${\mathcal O}(\alpha_s)$ corrections to $e^+e^-\rightarrow J/\psi+\eta_{c2}(\chi_{c1}^\prime)$ at $B$ factories

TL;DR

This paper calculates the first-order QCD corrections to specific double-charmonium production processes in electron-positron collisions at B factories, providing predictions for cross sections and polarization states relevant for experimental searches.

Contribution

It presents the ${ m O}(\alpha_s)$ correction calculations for $e^+e^- o J/+ ext{charmonium}$, offering new theoretical predictions and insights into polarization and cross sections.

Findings

Predicted cross section for $e^+e^- o J/+ ext{eta}_{c2}$ is about 0.3 fb.

Cross section for $e^+e^- o J/+ ext{chi'}_{c1}$ is roughly six times larger.

$J/$ is dominantly transversely polarized in the first process.

Abstract

We investigate the ${\cal O}(\alpha_s)$ correction to $e^+e^-\to J/\psi+\eta_{c2}$ in the NRQCD factorization approach. A detailed comparative study between $e^+e^-\to J/\psi+\eta_{c2}$ and $e^+e^-\to J/\psi+\chi^\prime_{c1}$ at $B$ factory energy is also carried out. After incorporating the ${\cal O}(\alpha_s)$ correction, we predict the cross section for the former process to be around 0.3 fb, while that of the latter about 6 times greater. The outgoing $J/\psi$ is found to be dominantly transversely-polarized in the former process, while longitudinally-polarized in the latter. These features may provide valuable guidance for the future experiment to examine the ${}^3P_1$ or ${}^1D_2$ charmonium option of the X(3872) meson through the exclusive double-charmonium production processes. The observation potential of $e^+e^-\to J/\psi+\chi^\prime_{c1}$ looks bright for the current data sample of the \textsc{Belle} experiment, provided that the $\chi^\prime_{c1}$ is indeed the narrow X(3872) state. In the appendix, we also identify the coefficients of the double logarithms of form $\ln^2(s/m_c^2)$ associated with all the relevant next-to-leading order Feynman diagrams, for the helicity-suppressed double-charmonium production channels $e^+ e^- \to J/\psi+ \eta_{c2}(\eta_c,\chi_{c0,1,2})$.