QCD corrections to e^+ e^- to J/\psi(\psi(2S))+\chi_{cJ} (J=0,1,2) at B Factories

TL;DR

This paper provides an analytical calculation of NLO QCD corrections to double charmonium production in electron-positron collisions, explaining experimental observations and reducing theoretical uncertainties.

Contribution

It presents the first NLO QCD correction calculations for $e^+ e^- o J/eta(eta(2S)) ext{ extbackslash}chi_{cJ}$ processes, clarifying differences in cross sections and experimental results.

Findings

NLO corrections are large and positive for $ ext{ extbackslash}chi_{c0}$ production.

NLO corrections are negative for $ ext{ extbackslash}chi_{c1,2}$, reducing their cross sections.

NLO corrections decrease $ ext{ extbackslash}mu$ dependence, improving theoretical precision.

Abstract

We analytically calculate the cross sections of double charmonium production in $e^+ e^- \to J/\psi(\psi(2S))\chi_{cJ}$ (J=0,1,2) at next-to-leading order (NLO) in $\alpha_s$ in nonrelativistic QCD, and confirm factorization of these processes. In contrast to $\chi_{c0}$ production, for which the NLO correction is large and positive, the NLO corrections for $\chi_{c1,2}$ production can be negative, resulting in decreased $K$ factors of 0.91 and 0.78 for J=1 and 2 respectively when $\mu = 2 m_{c}$. Consequently, the NLO QCD corrections markedly enlarge the difference between cross sections of $\chi_{c0}$ and $\chi_{c1,2}$. This may explain why $e^+ e^- \to J/\psi(\psi(2S))\chi_{c0}$ but not $e^+ e^- \to J/\psi(\psi(2S))\chi_{c1,2}$ is observed experimentally. Moreover, for $J/\psi(\psi(2S))\chi_{c1,2}$, the NLO QCD corrections substantially reduce the $\mu$ dependence and lead to predictions with small theoretical uncertainties.