Radiative corrections to neutral pion-pair production

Abstract

We calculate the one-photon loop radiative corrections to the neutral pion-pair photoproduction process $pi^-gamma to pi^-pi^0pi^0$. At leading order this reaction is governed by the chiral pion-pion interaction. Since the chiral $pi^_s16pi^-topi^0pi^0$ contact-vertex depends only on the final-state invariant-mass it factors out of all photon-loop diagrams. We give analytical expressions for the multiplicative correction factor $Rsim alpha/2pi$ arising from eight classes of contributing one-photon loop diagrams. An electromagnetic counterterm has to be included in order to cancel the ultraviolet divergences generated by the photon-loops. Infrared finiteness of the virtual radiative corrections is achieved (in the standard way) by including soft photon radiation below an energy cut-off $lambda$. The radiative corrections to the total cross section vary between $_s162%$ and $-2%$ for center-of-mass energies from threshold up to $7m_pi$. The finite part of the electromagnetic counterterm gives an additional constant contribution of about $1%$, however with a large uncertainty.