Measuringπ−πPhase Shifts in Colliding-Beam Experiments

The possibility of exploiting the unique features of the two-photon process $\mathrm{ee}\to \mathrm{ee}\pi \pi$ in colliding-beam experiments to measure the even partial-wave $\pi -\pi$ phase shifts is examined in detail. The commonly used Weizsäcker-Williams approximation is shown to be inadequate. An exact procedure of phenomenological analysis for extracting the relevant phase shifts is formulated. Dynamical (model-dependent) calculations are performed separately to study the expected effects due to the final-state pion-pion interaction. The sensitivity of the measured cross sections to various prominent features of the $s$-wave $\pi -\pi$ phase shifts (scattering length, existence of the scalar-meson resonance) is investigated.