Unified Resummation of Soft Gluon Radiation in Heavy Meson Pair Photoproduction

Abstract

We develop a unified resummation framework for heavy-meson pair photoproduction that treats soft-gluon radiation in a massive scheme for $|\mathbf{q}|\lesssim m_Q$ and is consistent with the massless limit $m_Q\ll |\mathbf{q}|$, where $\mathbf{q}$ denotes the transverse momentum of the pair and $m_Q$ the quark mass. This framework describes the full correlation regime $|\mathbf{q}|\ll |\mathbf{P}|$, with $\mathbf{P}$ 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 $\Delta \varphi$ correlation and the harmonic asymmetries $⟨\cos (2n{\varphi }_{qP})⟩$. Our results show that the resummation provides an excellent description of the H1 $\Delta \varphi$ data. We then find that the angular-asymmetry harmonics are sizable and their ratios in $\gamma A$ to $\gamma p$ 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.

Comments: 8 pages (main text) plus 5 pages (supplemental material), 5 figures. References added