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

TL;DR

This paper demonstrates that factorization holds at NLO in $ m ext{QCD}$ for the process $e^+ e^- o J/\psi(\psi(2S)) + \\chi_{c0}$, and NLO corrections significantly increase the predicted cross sections, aligning theory with experiment.

Contribution

It shows factorization validity at NLO for P-wave and S-wave charmonium production, with detailed analysis of IR divergence cancellation and improved cross section predictions.

Findings

NLO corrections increase cross sections by about 2.8 times.

Factorization holds at NLO in this double charmonium process.

Predicted cross sections match experimental lower bounds.

Abstract

In nonrelativistic QCD (NRQCD), we study $e^+ e^- \to J/\psi(\psi(2S)) +\chi_{c0}$ at $B$ factories, where the P-wave state $\chi_{c0}$ is associated with an S-wave state $J/\psi$ or $\psi(2S)$. 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 $\alpha_s$ 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 $e^+ e^- \to J/\psi(\psi(2S)) +\chi_{c0}$ 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 $\mu=2m_c$, the NLO cross sections are estimated to be $17.9(11.3)$ fb for $e^+ e^- \to J/\psi(\psi(2S))+ \chi_{c0}$, which reach the lower bounds of experiment.