Cross sections of muon and charged pion pair production in electron-positron annihilation near the threshold

The processes of muon (tau) and charged pion pair production at electron-positron annihilation with O({alpha}) radiative corrections are considered. The calculation results are presented assuming the energies of final particles (center of mass system implied) to be not far significantly from threshold production. The invariant mass distributions for the muon (tau) and pion pairs are obtained both for the initial and final state radiation. Some analytical calculations are illustrated numerically. The pions were assumed to be pointlike objects and scalar QED was applied for calculation. The QED radiative corrections related to the final state radiation, in addition to the well-known Coulomb factor, are treated near threshold region exactly.