Non-Perturbative Study of the Light Pseudoscalar Masses in Chiral Dynamics

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  • 28 August 2006
Abstract
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 scattering amplitudes. Values for the bare masses of pions and kaons are obtained as well as an estimate of the mass of the \eta_8. 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/\hat{m}, in terms of the O(p^4) CHPT low energy constant combinations 2L^r_8-L^r_5 and 2L^r_6-L^r_4. In this way, we give a range for the values of these low energy counterterms and for 3L_7+L^r_8, 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. An excellent reproduction of the MILC data is obtained, at the level of 1% of relative error in the pseudoscalar masses, and m_s/\hat{m}=25.6\pm 2.5 results. This value is consistent with 24.4\pm 1.5 from CHPT and phenomenology and more marginally with the value 27.4\pm 0.5 obtained from pure perturbative chiral extrapolations of the MILC lattice data to physical values of the lightest quark masses.

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