Domain Wall Fermions in Quenched Lattice QCD

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 of the parity broken phase and investigate the possible existence of such a phase in this model at finite Ns. The rho and pi meson decay constants obtained from the four-dimensional local currents with the one-loop renormalization factor show a good agreement with those obtained from the conserved currents

Standard-model prediction for direct CP violation in K→ππK\to\pi\pi decay

We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3\times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) \times 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) \times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re$(A_0) = 3.3201(18) \times 10^{-7}$ GeV while the second can be used to compute the direct CP violating ratio Re$(\varepsilon'/\varepsilon)=1.38(5.15)(4.59)\times 10^{-4}$, which is $2.1\sigma$ below the experimental value $16.6(2.3)\times 10^{-4}$. The real part of $A_0$ is CP conserving and serves as a test of our method while the result for Re$(\varepsilon'/\varepsilon)$ provides a new test of the standard-model theory of CP violation, one which can be made more accurate with increasing computer capability.Comment: 9 pages, 3 figures. Updated to match published versio

The K→(ππ)I=2K\to(\pi\pi)_{I=2} Decay Amplitude from Lattice QCD

We report on the first realistic \emph{ab initio} calculation of a hadronic weak decay, that of the amplitude $A_2$ for a kaon to decay into two \pi-mesons with isospin 2. We find Re$A_2=(1.436\pm 0.063_{\textrm{stat}}\pm 0.258_{\textrm{syst}})\,10^{-8}\,\textrm{GeV}$ in good agreement with the experimental result and for the hitherto unknown imaginary part we find {Im}$\,A_2=-(6.83 \pm 0.51_{\textrm{stat}} \pm 1.30_{\textrm{syst}})\,10^{-13}\,{\rm GeV}$. Moreover combining our result for Im\,$A_2$ with experimental values of Re\,$A_2$, Re\,$A_0$ and $\epsilon^\prime/\epsilon$, we obtain the following value for the unknown ratio Im\,$A_0$/Re\,$A_0$ within the Standard Model: $\mathrm{Im}\,A_0/\mathrm{Re}\,A_0=-1.63(19)_{\mathrm{stat}}(20)_{\mathrm{syst}}\times10^{-4}$. One consequence of these results is that the contribution from Im\,$A_2$ to the direct CP violation parameter $\epsilon^{\prime}$ (the so-called Electroweak Penguin, EWP, contribution) is Re$(\epsilon^\prime/\epsilon)_{\mathrm{EWP}} = -(6.52 \pm 0.49_{\textrm{stat}} \pm 1.24_{\textrm{syst}}) \times 10^{-4}$. We explain why this calculation of $A_2$ represents a major milestone for lattice QCD and discuss the exciting prospects for a full quantitative understanding of CP-violation in kaon decays.Comment: 5 pages, 1 figur

The kaon semileptonic form factor in Nf=2+1 domain wall lattice QCD with physical light quark masses

We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for a determination of the CKM-matrix element for which we predict |Vus|=0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.Comment: 21 pages, 7 figures, 6 table

Lattice determination of the K→(ππ)I=2K \to (\pi\pi)_{I=2} Decay Amplitude A2A_2

We describe the computation of the amplitude A_2 for a kaon to decay into two pions with isospin I=2. The results presented in the letter Phys.Rev.Lett. 108 (2012) 141601 from an analysis of 63 gluon configurations are updated to 146 configurations giving Re$A_2=1.381(46)_{\textrm{stat}}(258)_{\textrm{syst}} 10^{-8}$ GeV and Im$A_2=-6.54(46)_{\textrm{stat}}(120)_{\textrm{syst}}10^{-13}$ GeV. Re$A_2$ is in good agreement with the experimental result, whereas the value of Im$A_2$ was hitherto unknown. We are also working towards a direct computation of the $K\to(\pi\pi)_{I=0}$ amplitude $A_0$ but, within the standard model, our result for Im$A_2$ can be combined with the experimental results for Re$A_0$, Re$A_2$ and $\epsilon^\prime/\epsilon$ to give Im$A_0/$Re$A_0= -1.61(28)\times 10^{-4}$ . Our result for Im\,$A_2$ implies that the electroweak penguin (EWP) contribution to $\epsilon^\prime/\epsilon$ is Re$(\epsilon^\prime/\epsilon)_{\mathrm{EWP}} = -(6.25 \pm 0.44_{\textrm{stat}} \pm 1.19_{\textrm{syst}}) \times 10^{-4}$.Comment: 59 pages, 11 figure

The Spatial String Tension and Dimensional Reduction in QCD

We calculate the spatial string tension in (2+1) flavor QCD with physical strange quark mass and almost physical light quark masses using lattices with temporal extent N_tau=4,6 and 8. We compare our results on the spatial string tension with predictions of dimensionally reduced QCD. This suggests that also in the presence of light dynamical quarks dimensional reduction works well down to temperatures 1.5T_c.Comment: 8 pages ReVTeX, 4 figure

Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit

Quenched QCD simulations on three volumes, $8^3 \times$, $12^3 \times$ and $16^3 \times 32$ and three couplings, $\beta=5.7$, 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 $\beta=6.0$ and $L_s=16$, we find \mres/m_s=0.033(3), while for $\beta=5.7$, and $L_s=48$, \mres/m_s=0.074(5), where $m_s$ is the strange quark mass. These values are significantly smaller than those obtained from a more naive determination in our earlier studies. Important effects of topological near zero modes which should afflict an accurate quenched calculation are easily visible in both the chiral condensate and the pion propagator. These effects can be controlled by working at an appropriately large volume. A non-linear behavior of $m_\pi^2$ in the limit of small quark mass suggests the presence of additional infrared subtlety in the quenched approximation. Good scaling is seen both in masses and in $f_\pi$ over our entire range, with inverse lattice spacing varying between 1 and 2 GeV.Comment: 91 pages, 34 figure

Continuum Limit of BKB_K from 2+1 Flavor Domain Wall QCD

We determine the neutral kaon mixing matrix element $B_K$ in the continuum limit with 2+1 flavors of domain wall fermions, using the Iwasaki gauge action at two different lattice spacings. These lattice fermions have near exact chiral symmetry and therefore avoid artificial lattice operator mixing. We introduce a significant improvement to the conventional NPR method in which the bare matrix elements are renormalized non-perturbatively in the RI-MOM scheme and are then converted into the MSbar scheme using continuum perturbation theory. In addition to RI-MOM, we introduce and implement four non-exceptional intermediate momentum schemes that suppress infrared non-perturbative uncertainties in the renormalization procedure. We compute the conversion factors relating the matrix elements in this family of RI-SMOM schemes and MSbar at one-loop order. Comparison of the results obtained using these different intermediate schemes allows for a more reliable estimate of the unknown higher-order contributions and hence for a correspondingly more robust estimate of the systematic error. We also apply a recently proposed approach in which twisted boundary conditions are used to control the Symanzik expansion for off-shell vertex functions leading to a better control of the renormalization in the continuum limit. We control chiral extrapolation errors by considering both the NLO SU(2) chiral effective theory, and an analytic mass expansion. We obtain B_K^{\msbar}(3 GeV) = 0.529(5)_{stat}(15)_\chi(2)_{FV}(11)_{NPR}. This corresponds to $\hat{B}_K = 0.749(7)_{stat}(21)_\chi(3)_{FV}(15)_{NPR}$. Adding all sources of error in quadrature we obtain $\hat{B}_K = 0.749(27)_{combined}$, with an overall combined error of 3.6%.Comment: 65 page