Pseudoscalar Mass and Decay Constant in Lattice QCD with Exact Chiral Symmetry

Abstract

The masses and decay constants of pseudoscalar mesons $ D $, $ D_s $, and $ K $ are determined in quenched lattice QCD with exact chiral symmetry. For 100 gauge configurations generated with single-plaquette action at $ β= 6.1 $ on the $ 20^3 \times 40 $ lattice, we compute point-to-point quark propagators for 30 quark masses in the range $ 0.03 \le m_q a \le 0.80 $, and measure the time-correlation functions of pseudoscalar and vector mesons. The inverse lattice spacing $ a^{-1} $ is determined with the experimental input of $ f_π$, while the strange quark bare mass ($ m_s a = 0.08 $), and the charm quark bare mass ($ m_c a = 0.80 $) are fixed such that the masses of the corresponding vector mesons are in good agreement with $ ϕ(1020) $ and $ J/ψ(3097) $ respectively. Our results of pseudoscalar-meson decay constant are: $ f_K = 152(6)(10) $ MeV, $ f_D = 235(8)(14)$ MeV, and $ f_{D_s} = 266(10)(18) $ MeV [hep-ph/0506266]. The latest experimental result of $ f_{D^+} $ from CLEO [hep-ex/0508057] is in good agreement with our prediction.