Corrections to the Pagels-Stokar Formula for f_\pi

Abstract

Within the composite operator formalism we derive a formula for the pion decay constant $f_{\pi}$, as defined directly from the residue at the pion pole of the meson propagator, rather than from the matrix element of the axial current. The calculation is performed under some simplifying assumptions, and we verify the complete consistency with soft-pion results, in particular with the Adler-Dashen relation. The formula one obtains for (the pole-defined) $f_{\pi}^2$ differs from the previous Pagels-Stokar expression by an additive term, and it still provides $f_{\pi}^2$ in terms of the quark self-energy. We make some numerical estimates leading to $(30 \div 40)%$ deviation for $f_{\pi}^2$ with respect to the Pagels-Stokar formula.