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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 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/\( \hat{{m}}\), 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 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 masses.

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Oller, J.A., Roca, L. Pseudoscalar meson masses in unitarized chiral perturbation theory. Eur. Phys. J. A 31, 534–536 (2007). https://doi.org/10.1140/epja/i2006-10292-4

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  • DOI: https://doi.org/10.1140/epja/i2006-10292-4

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