Chiral corrections to image processes at low energies

We calculate in chiral perturbation theory the double-pion photoproduction processes image and image 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 image, image, image and image. The pertinent production amplitudes image and image depending on five kinematical variables are given in closed analytical form. We find that the total cross section for neutral pion-pair production image gets enhanced in the region image by a factor image by the next-to-leading order corrections. In contrast to this behavior the total cross section for charged pion-pair production image remains almost unchanged in the region image 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 (image versus image). We present also results for the complete set of two-pion invariant mass spectra. The predictions of chiral perturbation theory for the image 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 image reactions with various final states.