Isospin breaking in pion compton scattering

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Abstract

Using chiral perturbation theory we calculate for pion Compton scattering the isospin-breaking effects induced by the difference between the charged and neutral pion mass. At one-loop order this correction is directly proportional to m 2 π±- 2 πand free of any contributions from short-distance electromagnetic counterterms. The differential cross-section for charged pion Compton scattering π -γ→π -γ gets affected (in backward directions) at the level of a few permille only. At the same time the isospin-breaking correction leads to a small shift of the pion polarizability difference by δ(α ππ)≃1. 3·10 -5 fm 3. In the case of the low-energy γγ→π 0π 0 reaction isospin breaking manifests itself through a cusp effect at the π +π - threshold. We give an improved estimate for this cusp effect using the empirical ππ-scattering length difference a0-a2\≃ 0.26πm -.

Original languageEnglish
Article number1230009
JournalInternational Journal of Modern Physics E
Volume21
Issue number10
DOIs
StatePublished - Oct 2012

Keywords

  • Pion Compton scattering
  • charged and neutral pion mass difference
  • isospin-symmetry breaking correction
  • pion electromagnetic polarizabilities
  • pion-loop diagrams

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