Field-theory calculations of the pion mass to one-loop order

Abstract

We compute the pion mass to one-loop order in the SU(2) linear $\ensuremath{\sigma}$ and four-fermion model field theories both in terms of the nonstrange current-quark mass ${\stackrel{^}{m}}_{\mathrm{cur}}$. The answers in these two chiralsymmetry schemes are the same and predict ${\stackrel{^}{m}}_{\mathrm{cur}}\ensuremath{\approx}34$ MeV for two quark flavors.