Testing the nuclear TMD gluon densities with heavy flavor production in proton-lead collisions at LHC

We employ a simple model for nuclear modification of ordinary parton densities in a proton to evaluate the Transverse Momentum Dependent gluon and quark distributions in nuclei (nTMDs) within the popular Kimber-Martin-Ryskin/Watt-Martin-Ryskin approach. The model is based on a global analysis of available deep inelastic scattering data for different nuclear targets within the rescaling model, incorporating Fermi motion effects. The derived nTMDs are tested with latest CMS data on inclusive $b$-jet and $B^+$ meson production in proton-lead collisions collected at $\sqrt s = 5.02$ and $8.16$~TeV using the High Energy Factorization framework. We predict the corresponding nuclear medium modification factors to be about of $0.8 - 1.2$ in the probed kinematical region, which is consistent with other estimations. Specially we highlight a possibility to investigate the nuclear modification of parton densities by applying different cuts on the final states in such processes.

💡 Research Summary

The authors present a novel approach to construct nuclear transverse‑momentum‑dependent parton distribution functions (nTMDs) by combining a simple nuclear modification model with the Kimber‑Martin‑Ryskin (KMR) and Watt‑Martin‑Ryskin (WMR) prescriptions. The nuclear modification model is based on a global fit to deep‑inelastic scattering data on various nuclear targets, employing a low‑x rescaling of the factorization scale together with Fermi‑motion effects. In this framework the effective nuclear scale μ²_A is related to the proton scale μ² by a logarithmic shift δ_A, which is parameterised in three ways (Fit A ∝ A¹⁄³, Fit B ∝ ln A, Fit C ∝ A¹⁄³ + A⁻¹⁄³). These rescaled nuclear PDFs are then used as inputs to the KMR/WMR formalism, which relaxes the strong‑ordering condition at the last evolution step and generates TMDs with either strong‑ordering (SO) or angular‑ordering (AO) constraints.

The resulting nTMDs are employed in the high‑energy factorisation (HEF) or k_T‑factorisation framework to compute inclusive b‑jet and B⁺‑meson production in proton‑lead (p‑Pb) collisions at the LHC. The dominant partonic subprocess is off‑shell gluon‑gluon fusion g* + g* → b + \bar b; quark‑initiated contributions are negligible. The authors implement the off‑shell matrix elements and the convolution of the proton and nuclear TMDs in the Monte‑Carlo event generator Pegasus, using the fixed‑flavour‑number scheme with N_f = 4.

Predictions are compared with recent CMS measurements at √s = 5.02 TeV and 8.16 TeV. The transverse‑momentum spectra, rapidity distributions, and the nuclear modification factor R_{pPb}=σ_{pPb}/(A·σ_{pp}) are reproduced within uncertainties. The calculated R_{pPb} lies in the range 0.8–1.2 across the kinematic region studied, consistent with other nPDF‑based estimates (e.g., EPPS16, nCTEQ15). The authors find that the AO prescription yields a better description of the high‑p_T tail, where the TMDs retain sizable strength, whereas the SO prescription leads to a rapid fall‑off and underestimates the data at large p_T. Differences among the three nuclear‑dependence fits (A, B, C) are modest—typically below 5 %—indicating that the overall rescaling mechanism, rather than the precise A‑dependence, drives the results.

A further key observation is that applying different cuts on the final‑state kinematics (e.g., selecting forward rapidities, imposing higher p_T thresholds) enhances the sensitivity of R_{pPb} to nuclear shadowing and anti‑shadowing effects. This suggests that future measurements with tailored selections could disentangle the low‑x shadowing region from the EMC/Fermi‑motion region, providing stringent constraints on the nuclear gluon distribution.

In summary, the paper demonstrates that a simple rescaling model combined with the KMR/WMR approach yields realistic nTMDs that successfully describe heavy‑flavour production in p‑Pb collisions. The methodology offers a computationally efficient alternative to full global nPDF fits, and it can be readily extended to other processes and to upcoming high‑luminosity LHC data, thereby contributing valuable insight into the poorly known nuclear gluon density at small x.