Production of $χ_c$- and $χ_b$-mesons in high energy hadronic collisions

TL;DR

The paper analyzes χ_c and χ_b production in high-energy hadronic collisions within NRQCD, separating short-distance production from nonperturbative hadronization. By fitting χ_c data, especially the ratio σ(χ_c2)/σ(χ_c1) and the J/ψ spectrum from χ_c decays, it extracts nonperturbative matrix elements ⟨O_S⟩ and ⟨O_P⟩ and determines the color-singlet derivative |R'(0)|^2, finding color-singlet dominance in the χ_c p_T spectrum and octet-driven variation in the ratio. NRQCD scaling then predicts χ_b production, showing substantially smaller octet effects for bottomonium and predictions close to color-singlet expectations. The work demonstrates that ratio observables are highly sensitive probes of octet contributions and provides a data-informed framework for predicting χ_b production across kinematic regions. Overall, it advances the understanding of quarkonium production by quantifying nonperturbative NRQCD inputs and validating scaling relations between charmonium and bottomonium.

Abstract

This paper is devoted to phenomenological study of $χ_{c,b}$-mesons production in high energy hadronic collisions in the framework of NRQCD. We analyze all available experimental data on $χ_c$-mesons production and extract non-perturbative NRQCD matrix elements from fitting the data. We show, that measured $p_T$-spectrum of $χ_c$-mesons is mainly formed by color singlet components, while $σ(χ_{c2})/σ(χ_{c1})$ ratio depends strongly on color octet matrix elements; this ratio becomes a highly sensitive tool to study contribution of different terms from the NRQCD expansion. Obtained using NRQCD scaling rules predictions for $χ_b$-mesons cross sections are also given.

Figures (7)

• Figure 1: Typical Feynman diagrams for the processes $g + g \to Q\bar{Q}[r] + g$. Diagrams (a), (b) and (e) corresponds to both color singlet and color octet production, while diagrams (c), (d) and (f) only for color octet production of $^3S_1^{(8)}$ state.
• Figure 2: Acceptable regions of dimensionless parameters $M_{\chi_c}^2\langle O_S \rangle/\left|R'(0)\right|^2$ and $\langle O_P \rangle/\left|R'(0)\right|^2$ obtained by fitting each experiment on ratio $\sigma(\chi_{2})/\sigma(\chi_{1})$.
• Figure 3: Theoretical predictions for the ratio $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ with NRQCD parameters obtained by fitting different groups of experiments. The results of overall fit of all data shown as gray area with dashed boundaries. Upper dashed line corresponds to asymptotic NRQCD predictions for high $p_T$. Lower dashed line --- predictions of pure color singlet model.
• Figure 4: Theoretical predictions for the cross section of $J/\psi$-mesons produced via radiative $\chi_c$ decays with NRQCD parameters obtained by fitting a whole set of data on ratio LHCb:2012acChatrchyan:2012ubTheATLAScollaboration:2013bjaAaij:2013djaAbulencia:2007bra and CDF data on spectrum Abe:1997yz. CDF data shown with filled squares. The left figure shows the total cross section with uncertainties, right --- contribution of different NRQCD state using best fit parameters. Solid line --- sum over all states, dashed ---- color singlet, dot-dashed --- $P$-wave octet, dotted --- $S$-wave octet.
• Figure 5: Theoretical predictions for the cross sections of prompt $\chi_{c1,2}$-mesons with NRQCD parameters obtained by fitting a whole set of data on ratio LHCb:2012acChatrchyan:2012ubTheATLAScollaboration:2013bjaAaij:2013djaAbulencia:2007bra and CDF data on spectrum Abe:1997yz. ATLAS data on spectrum TheATLAScollaboration:2013bja (not included in fit) shown with points.