Factorization and next-to-leading-order QCD correction in e + e − → J / ψ ( ψ ( 2 S ) ) + χ c 0

In nonrelativistic QCD, we study ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}(\ensuremath{\psi}(2S))+{\ensuremath{\chi}}_{c0}$ at $B$ factories, where the P-wave state ${\ensuremath{\chi}}_{c0}$ is associated with a S-wave state $J/\ensuremath{\psi}$ or $\ensuremath{\psi}(2S)$. In contrast to the failure of factorization in most cases involving P-wave states, e.g. in $B$ decays, we find that factorization holds in this process at next-to-leading order (NLO) in ${\ensuremath{\alpha}}_{s}$ and leading order in $v$, where the associated S-wave state plays a crucial rule in canceling the infrared divergences. We also give some general analyses for factorization in various double charmonium production. The NLO corrections in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}(\ensuremath{\psi}(2S))+{\ensuremath{\chi}}_{c0}$ at $\sqrt{s}=10.6\text{ }\text{ }\mathrm{GeV}$ are found to substantially enhance the cross sections by a factor of about 2.8; hence crucially reducing the large discrepancy between theory and experiment. With ${m}_{c}=1.5\text{ }\text{ }\mathrm{GeV}$ and $\ensuremath{\mu}=2{m}_{c}$, the NLO cross sections are estimated to be 17.9(11.3) fb for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}(\ensuremath{\psi}(2S))+{\ensuremath{\chi}}_{c0}$, which reach the lower bounds of the experiment.