Pseudoscalar meson masses in unitarized chiral perturbation theory

Abstract

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, σ, f 0(980), a o(980) and κ. 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 η 8 mass are obtained. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to \( \mathcal{O} \)(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 /\( \hat m \), in terms of the \( \mathcal{O} \)(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 η-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 /\( \hat m \) = 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 masse