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

TL;DR

This paper calculates the NLO radiative corrections for inclusive $h_c$ production in $e^+e^-$ annihilation at Super B factory, improving the theoretical prediction of the $h_c$ energy spectrum with resummation techniques.

Contribution

It provides the first NLO calculation of the color-octet $h_c$ production and resums endpoint logarithms for a reliable energy spectrum prediction.

Findings

NLO correction is positive and significant.

Resummation yields well-behaved energy spectrum predictions.

Predictions are ready for experimental verification at Belle II.

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 $\mathcal{O}_8^{h_c}(^1S_0)$ 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.