Charge-odd and single-spin effects in two-pion production in e~ p collisions ∗

We consider double-photon and bremsstrahlung mechanisms for the production of two charged pions in high-energy electron (or proton) scattering off a transversely polarised proton. Interference between the relevant amplitudes generates a charge-odd contribution to the cross-section for the process. In the kinematical configuration with a jet nearly collinear to the electron, the spin-independent part may be used to the determine phase differences for pion-pion scattering in states with orbital momentum 0 or 2 and 1, while for the configuration with a jet nearly collinear to the proton, the spin-dependent part may be used to explain the experimental data for single-spin correlations in the production of negatively charged pions. We also discuss the backgrounds and estimate the accuracy of the results to be better than 10%. In addition, simplified formulae derived for specific kinematics, with small total transverse pion momenta, are given.