Evaluation of the derivative quartic terms of the meson chiral Lagrangian from forward dispersion relations

Abstract

Using the forward dispersion relations for \ensuremath{\pi}\ensuremath{\pi} scattering, we show that the coefficients of the derivative quartic terms in the chiral Lagrangian are positive. The Skyrme term is mainly given by the \ensuremath{\rho}-meson contribution to the I=1 total cross section and gives a proton mass of 1.27 GeV. The non-Skyrme term is found of comparable strength from the I=0 S-wave \ensuremath{\pi}\ensuremath{\pi} data.