Systematics of quarkonium production at the LHC and double parton fragmentation

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 _≥) and log(p _≥/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., nonfragmentation) production mechanisms. Though these contributions are suppressed by powers of m _Q/p _≥, they can be enhanced by inverse powers of v, the relative velocity between heavy quarks in the quarkonium. In the limit p _≥m _Q, short-distance production can be thought of as the fragmentation of a pair of partons (i.e., the heavy quark and antiquark) into the final state quarkonium. We derive an all-order factorization theorem for this process in terms of double parton fragmentation functions and calculate the one-loop anomalous dimension matrix for the double parton fragmentation functions.