Compton scattering off pions and electromagnetic polarizabilities

The electric (απ) and magnetic (βπ) Compton polarizabilities of both the charged and the neutral pion are of fundamental interest in the low-energy sector of quantum chromodynamics (QCD). Pion polarizabilities affect the shape of the γπ → γπ Compton scattering angular distribution at back scattering angles and γγ → ππ absolute cross sections. Theory derivations are given for the γπ → γπ Compton scattering differential cross section, dispersion relations, and sum rules in terms of the polarizabilities. We review experimental charged and neutral polarizability studies and theoretical predictions. The π0 polarizabilities were deduced from DESY Crystal Ball γγ → π0π0 data, but with large uncertainties. The charged pion polarizabilities were deduced most recently from (1) radiative pion Primakoff scattering π-Z → π-Zγ at CERN COMPASS, (2) two-photon pion pair production γγ → π+π- at SLAC Mark II, and (3) radiative pion photoproduction γp → γπ+n from the proton at MAMI in Mainz. A stringent test of chiral perturbation theory (ChPT) is possible based on comparisons of precision experimental charged pion polarizabilities with ChPT predictions. Only the CERN COMPASS charged pion polarizability measurement has acceptably small uncertainties. Its value απ±- βπ± = (4.0 ± 1.8) × 10-4fm3 agrees well with the two-loop ChPT prediction απ±- βπ± = (5.7 ± 1.0) × 10-4fm3, strengthening the identification of the pion with the Goldstone boson of chiral symmetry breaking in QCD.