Inclusive Production of Heavy Quarkonia in pNRQCD

TL;DR

This paper introduces a new formalism based on pNRQCD for calculating inclusive heavy quarkonium production cross sections, improving predictive power and aligning well with LHC data.

Contribution

It develops a formalism linking nonrelativistic QCD matrix elements to wavefunctions and gluonic correlators, applicable to strongly coupled quarkonia, enhancing theoretical predictions.

Findings

Good agreement with LHC measurements of P-wave quarkonia production

Reduces nonperturbative unknowns in production calculations

Enables first-principle determination of long-distance matrix elements

Abstract

We develop a formalism for computing inclusive production cross sections of heavy quarkonia based on the nonrelativistic QCD and the potential nonrelativistic QCD effective field theories. Our formalism applies to strongly coupled quarkonia, which include excited charmonium and bottomonium states. Analogously to heavy quarkonium decay processes, we express nonrelativistic QCD long-distance matrix elements in terms of quarkonium wavefunctions at the origin and universal gluonic correlators. Our expressions for the long-distance matrix elements are valid up to corrections of order $1/N_c^2$. These expressions enhance the predictive power of the nonrelativistic effective field theory approach to inclusive production processes by reducing the number of nonperturbative unknowns, and make possible first-principle determinations of long-distance matrix elements once the gluonic correlators are known. Based on this formalism, we compute the production cross sections of $P$-wave charmonia and bottomonia at the LHC, and find good agreement with measurements.