Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to ππ scattering

Abstract

We construct the generating functional of two flavor chiral perturbation theory including the effects of virtual photons in the one loop approximation. As an application, we calculate the electromagnetic corrections to the elastic ππ scattering amplitude, in particular to its S-wave threshold parameters. Numerical estimates are given for the reaction π 0 π 0 → π 0 π 0 . These electromagnetic effects are found to be smaller than the hadronic two-loop corrections for the scattering length a 0 . The effective range b 0 increases by 36% due to the unitary cusp.

Chiral Perturbation Theory

“…A similar effect in the vector form factor is washed out by the kinematical P-wave prefactors. Another cusp effect that was long considered an academic curiosity appears in π 0 π 0 → π 0 π 0 scattering due to the opening of the π + π − threshold just 9.2 MeV about the π 0 π 0 threshold, as first found in [34] (and graphically shown in Ref. [78]).…”

“…Space forbids to discuss the many interesting aspects of these extensions, the interested reader might consult some of the classics, see Refs. [32,33,34,35,36,37].…”

Radiative corrections in K→3π decays

“…9, with a solid line, with tree-level couplings L 0 = −1.4K 0 , see Eq. (8). The grey band denotes the region discarded in the NA48/2 analysis.…”

π0−η−η′mixing in a generalized multiquark interaction scheme

“…A detailed quantitative analysis however requires isospin breaking corrections to be taken into account in a series of low energy phenomena, such as the description of mass splittings of mesons and Dashen's theorem [3]; sum rules for quark condensates [2,4]; kaon decays [5]; π − π [6,7] and π − K scattering [8,9] in relation to mesonic atoms; [10,11], ρ and τ decays involving ηðη 0 Þ mesons [12]; and a 0 − f 0 mixing [13] in the scalar meson sector.…”