Refactorizing NRQCD short-distance coefficients in exclusive quarkonium production

TL;DR

This paper refines the calculation of short-distance coefficients in exclusive quarkonium production by separating the hard and collinear regimes, enabling all-order summation of large logarithms to improve perturbative predictions.

Contribution

It introduces a factorization approach that further separates the hard and collinear regimes in NRQCD, allowing for the summation of large logarithms using light-cone techniques.

Findings

Large kinematic logarithms identified in NRQCD coefficients.

Summation of leading logarithms achieved with Brodsky-Lepage evolution.

Application to specific processes demonstrates improved perturbative accuracy.

Abstract

In a typical exclusive quarkonium production process, when the center-of-mass energy, $\sqrt{s}$, is much greater than the heavy quark mass $m$, large kinematic logarithms of $s/m^2$ will unavoidably arise at each order of perturbative expansion in the short-distance coefficients of the nonrelativistic QCD (NRQCD) factorization formalism, which may potentially harm the perturbative expansion. This symptom reflects that the hard regime in NRQCD factorization is too coarse and should be further factorized. We suggest that this regime can be further separated into "hard" and "collinear" degrees of freedom, so that the familiar light-cone approach can be employed to reproduce the NRQCD matching coefficients at the zeroth order of $m^2/s$ and order by order in $\alpha_s$. Taking two simple processes, exclusive $\eta_b+\gamma$ production in $e^+ e^-$ annihilation and Higgs boson radiative decay into $\Upsilon$, as examples, we illustrate how the leading logarithms of $s/m^2$ in the NRQCD matching coefficients are identified and summed to all orders in $\alpha_s$ with the aid of Brodsky-Lepage evolution equation.