Pseudoscalar meson masses in unitarized chiral perturbation theory

This contribution summarizes the work explained in arXiv:hep-ph/0608290 where we perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. The pseudoscalar self-energies are calculated by the evaluation of the scalar self-energy loops with full S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT). These amplitudes, among other features, contain the lightest nonet of scalar resonances sigma, f(0)(980), a(0)(980) and kappa. The self-energy loops are regularized by a proper subtraction of the infinities within a dispersion relation formulation of the amplitudes. Values for the bare masses of pions and kaons and the eta(8) mass are obtained. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to O(p(4)) and resum higher orders from our calculated scalar self-energies. The dependence of the self-energies on the quark masses allows a determination of the ratio of the strange-quark mass over the mean of the lightest-quark masses, m(s)/(m) over cap, in terms of the O(p(4)) CHPT low-energy constant combinations 2L(8)(r)-L-5(r) and 2L(6)(r)-L-4(r). In this way, we give a range for the values of these low-energy counterterms and for 3L(7) + L-8(r), once the eta-meson mass is invoked. The low-energy constants are further constraint by performing a fit to the recent MILC lattice data on the pseudoscalar masses, and m(s)/(m) over cap = 25.6 +/- 2.5 results. This value is consistent with 24.4 +/- 1.5 from CHPT and phenomenology and more marginally with the value 27.4 +/- 0.5 obtained from pure perturbative chiral extrapolations of the MILC lattice data to physical values of the lightest-quark masses.