The Systematics of Quarkonium Production at the LHC and Double Parton Fragmentation

TL;DR

This paper analyzes the systematic aspects of quarkonium production at the LHC, emphasizing the role of logarithmic contributions and deriving a factorization theorem involving double parton fragmentation functions.

Contribution

It introduces an all-order factorization theorem for quarkonium production using double parton fragmentation functions and computes the one-loop anomalous dimension matrix.

Findings

Power suppression of certain logarithmic contributions.

Identification of the role of inverse powers of v in production mechanisms.

Derivation of the all-order factorization theorem.

Abstract

In this paper we discuss the systematics of quarkonium production at the LHC. In particular, we focus on the necessity to sum logs of the form log(Q/p_perp) and log(p_perp/m_Q). We show that the former contributions are power suppressed, while the latter, whose contribution in fragmentation is well known, also arise in the short distance (i.e., non-fragmentation) production mechanisms. Though these contributions are suppressed by powers of m_Q/p_perp, they can be enhanced by inverse powers of v, the relative velocity between heavy quarks in the quarkonium. In the limit p_perp >> m_Q short distance production can be thought of as the fragmentation of a pair of partons (i.e., the heavy quark and anti-quark) into the final state quarkonium. We derive an all order factorization theorem for this process in terms of double parton fragmentation functions (DPFF) and calculate the one-loop anomalous dimension matrix for the DPFF.