Electromagnetic Corrections to Pi Pi Scattering: Some Lessons for the Implementation of Meson Exchange Models

Abstract

The leading non-Coulombic electromagnetic contributions to pi pi s-wave scattering lengths are computed in Chiral Perturbation Theory. It is shown that these corrections are zeroth order in the chiral expansion and associated with electromagnetic contact terms in the effective Lagrangian, i.e. that they do not involve explicit photon fields in the low-energy effective theory. It is pointed out that, if one followed the standard meson-exchange-model ansatz for removing electromagnetic effects, i.e. of subtracting contributions associated with explicit photon exchange and radiative corrections, as determined by the photon coupling vertices of the effective hadronic theory, one would completely miss these contributions and arrive at the erroneous conclusion that the strong interactions exhibited very large isospin breaking in pi pi scattering. Implications for electromagnetic "subtraction" procedures in other hadronic systems and the utility of the effective Lagrangian method for avoiding such errors are obvious.

16 pages, REVTEX

References in corpus (6)

• Chiral Dynamics in Nucleons and Nuclei
• Chiral perturbation theory
• Virtual Photons in Chiral Perturbation Theory
• The reaction $\pi N\to \pi \pi N$ at threshold in chiral perturbation theory
• Phenomenological Aspects of Isospin Violation in the Nuclear Force
• Baryon Masses at Second Order in Chiral Perturbation Theory

Cited by in corpus (8)

• ππscattering
• Virtual Photons in Low Energy pi-pi Scattering
• Virtual photons in SU(2) chiral perturbation theory and electromagnetic corrections to $\pi \pi$ scattering
• Precise Determination of the I=2 pipi Scattering Length from Mixed-Action Lattice QCD
• Observation of a cusp-like structure in the pizero-pizero invariant mass distribution from K+- ==> pi+- pizero pizero decay and determination of the pi-pi scattering lengths
• Determination of the S-wave pi pi scattering lengths from a study of K+- -> pi+- pi0 pi0 decays
• Hadronic Interactions from Lattice QCD
• Isospin Breaking in $K_{\ell 4}$ Decays of the Neutral Kaon