Inclusive Hadroproduction of $P$-Wave Heavy Quarkonia in Potential Nonrelativistic QCD

TL;DR

This paper develops a potential NRQCD framework to compute color-singlet and octet long-distance matrix elements for P-wave quarkonia, enabling predictions of production cross sections that agree with LHC data.

Contribution

It introduces a method to determine color-octet NRQCD matrix elements without relying on experimental cross section data.

Findings

Predicted inclusive cross sections for $oldsymbol{ ext{chi}_cJ}$ and $oldsymbol{ ext{chi}_bJ}$ match LHC measurements.

Developed a formalism applicable to all inclusive heavy quarkonia production processes.

Provided a new way to extract nonperturbative matrix elements theoretically.

Abstract

We compute the color-singlet and color-octet nonrelativistic QCD (NRQCD) long-distance matrix elements for inclusive production of $P$-wave quarkonia in the framework of potential NRQCD. In this way, the color-octet NRQCD long-distance matrix element can be determined without relying on measured cross section data, which has not been possible so far. We obtain inclusive cross sections of $\chi_{cJ}$ and $\chi_{bJ}$ at the LHC, which are in good agreement with data. In principle, the formalism developed in this Letter can be applied to all inclusive production processes of heavy quarkonia.