameters are presented.
The $B_K$ parameter is computed in quenched lattice QCD with Wilson twisted mass fermions. Two variants of tmQCD are used; in both of them the relevant $ΔS = 2$ four-fermion operator is renormalised multiplicatively. The renormalisation adopted is non-perturbative, with a Schroedinger functional renormalisation condition. Renormalisation group running is also non-perturbative, up to very high energy scales. In one of the two tmQCD frameworks the computations have been performed at the physical $K$-meson mass, thus eliminating the need of mass extrapolations. Simulations have been performed at …
