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

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

1997-04-22

arxiv.org/abs/hep-ph/9704377v3

Phys.Lett. B406 (1997) 154-160; Erratum-ibid. B407 (1997) 454

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pp, LaTeX file, 2 figures (uses epsf), two entries in table 1 changed due to change of basis, one footnote added, refs upda

Scientific paper

10.1016/S0370-2693(97)00666-7

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 $\pi\pi$ scattering amplitude, in particular to its S--wave threshold parameters. Numerical estimates are given for the reaction $\pi^0 \pi^0 \to \pi^0 \pi^0$. 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.

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