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

JLQCD Collaboration; S. Aoki; M. Fukugita; S. Hashimoto; K-I. Ishikawa; N. Ishizuka; Y. Iwasaki; K. Kanaya; T. Kaneda; S. Kaya; Y. Kuramashi; M. Okawa; T. Onogi; S. Tominaga; N. Tsutsui; A. Ukawa; N. Yamada; T. Yoshié

doi:10.1103/physrevd.62.094501

arXiv · hep-lat/9912007

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

JLQCD Collaboration·S. Aoki·M. Fukugita·S. Hashimoto·K-I. Ishikawa·N. Ishizuka·Y. Iwasaki·K. Kanaya·T. Kaneda·S. Kaya·Y. Kuramashi·M. Okawa·T. Onogi·S. Tominaga·N. Tsutsui·A. Ukawa·N. Yamada·T. Yoshié

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Abstract

We present a study for the pion decay constant $f_π$ 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 $β= 6.0$ 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 $f_π= 89(6)$ 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.

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JLQCD Collaboration, S. Aoki, M. Fukugita, S. Hashimoto, K-I. Ishikawa, N. Ishizuka, Y. Iwasaki, K. Kanaya, T. Kaneda, S. Kaya, Y. Kuramashi, M. Okawa, T. Onogi, S. Tominaga, N. Tsutsui, A. Ukawa, N. Yamada, T. Yoshié. 1999-12-06. Pion decay constant for the Kogut-Susskind quark action in quenched lattice QCD. https://doi.org/10.1103/physrevd.62.094501

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