Chiral corrections to pi- gamma to 3pi processes at low energies

Abstract

We calculate in chiral perturbation theory the double-pion photoproduction processes $pi^-gamma to pi^- pi^0pi^0$ and $pi^-gamma to pi^_s16pi^-pi^-$ 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 $barl_1, barl_2, barl_3$ and $barl_4$. 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 $pi^-gamma topi^-pi^0pi^0$ gets enhanced in the region $sqrt{s}< 7m_pi$ 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 $pi^-gammato pi^_s16 pi^-pi^-$ remains almost unchanged in the region $sqrt{s}< 6m_pi$ 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 ($pi^_s16pi^- to pi^0pi^0$ versus $pi^-pi^- to pi^-pi^-$). We present also results for the complete set of two-pion invariant mass spectra. The predictions of chiral perturbation theory for the $pi^-gammato 3pi$ 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 $pi^-gamma$ reactions with various final states.