Factorization and NLO QCD correction in e^+ e^- \to J/ψ(ψ(2S))+ χ_{c0} at B Factories}

Zhang, Yu-Jie; Ma, Yan-Qing; Chao, Kuang-Ta

Factorization and NLO QCD correction in e^+ e^- \to J/ψ(ψ(2S))+ χ_{c0} at B Factories}

Authors

Zhang, Yu-Jie

Ma, Yan-Qing

Chao, Kuang-Ta

Description

In nonrelativistic QCD (NRQCD), we study $e^+ e^- \to J/ψ(ψ(2S)) +χ_{c0}$ at $B$ factories, where the P-wave state $χ_{c0}$ is associated with an S-wave state $J/ψ$ or $ψ(2S)$. 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 $α_s$ and leading order (LO) in $v$, where the associated S-wave state plays a crucial rule in canceling the infrared (IR) divergences. We also give some general analyses for factorization in various double charmonium production. The NLO corrections in $e^+ e^- \to J/ψ(ψ(2S)) +χ_{c0}$ at $\sqrt{s}=10.6$ GeV are found to substantially enhance the cross sections by a factor of about 2.8; hence crucially reduce the large discrepancy between theory and experiment. With $m_c=1.5{\rm GeV}$ and $μ=2m_c$, the NLO cross sections are estimated to be $17.9(11.3)$ fb for $e^+ e^- \to J/ψ(ψ(2S))+ χ_{c0}$, which reach the lower bounds of experiment.
Version published in PRD, implications from eq.(5) on factorization are emphasized, references are added