Chiral corrections to π−γ→3π processes at low energies

We calculate in chiral perturbation theory the double-pion photoproduction processes π−γ→π−π0π0 and π−γ→π+π−π− at low energies. At leading order these reactions are governed by the chiral pion-pion interaction. The next-to-leading order corrections arise from pion-loop diagrams and chiral-invariant counterterms involving the low-energy constants , , and . The pertinent production amplitudes A1 and A2 depending on five kinematical variables are given in closed analytical form. We find that the total cross section for neutral pion-pair production π−γ→π−π0π0 gets enhanced in the region by a factor 1.5–1.8 by the next-to-leading order corrections. In contrast to this behavior the total cross section for charged pion-pair production π−γ→π+π−π− remains almost unchanged in the region in comparison to its tree-level result. Although the dynamics of the pion-pair production reactions is much richer, this observed pattern can be understood from the different influence of the chiral corrections on the pion-pion final state interaction (π+π−→π0π0 versus π−π−→π−π−). We present also results for the complete set of two-pion invariant mass spectra. The predictions of chiral perturbation theory for the π−γ→3π processes can be tested by the COMPASS experiment which uses Primakoff scattering of high-energy pions in the Coulomb field of a heavy nucleus to extract cross sections for π−γ reactions with various final states.