Chiral corrections to [formula omitted] processes at low energies

Abstract

We calculate in chiral perturbation theory the double-pion photoproduction processes π − γ → π − π 0 π 0 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 ℓ ¯ 1 , ℓ ¯ 2 , ℓ ¯ 3 and ℓ ¯ 4 . The pertinent production amplitudes A 1 and A 2 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 − π 0 π 0 gets enhanced in the region s < 7 m π 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 s < 6 m π 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 − → π 0 π 0 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 → 3 π 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.