Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1999-12-06
Phys.Rev. D62 (2000) 094501
Physics
High Energy Physics
High Energy Physics - Lattice
LaTex, 27 pages, 35 eps figures, uses revtex and epsf
Scientific paper
10.1103/PhysRevD.62.094501
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 $\beta = 6.0$ 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 $f_\pi = 89(6)$ 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 $\rm SU(4)_A$ flavor symmetry, while perturbative renormalization still leaves an apparent flavor breaking effect even in the continuum limit.
Aoki Sadao
Fukugita Masaaka
Hashimoto Shigehira
Ishikawa Kei-Ichi
Ishizuka Naruhito
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