QCD with domain wall quarks and applications to weak matrix elements

Using domain wall fermions, we estimate BK (µ ≈ 2 GeV) = 0.628(47) in quenched QCD which is consistent with previous calculations. At 6/g 2 = 6.0 and 5.85 we find the ratio fK /mρ in agreement with the experimental value, within errors. These results support expectations that O(a) errors are exponentially suppressed in low energy (E ≪ a −1) observables, and indicate that domain wall fermions have good scaling behavior at relatively strong couplings. We also demonstrate that the axial current numerically satisfies the lattice analog of the usual continuum axial Ward identity. A basic feature of the strong interactions has been missing in lattice calculations, the SU(N f) L × SU(N f) R chiral flavor symmetry of the light quarks. We recently reported[1] on calculations using a new discretization for simulations of QCD, domain wall fermions (DWF) [2,3], which preserve chiral symmetry on the lattice in the limit of an infinite extra 5th dimension. There it was demonstrated that DWF exhibit remarkable chiral behavior[1] even at relatively large lattice spacing and modest extent of the fifth dimension. Here we give further results using DWF which are of direct phenomenological interest[4]. In addition to retaining chiral symmetry, DWF are also " improved " in another important way. In the limit that the number of sites in the extra dimension, N s , goes to infinity, the leading dis-cretization error in the effective four dimensional action for the light degrees of freedom goes like O(a 2). This theoretical dependence is deduced from the fact that the only operators available to cancel O(a) errors in the effective action are not chirally symmetric. For finite N s , O(a) corrections are expected to be exponentially suppressed with the size of the extra fifth dimension. Our calculations for B K show a weak dependence on a that is easily fit to an a 2 ansatz. We use the boundary fermion variant of DWF developed by Shamir. For details, consult Ka-plan[2] and Shamir[3]. See Ref. [6] for a discussion of the 4d chiral Ward identities (CWI) satisfied by DWF. Our simulation parameters are summarized in Table 1. Table 1 Summary of simulation parameters. M is the five dimensional Dirac fermion mass, and m is the coupling between layers s = 0 and N s − 1.