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

We present a study for the pion decay constant $f_{\pi }$ 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 $\beta =6.0\mathrm{}$ 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 noninvariant axial vector currents with the renormalization constants calculated by both the nonperturbative method and perturbation theory. We obtain $f_{\pi }=89\mathrm{}\left(6\right)\mathrm{}\hspace{0.5em}\mathrm{MeV}$ 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 nonperturbative renormalization constants are well convergent among the KS flavors in the continuum limit, confirming restoration of $\mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}_A,$ flavor symmetry, while perturbative renormalization still leaves an apparent flavor breaking effect even in the continuum limit.