  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. The accuracy is estimated to remain at the
same level despite the lower energy.
