Probing Saturation Effect in Heavy Meson Pair Correlation in Forward $pA$ Collisions

Forward two-particle angular correlations in $pA$ collisions have long been recognized as a particularly sensitive observable for exploring gluon saturation effects. In the back-to-back regime, two-particle correlations receive substantial contributions from both soft-gluon radiation and saturation effects. In this work, we study heavy meson pair correlation in forward proton-nucleus collisions by incorporating a unified Sudakov resummation for heavy meson pair correlations in the Color Glass Condensate effect theory. Our results are in good agreement with the $\Delta\phi$ data measured by the LHCb Collaboration for $D^0 \bar D^0$ pairs in forward $pp$ and $pA$ collisions, as well as $J/\psi$ pairs from $b\bar b$ decays in forward $pp$ collisions. Furthermore, we present predictions for $D\bar D$ and $B\bar B$ correlations in the forward rapidity regions at the Large Hadron Collider. A pronounced mass-hierarchy is observed in the nuclear modification factor, $R_{pA}\big|_{m_b}<R_{pA}\big|_{m_c}$, indicating stronger sensitivity to saturation effects at small $x$. As the rapidity increases, the suppression becomes more pronounced while the mass hierarchy remains robust. This study will help us to search for the saturation signal via heavy-meson pair correlations in forward $pA$ collisions.