Pion decay constant for the Kogut-Susskind quark action in quenched lattice QCD

Abstract

We present a study for the pion decay constant $f_{\ddot{I}}€$ in the quenched approximation to lattice QCD with the Kogut-Susskind (KS) quark action, with the emphasis given to the renormalization problems. Numerical simulations are carried out at the couplings ${\hat{I}}^2=6.0$ and 6.2 on $32^3\times 64$ and $48^3\times 64$ lattices, respectively. The pion decay constant is evaluated for all KS flavors via gauge invariant and non-invariant axial vector currents with the renormalization constants calculated by both non-perturbative method and perturbation theory. We obtain $f_{\ddot{I}}€=89(6)$ MeV in the continuum limit as the best value using the partially conserved axial vector current, which requires no renormalization. From a study for the other KS flavors we find that the results obtained with the non-perturbative renormalization constants are well convergent among the KS flavors in the continuum limit, confirming restoration of $\mathrm{SU}(4{)}_{\mathrm{A}}$ flavor symmetry, while perturbative renormalization still leaves an apparent flavor breaking effect even in the continuum limit.

LaTex, 27 pages, 35 eps figures, uses revtex and epsf