$O({\alpha }_s)$ corrections to $J/\psi +{\chi }_{cJ}$ production at $B$ factories

Abstract

We investigate the $\mathcal{O}({\alpha }_s)$ corrections to $e^{+}{e}^{-}\to J/\psi ({\psi }^{\prime })+{\chi }_{cJ}$ ($J=0,1,2$) in the NRQCD factorization approach. These next-to-leading order (NLO) corrections are calculated at the level of helicity amplitude. We have made a detailed analysis for both polarized and unpolarized cross sections, and compared our predictions with the measurements at the $B$ factories. We also derive the asymptotic expressions for each of the NLO helicity amplitudes, and confirm the earlier speculation that at NLO in ${\alpha }_s$, the double logarithm of type ${\ln }^2(s/m_c^2)$ appearing in the NRQCD short-distance coefficient is always associated with the helicity-suppressed channels.

Comments: v3, 18+3 pages, 6 figures, 3 tables; some formulas corrected, erratum added