Higher order corrections to the cross section ofe+e−→quarkonium+γ

Abstract

The cross sections of ${e}^{+}{e}^{\ensuremath{-}}$ to $S$-wave and $P$-wave quarkonia with $C$-parity even associated with a photon are analyzed in the framework of nonrelativistic Quantum Chromodynamics (NRQCD) factorization formulism. The short-distance coefficients are analytically determined up to the next-to-leading order (NLO) QCD radiative corrections to $S$-wave and $P$-wave quarkonium production and NLO relativistic correction to ${\ensuremath{\eta}}_{c}$ production. We also invoke the analytical expressions to estimate the cross sections. Our numerical results indicate that both the QCD and the relativistic corrections are considerable.