Corrections to the Pagels-Stokar formula for fπ

Within the composite operator formalism we derive a formula for the pion decay constant fπ, 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) fπ2 differs from the previous Pagels-Stokar expression by an additive term, and it still provides fπ2 in terms of the quark self-energy. We make some numerical estimates leading to (30–40)% deviation for fπ2 with respect to the Pagels-Stokar formula.