Resonance contributions to the electromagnetic low energy constants of chiral perturbation theory

Abstract

The effective chiral Lagrangian of the strong and electromagnetic interactions of the pseudoscalar mesons at low energies depends on a set of low energy constants. We determine the contributions to the electromagnetic coupling constants at order O(e 2 p 2 ), which arise from resonances within a photon loop. We give some implications of our results, in particular we discuss in detail the effects on the corrections to Dashen's theorem.

Isospin breaking corrections to low-energy π-Kscattering

“…, K 16 , to render any observable free of ultraviolet divergences. To gain some information on these low-energy constants one has to resort to models [16], to sum-rules [17] or to a simple crude order estimates. All in all, one can see that the inclusion of electromagnetic corrections to hadronic processes increases enormously the number of low-energy constants thus washing out any predictability.…”

Isospin violation in low-energy charged pion–kaon scattering

“…Inserting the values for the low-energy constants as given in [12,13], we find the following corrections to the one-loop isospin symmetric prediction:…”

“…For numerical evaluations, we use the central values and error estimates for the hadronic low-energy constants as given in [12]. For the electromagnetic ones, we use the estimates obtained via resonance saturation in [13], and add error bars of natural size (±1/16π 2 ) uniformly.…”

Splitting strong and electromagnetic interactions inKl4decays

“…We will use for the constants K i in the mesonic sector the following central values obtained by means of resonance saturation [18],…”