Probing gluon saturation with forward di-hadron correlations in proton-nucleus collisions

TL;DR

This work develops a state-of-the-art CGC-based treatment of forward di-hadron production in $pA$ collisions by combining small-$x$ TMDs with rcBK evolution and Sudakov resummation within an improved ITMD framework. The authors constrain initial dipole distributions from HERA data, implement nuclear saturation scaling, and compare to STAR forward di-hadron measurements, finding reasonable agreement for $pA$ while highlighting fragmentation uncertainties in $pp$. They also provide predictions for ALICE FoCal kinematics, showing weaker saturation signals at higher energy due to larger $\langle k_T/Q_s\rangle$ and smaller $\langle z\rangle$, and discuss the robustness of ratio observables against fragmentation. The study underscores the potential of forward di-hadron correlations as a discriminant of gluon saturation and outlines paths toward full NLO precision and complementary observables to sharpen the saturation picture.

Abstract

We present a detailed numerical investigation of semi-inclusive forward di-hadron production in proton-nucleus collisions employing the Color Glass Condensate effective theory. We focus on the regime where di-hadrons are produced nearly back-to-back in the transverse plane, thereby justifying a transverse-momentum-dependent factorization approach in terms of small-$x$ gluon distributions. Our computation integrates several key elements: i) non-linear rapidity evolution via the Balitsky-Kovchegov equation with running coupling, ii) both perturbative and non-perturbative Sudakov resummation, and iii) a phenomenologically constrained model for the initial conditions for small-$x$ gluon distributions. We compare this phenomenological framework to experimental data from the STAR Collaboration on azimuthal correlations in forward di-pion production in both proton-proton and proton-gold collisions. We analyze the systematic theoretical uncertainties associated with the saturation scales of nuclei at the initial scale for rapidity evolution and with those associated with the hadronization process. Finally, we make predictions for the kinematics anticipated to be covered by the ALICE Forward Calorimeter (FoCal) upgrade at the Large Hadron Collider.

Figures (9)

• Figure 1: Coincidence probability in the away-side region of di-$\pi^0$ production in p-p and p-Au collisions at $\sqrt{s_{NN}}=200$ GeV, $2.6<\eta<4.0$ for various $p_T$ ranges. The band is obtained by changing the $Q^2_{\rm s, Au}$ by a factor of 1.2. The STAR data is from STAR:2021fgw.
• Figure 2: Relative area and width of back-to-back di-$\pi^0$ correlations at forward pseudorapidities in p-Au relative to p-p collisions for $p_{T,\rm trig}$ = 2.5 - 3 GeV/c as a function of $p_{T,\rm asso}$ (left two panels) and for $p_{T,\rm asso}$ = 1.5 - 2 GeV/c as a function of $p_{T,\rm trig}$ (right two panels). The band is obtained by changing the $Q^2_{s,\rm Au}$ by a factor of 1.2. The STAR data is from STAR:2021fgw.
• Figure 3: Relative area and width of back-to-back di-$\pi^0$ correlations at forward pseudorapidities with three different fragmentation functions in p-Au relative to p-p collisions for $p_{T,\rm trig}$ = 2.5 - 3 GeV/c as a function of $p_{T,\rm asso}$ (left two panels) and for $p_{T,\rm asso}$ = 1.5 - 2 GeV/c as a function of $p_{T,\rm trig}$ (right two panels). The STAR data is from STAR:2021fgw.
• Figure 4: Coincidence probability in the away-side region of di-$\pi^0$ production in p-p and p-Pb collisions at $\sqrt{s_{NN}}=5.36$ TeV, $3.2<\eta<5.8$ for various $p_T$ ranges. The band is obtained by changing the $Q^2_{\rm s, Pb}$ by a factor of 1.2.
• Figure 5: Relative area and width of back-to-back di-$\pi^0$ correlations at forward pseudorapidities in p-Au and p-Pb relative to p-p collisions for $p_{T,\rm trig}$ = 2.5 - 3 GeV/c as a function of $p_{T,\rm asso}$ (left two panels) and for $p_{T,\rm asso}$ = 1.5 - 2 GeV/c as a function of $p_{T,\rm trig}$ (right two panels). The band is obtained by changing the $Q^2_{s,\rm Au/Pb}$ by a factor of 1.2.