Precise Determination of {$f_{P_{s}}/f_P$}} {\bf and Measurement of the ``Perturbative'' Pole Mass from {$f_P$}}

Abstract

We present a compact analytic two-loop expression of the $SU(3)_f$ breaking effects on the ratio of the pseudoscalar decay constants $R_P \equiv f_{P_S}/f_P$ ($P \equiv D,B $), from which, we extract the precise values : $R_D = 1.15 \pm .04$, $R_B = 1.16 \pm .05 $, where the errors are mainly due to the uncalculated $α_s^2$-corrections. We also scan carefully the $M_c$ (resp. $M_b$) mass dependence of $f_D$ (resp. $f_B$) in view of precise measurements of the ``perturbative'' c and b pole quark masses from the future data of the decay constants $f_P$.