Probing gluon and heavy-quark nuclear PDFs with photon + heavy quark production in pA collisions

TL;DR

This work addresses the poor knowledge of nuclear gluon and heavy-quark PDFs by performing a detailed NLO QCD calculation of direct photon production in association with a heavy-quark jet in pA collisions at RHIC and the LHC. The dominant $gQ\to\gamma Q$ channel makes the observable $R^{\gamma+Q}_{pA}$ particularly sensitive to gluon and heavy-quark nPDFs across complementary $x$-ranges, with predictions compared across nCTEQ, EPS09, and HKN07. The study provides cross-sections, differential distributions, and event-rate estimates for RHIC’s PHENIX and LHC’s ALICE detectors, showing that measurements of $\gamma+c$ (and $\gamma+b$ at the LHC) can meaningfully distinguish among nPDF sets and constrain the nuclear gluon distribution. These results offer a concrete path to reduce uncertainties in heavy-ion predictions and motivate future work on intrinsic charm in nuclei.

Abstract

We present a detailed phenomenological study of direct photon production in association with a heavy-quark jet in pA collisions at the Relativistic Heavy Ion Collider (RHIC) and at the Large Hadron Collider (LHC) at next-to-leading order in QCD. The dominant contribution to the cross-section comes from the gluon--heavy-quark (gQ) initiated subprocess, making γ+ Q production a process very sensitive to both the gluon and the heavy-quark parton distribution functions (PDFs). Additionally, the RHIC and LHC experiments are probing complementary kinematic regions in the momentum fraction x_2 carried by the target partons. Thus, the nuclear production ratio R^{γ+Q}_{pA} can provide strong constraints, over a broad x-range, on the poorly determined nuclear parton distribution functions which are extremely important for the interpretation of results in heavy-ion collisions.

Figures (11)

• Figure 1: Nuclear modifications ${R_g^{A}}=g^{p/A}(x,Q)/g^{p}(x,Q)$. Left: for gold at $Q=15$ GeV. Right: for lead at $Q=50$ GeV. Shown are results for nCTEQ decut3 (solid, black line), EPS09 (dashed, blue line) + error band, HKN07 (dash-dotted, red line) + error band. The boxes exemplify the $x$-regions probed at RHIC ($\sqrt{s_{_{\rm NN}}}=200$ GeV) and the LHC ($\sqrt{s_{_{\rm NN}}}=8.8$ TeV), respectively.
• Figure 2: Left: nPDF ratio $R_g^{Pb}$ at $Q_0=1.3$ GeV predicted within the different nCTEQ sets -- fits from top to bottom: decut3g9, decut3g5, decut3g7, decut3g8, decut3g3, decut3g4, decut3g2, decut3g1, decut3g. Right: nCTEQ gluon nPDFs for different A (1, 2, 4, 9, 12, 27, 56, 108, 207) vs x at $Q_0=1.3$ GeV -- from left to right, and top to bottom: decut3g, decut3g1, decut3g2, decut3g3, decut3g4, decut3g5, decut3g7, decut3g8, decut3g9.
• Figure 3: Nuclear modifications to deuteron, ${R_g^{d}}=g^{p/d}(x,Q)/g^{p}(x,Q)$ at $Q=15$ GeV, nCTEQ (solid black line), EPS09 (dashed blue line), HKN (dash-dotted red line) + error band
• Figure 4: Left: nPDF ratios $R_g^{Pb}=g^{p/Pb}(x,Q)/g^{p}(x,Q)$ (top) , $R_c^{Pb}=c^{p/Pb}(x,Q)/c^{p}(x,Q)$ (middle), $R_{u_v}^{Pb}=u_v^{p/Pb}(x,Q)/u_v^{p}(x,Q)$ (bottom) at $Q=50$ GeV within nCTEQ (solid black line), EPS09 (dashed blue line), and HKN07 (dash-dotted red line). The shaded regions correspond to the $x$-values probed at RHIC ($x\sim 10^{-1}$) and the LHC ($x\sim 10^{-2}$). Right: double ratios $R_c^{Pb}/R_g^{Pb}$ and $R_c^{Pb}/R_{u_v}^{Pb}$ using the same nPDF sets.
• Figure 5: Differential cross-section for $\gamma+c$ (left) and $\gamma+b$ (right) production in $d$--Au collisions at a center-of-mass energy of $\sqrt{s_{_{\rm NN}}}=200$ GeV: NLO (solid black line + band), LO (dashed blue line).