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We present a study for the pion decay constant $f_\pi$ in the quenchedapproximation to lattice QCD with the Kogut-Susskind (KS) quark action, withthe emphasis given to the renormalization problems. Numerical simulations arecarried out at the couplings $\beta = 6.0$ and 6.2 on $32^3\times 64$ and$48^3\times 64$ lattices, respectively. The pion decay constant is evaluatedfor all KS flavors via gauge invariant and non-invariant axial vector currentswith the renormalization constants calculated by both non-perturbative methodand perturbation theory. We obtain $f_\pi = 89(6)$ MeV in the continuum limitas the best value using the partially conserved axial vector current, whichrequires no renormalization. From a study for the other KS flavors we find thatthe results obtained with the non-perturbative renormalization constants arewell convergent among the KS flavors in the continuum limit, confirmingrestoration of $\rm SU(4)_A$ flavor symmetry, while perturbativerenormalization still leaves an apparent flavor breaking effect even in thecontinuum limit.Comment: LaTex, 27 pages, 35 eps figures, uses revtex and eps

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