Color-octet contributions for $J/\psi$ inclusive production at B factories in soft gluon factorization

TL;DR

This paper investigates color-octet contributions to $J/ar{c}$ production at B factories using the soft gluon factorization approach, providing analytic calculations and resummations that improve understanding of nonperturbative effects and universality in NRQCD.

Contribution

It introduces the soft gluon factorization method for $J/ar{c}$ production, including analytic NLO calculations and resummation of velocity and Sudakov logarithms, addressing universality issues in NRQCD.

Findings

Resummed velocity corrections are significant for phenomenology.

Sudakov logarithms from soft gluon emissions are crucial, while those from jet functions are less so.

The results set an upper bound for color-octet matrix elements consistent with collider data.

Abstract

We have studied color-octet contributions for $J/\psi$ inclusive production at B factories, i.e., $e^+e^-\to J/\psi(^3P_J^{[8]},^1S_0^{[8]}) + X_{\mathrm{non}-c\bar c}$, using the soft gluon factorization (SGF) approach, in which the $J/\psi$ energy spectrum is expressed in a form of perturbatively calculable short-distance hard parts convoluted with one-dimensional soft gluon distributions (SGDs). The series of velocity corrections originated from kinematic effect can be naturally resummed in this approach. Short-distance hard parts have been calculated analytically to next-to-leading order in $\alpha_s$. Renormalization group equations for SGDs have been derived and solved, which resums Sudakov logarithms originated from soft gluon emissions. Our final result gives a upper bound for color-octet matrix elements consistent with that extracted from hadron colliders. This may relieve the well-known universality problem in the NRQCD factorization. As a comparison, we also analytically calculated short-distance hard parts in the NRQCD factorization, with Sudakov logarithms resummed by using soft collinear effective theory. The comparison shows that velocity corrections from kinematic effect, which have been resummed in SGF, are significant for phenomenological study. Furthermore, it is found that Sudakov logarithms originated from soft gluon emissions are very important, while it is not the case for Sudakov logarithms originated from jet function. Therefore, the partial Sudakov resummation in SGF has already captured the main physics.