Eur. Phys. J. A (2007) 34: 371-386
https://doi.org/10.1140/epja/i2006-10516-7

Regular Article - Theoretical Physics

Non-perturbative study of the light pseudoscalar masses in chiral dynamics

Departamento de Fısica, Universidad de Murcia, E-30071, Murcia, Spain

^* e-mail: oller@um.es

Received: 13 November 2006
Accepted: 8 January 2008
Published online: 6 February 2008

Abstract

We perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. In the calculation of the self-energies we employ the S -wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT) that include the lightest nonet of scalar resonances. Values for the bare masses of pions and kaons are obtained, as well as an estimate of the mass of the η₈ . The former are found to dominate the physical pseudoscalar masses. We also match our results with the self-energies from Chiral Perturbation Theory (CHPT) to O(p ⁴) , and resum higher orders from our calculated self-energies. A robust relation between several O(p ⁴) CHPT counterterms is then obtained. By taking into account values determined from previous chiral phenomenological studies of m _s/ and 3L ₇ + L ^r ₈(M _ρ) , we determine a tighter region of favoured values for the O(p ⁴) CHPT counterterms 2L ^r ₆(M _ρ) - L ^r ₄(M _ρ) and 2L ^r ₈(M _ρ) - L ^r ₅(M _ρ) . This determination perfectly overlaps with the recent determinations to O(p ⁶) in CHPT. We warn about a likely reduction in the value of m _s/ by higher loop diagrams and that this is not systematically accounted for by present lattice extrapolations. We also provide a favoured interval of values for m _s/ and 3L ₇ + L ^r ₈(M _ρ) .