Hadronic production of S- and P-wave states of (b-bar c)-quarkonium

TL;DR

This study computes hadronic production cross-sections for both S- and P-wave ar{b}c quarkonium states at leading O(α_s^4) in perturbative QCD, highlighting a two-step factorization into heavy-quark production and bound-state formation via a projection operator. It develops a detailed calculation framework that expands in the relative quark momentum q and employs numerical derivatives and RAMBO phase-space integration. The results reveal large discrepancies with fragmentation-model predictions, showing recombination diagrams dominate and fragmentation poorly describes p_T and z distributions; P-wave production is non-negligible but an order of magnitude smaller than S-wave. Overall, the paper demonstrates the limits of fragmentation approaches in hadronic B_c production and provides the first complete perturbative results for P-wave states, with important implications for theoretical modeling and phenomenology in heavy-quarkonium production.

Abstract

In the leading $O(α_s^4)$ order of the perturbative QCD, the hadronic production cross-sections of $S$- and $P$-wave states of $B_c$ meson are calculated. The results for the $S$-wave levels are compared with the values given in other papers as well as in the model of the $b$ quark fragmenatation into $B_c$. In the given order, the cross-sections of the hadronic production of the $P$-wave states are calculated for the first time. Their contribution into the $B_c$ meson production is less than 10\%. There is a strong difference between the predictions of the fragmentation model and the exact perturbative calculations. These difeerences are discussed in details for the differential distributions over various kinematical quantities.