Unified Resummation of Soft Gluon Radiation in Heavy Meson Pair Photoproduction

TL;DR

This work develops a unified Sudakov resummation framework for heavy-quark pair photoproduction that interpolates between the massive regime $|\boldsymbol q|\lesssim m_Q$ and the massless limit $m_Q\ll|\boldsymbol q|$, within the CGC description of small-$x$ gluons. The cross-section is resummed in coordinate space, combining massive- and massless-type Sudakov factors with WW gluon TMDs (unpolarized $xf$ and linearly polarized $xh$) and non-perturbative broadening, and is evolved using rcBK for the small-$x$ dynamics. The framework yields quantitative descriptions of the H1 $\Delta\phi$ data and robust predictions for azimuthal harmonics $\langle \cos(2n\phi_{qP})\rangle$ and their nuclear-to-proton ratios, demonstrating strong sensitivity of these observables to gluon saturation, enhanced by the heavy-quark mass through dead-cone suppression. A mass-dependent suppression of soft radiation amplifies genuine saturation signals, making heavy-quark pair photoproduction a powerful probe for gluon saturation at future EIC and UPC measurements, with broad applicability to other processes involving massive particles and jets. The approach provides a practical path to disentangle perturbative Sudakov effects from nonlinear small-$x$ dynamics across a wide kinematic range, via both total- and angular-observables.

Abstract

We develop a unified resummation framework for heavy-meson pair photoproduction that treats soft-gluon radiation in a massive scheme for $|\boldsymbol q| \lesssim m_Q$ and is consistent with the massless limit $m_Q \ll |\boldsymbol q|$, where $\boldsymbol q$ denotes the transverse momentum of the pair and $m_Q$ the quark mass. This framework describes the full correlation regime $|\boldsymbol q| \ll |\boldsymbol P|$, with $\boldsymbol P$ the pair's relative transverse momentum. Next, within the Color Glass Condensate framework, we quantify the impact of soft gluon radiation on two important phenomenological observables, namely, the azimuthal $Δφ$ correlation and the harmonic asymmetries $\langle \cos(2nφ_{qP})\rangle$. Our results show that the resummation provides an excellent description of the H1 $Δφ$ data. We then find that the angular-asymmetry harmonics are sizable and their ratios in $γA$ to $γp$ collisions are highly sensitive to gluon saturation. We further find a clear mass hierarchy in both observables, indicating that heavy-quark masses suppress soft radiation and thereby enhance genuine small-$x$ saturation signals. Our work demonstrates that heavy-quark pair photoproduction provides a quantitative probe of gluon saturation, directly measurable in forthcoming EIC and UPC measurements. Finally, the unified resummation is readily extendable to other processes involving massive particles and jets in both $eA$ and $pA$ collisions.

Figures (5)

• Figure 1: Comparison of our resummed predictions with H1 data on the $\Delta \phi$ distribution in D-meson–triggered dijet and D-meson+jet events H1:2006aloH1:2011myz.
• Figure 2: Predictions for the nuclear modification factor for D- and B-meson pair photoproduction in UPCs at the LHC with $\sqrt{s}=5.36$ TeV, shown as a function of $\Delta \phi$.
• Figure 3: Predictions for the azimuthal asymmetry $\langle \cos(2\phi_{qP}) \rangle$ (upper panel) and its ratio (lower panel) for D-meson pair production in the EIC regime with $Q^2=1$ GeV$^2$, plotted as a function of $\boldsymbol{q}_h$.
• Figure 4: Predicted azimuthal asymmetries $\langle \cos(2n\phi_{qP}) \rangle$ (upper) and their ratios (lower) for B- and D-meson pair photoproduction in UPCs at the LHC ($\sqrt{s}=5.36$ TeV), plotted as functions of $\boldsymbol{q}_h$.
• Figure 5: Comparison of resummed results from new unified and conventional (massive-only) schemes, for the $\Delta\phi$ correlation (left, as a function of $\Delta\phi$) and the angular asymmetry $\langle \cos(2\phi_{qP})\rangle$ (right, as a function of $\boldsymbol{q}_h$) in D- and B-meson pair photoproduction in UPCs at LHC with $\sqrt{s}=5.36~\mathrm{TeV}$.