Pion decay constant and effective quark mass from relativisticqq¯wave function

Abstract

Expressions for the pion decay constant and ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decay amplitude are given in terms of the effective quark mass ${m}_{q}$ assuming a $q\overline{q}$ bound-state structure for massless pion. The pion decay constant is found to be given by ${f}_{\ensuremath{\pi}}=(\frac{3}{2\ensuremath{\pi}}){m}_{q}$, which gives, for ${m}_{q}=330$ MeV, ${f}_{\ensuremath{\pi}}=160$ MeV, in good agreement with the measured value of 135 MeV.