Multiprocess imaging of nuclear modifications on parton distributions in proton-nucleus collisions

TL;DR

The paper tackles the challenge of extracting explicit $x$- and $Q^2$-dependent nuclear modifications $r^{\textrm{A}}_i(x,Q^2)$ to parton distribution functions by proposing an observable-level imaging strategy in $p$A collisions at the LHC. It reorganizes differential cross sections for $Z$, $Z+$jet, and $Z+c$-jet production to map onto $x$ and $Q^2$ via the variables $X_B$, $M_V$, $M_{VJ}$ and $p_{T,avg}$, and validates this approach with NLO calculations using three nuclear PDF sets: EPPS21, nCTEQ15, and TUJU19. The authors introduce flavor-specific observables $C_g(X_B)$ and $C_{\textrm{charm}}(X_B)$ that isolate gluon and charm signals, showing that $R_{pA}$ for these observables effectively images the corresponding $r^{\textrm{A}}_i(x,Q^2)$ up to $x_{\textrm{Pb}}\sim 0.1$ with controlled scale uncertainties. This imaging framework provides a direct, observable-level handle on flavor-separated nuclear modifications and can be extended to other processes and future facilities to improve global nPDF fits and probe non-perturbative nuclear dynamics.

Abstract

Nuclear modifications to collinear parton distribution functions are conventionally quantified by the ratios $ r^{\textrm{A}}_i(x,Q^2) = f^\textrm{A,proton}_i(x,Q^2) / f^\textrm{proton}_i(x,Q^2) $. For a given nucleus $A$, these ratios generally depend on the parton momentum fraction $ x $, the probing scale $ Q^{2} $, and the parton species $ i $. Determining these dependencies relies on a global analysis of diverse experimental data. However, in realistic observables, these dependencies are intricately intertwined, making their extraction challenging. In this paper, we propose a novel approach to effectively image the nuclear modification factors $ r^{\textrm{A}}_i(x,Q^2) $ at the observable level in proton-nucleus collisions at the Large Hadron Collider. Specifically, through a combined study of $ Z $-boson production, $ Z $+jet production, and $ Z+c $-jet production, we separately enhance signals arising from light-quark, gluon, and heavy-flavor (charm) distributions in nuclei. This enables us to effectively image the $ r^{\textrm{A}}_i(x,Q^2) $ for specific parton species. The feasibility of this method is validated through perturbative calculations at next-to-leading order in the strong coupling constant, employing three sets of nuclear PDF parametrizations: EPPS21, nCTEQ15, and TUJU19. Future measurements of these observables are expected to provide more efficient constraints on nuclear PDFs and yield new insights into the detailed partonic structures of nuclei.

Figures (8)

• Figure 1: Typical measurements of differential cross sections for $Z$-boson production (left panel), $Z\!+\!$jet production (middle panel), and $Z\!+\!c\!-\!$jet production (right panel) in $pp$ collisions at $\sqrt{s}=8$ TeV at the LHC. Measurements are binned according to the rapidity $y^Z$ and transverse momentum $p_T^Z$ for $Z$-boson production CMS:2015hyl, the rapidity $y^{\textrm{jet}}$ and transverse momentum $p_T^{\textrm{jet}}$ for $Z\!+\!$jet production ATLAS:2019bsa, and the transverse momentum $p_T^{\textrm{jet}}$ for $Z\!+\!c\!-\!$jet production CMS:2017snu. Experimental data are represented by black discs, while NLO predictions computed with MCFM Campbell:1999ahCampbell:2011bnCampbell:2015qmaCampbell:2021vlt are depicted by red lines.
• Figure 2: Nuclear correction factors $r_i^{Pb}(x, Q^2)$ for light-quark (left panel), gluon (middle panel), and charm quark (right panel) distributions, as provided by the EPPS21, nCTEQ15, and TUJU19 nuclear PDFs at $Q\!=\!M_Z/2\!=\!45$ GeV. Light quark distribution is defined as $f_q(x)=\sum_{i=u,d,s}[f_i(x)+\bar{f}_i(x)]$.
• Figure 3: Nuclear modification factors $R_{pA}$ as functions of $X_B$, calculated at NLO for reorganized cross section of $Z$-boson production (blue squares). Results corrected for isospin effects are represented by red discs. Predictions using EPPS21, nCTEQ15, and TUJU19 nuclear PDFs are displayed in left, middle, and right panels, respectively. Underlying $r^{\textrm{A}}_i(x,Q^2)$ factors for light quarks and gluons from corresponding nuclear PDFs are included in each panel for comparison. Bottom panels illustrate differences between each result and $r^{\textrm{A}}_i$ for light quarks. NLO calculations are conducted at scale $\mu_{0} = M_{Z}/2$. Uncertainties in the results, evaluated by varying scale between $\mu_{0}/2$ and $2\mu_{0}$, are represented by shaded bands.
• Figure 4: Reorganized differential cross sections as functions of $X_B$, calculated at LO. Left panel: Results for $Z+$jet production, with contributions from nuclear quarks and gluons depicted as blue and red areas, respectively (inserted panel displays corresponding contribution fractions). Middle panel: Results for $Z$-boson production. Right panel: Rescaled results for $Z+$jet production, where nuclear quark contribution aligns with $Z$-boson cross section shown in middle panel. Calculations are performed at $\mu_F\!=\!\mu_R\!=\!\mu_0\!=\!M_Z/2$, using $pp$ collisions with backward-going proton treated as a nucleus.
• Figure 5: Nuclear modification factors $R_{pA}$ as functions of $X_B$, calculated at NLO for reorganized cross section of $Z+$jet production (blue squares) and for combined observable $C_g(X_B)$ (red discs). Predictions using EPPS21, nCTEQ15, and TUJU19 nuclear PDFs are displayed in left, middle, and right panels, respectively. Underlying $r^{\textrm{A}}_i(x,Q^2)$ factors for light quarks and gluons from corresponding nuclear PDFs at $Q\!=\!M_Z/2$ are included in each panel for comparison. Bottom panels illustrate differences between each result and $r^{\textrm{A}}_i$ for gluon. NLO calculations are conducted at scale $\mu_{0} \!=\!M_{Z}/2$ for $Z$-boson and at $\mu_{0}\!=\!(M_{V\!J}\!+\!p_{T,avg})/4$ for $Z+$jet. Uncertainties in the results, evaluated by varying scale between $\mu_{0}/2$ and $2\mu_{0}$, are represented by shaded bands.