${\mathcal O}(α_s)$ corrections to $e^+e^-\rightarrow J/ψ+η_{c2}(χ_{c1}^\prime)$ at $B$ factories (1301.1946v1)
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 $\ln2(s/m_c2)$ associated with all the relevant next-to-leading order Feynman diagrams, for the helicity-suppressed double-charmonium production channels $e+ e- \to J/\psi+ \eta_{c2}(\eta_c,\chi_{c0,1,2})$.