Probing the small-$x$ nuclear gluon distributions with isolated photons at forward rapidities in p+Pb collisions at the LHC

TL;DR

This paper investigates how inclusive direct photon production in p+Pb collisions at the LHC can illuminate the small-$x$ behavior of nuclear gluon PDFs. It applies NLO perturbative QCD with EPS09 nPDFs to map the $x_2$ regions probed by photons at forward rapidities and analyzes how photon isolation and kinematics affect sensitivity, comparing with inclusive hadrons. It finds that photons, especially with isolation, probe smaller $x_2$ than hadrons, but gluon-DGLAP evolution reduces the rapidity dependence of $R_{\rm pPb}^{\gamma}$ and the impact of isolation, and it introduces the forward-backward yield asymmetry $Y_{\rm pPb}^{\rm asym}$ as a robust, normalization-free observable. The work informs forward-detector strategies like the ALICE FoCal and provides practical constraints on small-$x$ gluon nPDFs as well as a potential window for nonlinear QCD dynamics.

Abstract

Inclusive direct photon production in p+Pb collisions at the LHC is studied within the NLO perturbative QCD. Our aim is to quantify the dominant $x$ regions probed at different rapidities and to identify the best conditions for testing the nuclear gluon parton distribution functions (nPDFs) at small $x$. A comparison to the inclusive pion production reveals that from these two processes the photons carry more sensitivity to the small-$x$ partons and that this sensitivity can be further increased by imposing an isolation cut for the photon events. The details of the isolation criteria, however, seem to make only a small difference to the studied $x$ sensitivity and have practically no effect on the expected nuclear modifications. We consider also the yield asymmetry between forward and backward rapidities which can be used to probe the nPDFs irrespectively of whether an accurate p+p baseline is available.

Figures (17)

• Figure 1: The NLO nuclear modification for valence $u$-quarks (left), sea $u$-quarks (middle) and gluons (right) of a lead nucleus at $Q^2=25\,\mathrm{GeV^2}$, and their uncertainties, from the EPS09 analysis. The dashed curves are for the EPS09 initial scale $Q_0^2=1.69\,\mathrm{GeV^2}$, and the dotted lines show the uncertainties at $Q_0^2$.
• Figure 2: The $x_2$ distribution for $\pi^0$ production in p+Pb collisions at $\sqrt{s_{NN}}=8.8\,\mathrm{TeV}$ and $\eta=0$ for $p_T=5\,\mathrm{GeV/c}$ (blue dashed), and at $\eta=4.5$ for $p_T=2\,\mathrm{GeV/c}$ (red), $p_T=5\,\mathrm{GeV/c}$ (blue) and $p_T=10\,\mathrm{GeV/c}$ (green).
• Figure 3: The nuclear modification ratio $R_{\rm pPb}^{\pi^0}$ for $\pi^0$ production at $\eta=0$ (blue dashed) and $\eta=4.5$ (green solid) using the EPS09 NLO nPDFs. The lightblue uncertainty band (the blue dotted lines for $\eta=0$) is calculated from the error sets of EPS09.
• Figure 4: Relative contributions of the prompt (solid) and fragmentation (dashed) components in inclusive direct photon production cross section $\mathrm{d} \sigma^{\gamma+X}_{\rm pPb}/dp_Td\eta$ as a function of the photon $p_T$ in p+Pb collisions at the LHC at $\eta=0$, with the scales fixed to $\mu=Q=Q_F=p_T/2$ (red), $p_T$ (black) and $2p_T$ (green).
• Figure 5: Same as fig. \ref{['fig:frag_dir_0']} but for $\eta=4.5$.