Factorization in exclusive quarkonium production

TL;DR

This paper establishes factorization theorems for exclusive heavy-quarkonium production in e^+e^- annihilation and B-meson decays, analyzing soft-gluon effects and suppression of factorization violations.

Contribution

It provides the first comprehensive proofs of factorization for these processes, including explicit one-loop analyses and suppression estimates for factorization violations.

Findings

Factorization is generally valid with suppressed violations.

Violations are suppressed by v^2m_c/Q for S-wave and m_c/Q for L-wave quarkonia.

Explicit one-loop analyses illustrate soft-gluon cancellation features.

Abstract

We present factorization theorems for two exclusive heavy-quarkonium production processes: production of two quarkonia in e^+e^- annihilation and production of a quarkonium and a light meson in B-meson decays. We describe the general proofs of factorization and supplement them with explicit one-loop analyses, which illustrate some of the features of the soft-gluon cancellations. We find that violations of factorization are generally suppressed relative to the factorized contributions by a factor v^2m_c/Q for each S-wave charmonium and a factor m_c/Q for each L-wave charmonium with L>0. Here, v is the velocity of the heavy quark or antiquark in the quarkonium rest frame, Q=sqrt{s} for e^+e^- annihilation, Q=m_B for B-meson decays, sqrt{s} is the e^+e^- center-of-momentum energy, m_c is the charm-quark mass, and m_B is the B-meson mass. There are modifications to the suppression factors if quantum-number restrictions apply for the specific process.