Central exclusive production of scalar and pseudoscalar charmonia in the light-front $k_T$-factorization approach

TL;DR

The paper develops a $k_T$‑factorization framework to study central exclusive production of scalar and pseudoscalar charmonia, deriving the hard gluon fusion amplitudes with off‑shell gluons and incorporating light‑front quarkonia wave functions. It systematically explores multiple off‑diagonal gluon density prescriptions (KMR, CDHI, PST, GBW, RS) and saturations, assessing their impact on cross sections and differential distributions, including rapidity, $p_T$, and azimuthal correlations. A key finding is that exclusive $\eta_c$ production is significantly suppressed compared to $\chi_{c0}$ under typical UGD schemes, though saturation-based approaches can mitigate the gap; absorptive corrections further modulate the rates with state‑dependent gap survival factors. Distinctive patterns in $(t_1,t_2)$ and $\Delta\phi$ distributions offer a handle to constrain the soft QCD dynamics and the underlying off‑diagonal UGDs, making this work a step toward experimentally probing exclusive heavy quarkonia production and the associated nonperturbative inputs.

Abstract

We study exclusive production of scalar $χ_{c0}\equiv χ_c(0^{++})$ and pseudoscalar $η_c$ charmonia states in proton-proton collisions at the LHC energies. The amplitudes for $gg \to χ_{c0}$ as well as for $gg \to η_c$ mechanisms are derived in the $k_{T}$-factorization approach. The $p p \to p p η_c$ reaction is discussed for the first time. We have calculated rapidity, transverse momentum distributions as well as such correlation observables as the distribution in relative azimuthal angle and $(t_1,t_2)$ distributions. The latter two observables are very different for $χ_{c0}$ and $η_c$ cases. In contrast to the inclusive production of these mesons considered very recently in the literature, in the exclusive case the cross section for $η_c$ is much lower than that for $χ_{c0}$ which is due to a special interplay of the corresponding vertices and off-diagonal UGDFs used to calculate the cross sections. We present the numerical results for the key observables in the framework of potential models for the light-front quarkonia wave functions. We also discuss how different are the absorptive corrections for both considered cases.

Figures (11)

• Figure 1: Generic diagram for the Durham model approach to the considered exclusive production processes.
• Figure 2: Collinear gluon PDF as a function of the hard scale of the process and for typical longitudinal gluon momentum fractions, $x = 10^{-4}$ (upper plot) and $x=10^{-2}$ (lower plot).
• Figure 3: The rapidity distribution for $\chi_{c0}$, $\eta_{c}$ quarkonia CEP and effective $R_g$ factor calculated with the GJR08NLO parton distribution function. No gap survival factor is included here.
• Figure 4: Distribution in transverse momentum of the $\chi_{c0}$ (left) and $\eta_{c}$ (right) quarkonia CEP, respectively, with different treatment of $R_{g}$ factor. No gap survival factor is included here.
• Figure 5: Distribution in $t_{1}\times t_{2}$ for CDHI (left-upper), BPSS (right-upper) and Durham (left-lower) prescriptions calculated with the GJR08NLO gluon distribution function and for the PST off-diagonal UGD computed with the diagonal GBW UGD (right-lower) for $\eta_{c}$ CEP for $\sqrt{s} = 13\,{\rm TeV}$. No gap survival factor is included here.