Pseudoscalar meson masses in unitarized chiral perturbation theory
Departamento de Fısica, Universidad de Murcia, E-30071, Murcia, Spain
* e-mail: firstname.lastname@example.org
Accepted: 1 January 2007
Published online: 22 March 2007
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 0(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 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/, 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 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/ = 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.
PACS: 14.65.Bt Light quarks – / 12.40.Yx Hadron mass models and calculations – / 14.40.Aq π, K, and η mesons – / 12.39.Fe Chiral Lagrangians –
© Società Italiana di Fisica and Springer-Verlag, 2007