Global analysis of the experimental data on $χ_c$ meson hadroproduction

TL;DR

This paper tests NRQCD factorization in χ_c hadroproduction by analyzing cross sections and the ratio σ(χ_{c2})/σ(χ_{c1}) at hadron colliders. It develops LO and NLO calculations, incorporating color-singlet and color-octet channels, and studies the μ_Λ-scale dependence of LDMEs, including a global fit across multiple data sets and renormalization schemes. The main finding is that LO cannot describe all data with a single CO LDME, while NLO analyses yield consistent LDME values and excellent agreement with all measured χ_c data, albeit with some residual scale sensitivity at high rapidity. Overall, the results support NRQCD factorization for χ_c production and highlight the need for potential resummation at large rapidity to further improve high-p_t predictions.

Abstract

We carry out a global analysis of the experimental data on the $χ_c$ production cross section and the ratio $σ(χ_{c2})/σ(χ_{c1})$ at the LHC and the Tevatron. The related long-distance matrix elements (LDMEs) at both leading order (LO) and next-to-leading order (NLO) in the QCD coupling constant are renewed. We also present the transverse momentum distribution of the $χ_c$ production cross section and the ratio $σ(χ_{c2})/σ(χ_{c1})$ for several experimental conditions and find that NLO predictions agree with all sets of experimental data. By contrast, at LO, one cannot explain all the data with a unique value of the color-octet LDME. A brief analysis of the nonrelativistic QCD scale dependence of the cross sections shows that, for the conditions we are concerned with in this paper, the dependence can be almost totally absorbed into the LDME.

Figures (6)

• Figure 1: Typical diagrams where the soft gluon connects to the quarkonium.
• Figure 2: The value of $r$ defined in Eq.(\ref{['eqn:defr']}) as a function of $p_t^{\chi_c}$.
• Figure 3: The $p_t$ distribution of $\chi_c$ production at the Tevatron and LHC. The blue and black curves are for LO and NLO, respectively. The experimental data are taken from Refs. LHCb:2012afATLAS:2014ala.
• Figure 4: The ratio $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ as a function of $p_t$ at the Tevatron and LHC. The blue and black curves are for LO and NLO, respectively. The experimental data are taken from Refs. Abulencia:2007braAaij:2013djaLHCb:2012acChatrchyan:2012ub.
• Figure 5: The LO results for the $\chi_c$ production cross section and the ratio $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ as a function of $p_t$ at the Tevatron and LHC. The band corresponds to the LO prediction between the results for ${\cal O}=0.13$ and ${\cal O}=1.88$. The experimental data are taken from Refs. Abulencia:2007braLHCb:2012afAaij:2013djaLHCb:2012acChatrchyan:2012ubATLAS:2014ala.