${\mathcal O}(\alpha_s^2)$ corrections to $J/\psi+\chi_{c0,1,2}$ production at $B$ factories

TL;DR

This paper calculates second-order QCD corrections to exclusive double-charmonium production in electron-positron collisions, confirming NRQCD validity and improving theoretical predictions to match experimental data.

Contribution

It provides the first ${ m O}(\alpha_s^2)$ corrections for $e^+e^- o J/+J$ processes, enhancing the accuracy of NRQCD predictions and analyzing their impact on cross sections and angular distributions.

Findings

Corrections reduce renormalization scale dependence.

Predictions align with Belle and BaBar measurements within uncertainties.

Angular distribution predictions still show tension with experimental data.

Abstract

We compute the ${\mathcal O}(\alpha_s^2)$ corrections to the exclusive channels $e^+e^-\to J/\psi+\chi_{cJ}$ ($J=0,1,2$) at $\sqrt{s}=10.58$ GeV within the nonrelativistic QCD (NRQCD) factorization framework. The validity of NRQCD factorization at ${\cal O}(\alpha_s^2)$ has been confirmed for these double-charmonium exclusive production processes. We analyze the impact of the $\mathcal{O}(\alpha_s^2)$ corrections on the polarized and unpolarized cross sections, as well as the $J/\psi$ angular distributions, which largely reduce the renormalization scale dependence but increase the ${\mathcal O}(\alpha_s)$ NRQCD predictions to some extent for $\chi_{c0,1}$. With high numerical accuracy, our predictions for $\sigma(J/\psi+\chi_{c1,2})$ through ${\mathcal O}(\alpha_s^2)$ are compatible with the upper limit of the \texttt{Belle} measurement. Although the theoretical prediction for $\sigma(J/\psi+\chi_{c0})$ is consistent with both \texttt{Belle} and \texttt{BaBar} measurements within uncertainties, there still exists serious tension between the predicted and the measured profiles for the $J/\psi$ angular distribution. Regarding the bright observation prospect of the $e^+e^-\to J/\psi+\chi_{c1,2}$ channels in \texttt{Belle 2} experiment, it is interesting to compare the future measurements with our NRQCD predictions. The more accurate measurement of $e^+e^-\to J/\psi+\chi_{0}$ at \texttt{Belle 2} will also help to clarify the long-standing puzzle of $J/\psi$ angular distribution.