Inclusive $h_c$ production and energy spectrum from $e^{+}{e}^{-}$ annihilation at Super $B$ factory

Abstract

We calculate the next-to-leading order (NLO) radiative correction to the color-octet $h_c$ inclusive production in $e^{+}{e}^{-}$ annihilation at Super $B$ factory, within the nonrelativistic QCD factorization framework. The analytic expression for the NLO short-distance coefficient (SDC) accompanying the color-octet production operator ${\mathcal{O}}_8^{h_c}{(}^1{S}_0)$ is obtained after summing both virtual and real corrections. The size of NLO correction for the color-octet production channel is found to be positive and substantial. The NLO prediction to the $h_c$ energy spectrum is plagued with unphysical endpoint singularity. With the aid of the soft-collinear effective theory, those large endpoint logarithms are resummed to the next-to-leading logarithmic (NLL) accuracy. Consequently, further supplemented with the non-perturbative shape function, we obtain the well-behaved predictions for the $h_c$ energy spectrum in the entire kinematic range, which awaits the examination by the forthcoming Belle II experiment.

Comments: 19 pages, 1 table, 5 figures, version accepted for publication at PRD