The radiative return at phi- and B-factories: small-angle photon emission at next to leading order

The radiative return offers the unique possibility for a measurement of the cross section of electron--positron annihilation into hadrons over a wide range of energies. The large luminosity of present phi- and B-factories easily compensates for the additional factor of alpha due to the emission of a hard photon. Final states with photons at large angles can be easily identified. The rate for events with collinear photons, however, is enhanced by a large logarithm and allows, in particular at lower energies, for a complementary measurement. The Monte Carlo generator PHOKHARA, which includes next to leading order corrections from virtual and real photon emission, has been extended from large photon angles into the collinear region, using recent results for the virtual corrections. In addition, the present version includes final state radiation for muon and pion pair production and final states with four pions. Implications for the experimental analysis at three typical energies, 1.02, 4 and 10.6 GeV, are presented: the magnitude of these new corrections is studied, possibilities for the separation of initial and final state radiation are proposed, and the differences with respect to the previous treatment based on structure functions are investigated.