Complete QED NLO contributions to the reaction $e^+e^- \to \mu^+\mu^-\gamma$ and their implementation in the event generator PHOKHARA

KLOE and Babar have an observed discrepancy of 2% to 5% in the invariant pion pair production cross section. These measurements are based on approximate NLO $ \mu^+ \mu^- \gamma $ cross section predictions of the Monte Carlo event generator PHOKHARA7.0. In this article, the complete NLO radiative corrections to $ \mu^+ \mu^- \gamma $ production are calculated and implemented in the Monte Carlo event generator PHOKHARA9.0. Numerical reliability is guaranteed by two independent approaches to the real and the virtual corrections. The novel features include the contribution of pentagon diagrams in the virtual corrections, which form a gauge-invariant set when combined with their box diagram par…