Exploring parameter dependence of heavy-flavor dynamics in small collision systems

TL;DR

This work investigates how initial-state effects (Cronin broadening and shadowing) and final-state interactions in a fluctuating small QGP medium shape the $R_{pPb}$ and $v_2$ of $D$ mesons in $p$-Pb collisions. Heavy quarks are propagated using Langevin dynamics with drag, diffusion, and medium-induced radiation, and hadronize via coalescence; initial charm spectra are drawn from FONLL and modified by Cronin and EPS09. The study shows that while $R_{pPb}$ can be reproduced by the combined effects, the measured $v_2$ cannot be accounted for by final-state interactions alone and requires initial-state azimuthal anisotropy. Hydrodynamic evolution via MUSIC with fluctuating initial conditions connects spatial eccentricities to momentum anisotropies, but even with varying initial geometries, final-state dynamics contribute only part of the observed heavy-flavor elliptic flow, underscoring the role of initial-state effects. The results highlight the need for a more complete treatment of initial-state fluctuations and event-by-event hydrodynamics to fully describe heavy-quark observables in small collision systems.

Abstract

Observations from high-multiplicity proton-lead ($p$-Pb) collisions indicate that small systems may exhibit collective behavior in both heavy and light hadrons. This work investigates the roles of initial- and final-state interactions in shaping the nuclear modification factor and elliptic flow of $D$ mesons measured in $p$-Pb collisions. Initial-state effects, including the Cronin and shadowing effects, are considered in the heavy-quark initial conditions, while final-state interactions are simulated through Langevin evolution combined with the coalescence model of hadronization. Different initial geometries attributed to fluctuations in the medium's energy density are parametrized and translated into the momentum anisotropies of both light and heavy quarks. The corresponding $R_{pPb}$ and $v_2$ of D mesons in 8.16 TeV $p$-Pb collisions are calculated under different assumptions for the final-state interactions. Assuming that the initial-state effects only modify the transverse momentum spectra without altering the azimuthal distribution of heavy quarks, the measured $R_{pPb}$ of D mesons can be qualitatively reproduced by the combined influence of initial- and final-state effects. However, the observed $v_2$ cannot be accounted for by final-state interactions alone. These results suggest that additional contributions to azimuthal anisotropies of heavy quarks originating from initial-state effects are required to explain the experimentally observed $v_2$.

Figures (5)

• Figure 1: The normalized initial transverse momentum distribution of charm quarks in the central rapidity bin of 5.02 TeV $pp$ collisions from the FONLL model.
• Figure 2: Modification factors from the Cronin effect and the cold nuclear matter effect, the latter defined as a product of the Cronin factor and the shadowing factor obtained from the EPS09 NLO model. The calculations are performed for $p$-Pb collisions at 8.16 TeV.
• Figure 3: (Color online) Initial temperature profiles in the transverse plane of the medium in 5.02 TeV $p$-Pb collisions, with spatial anisotropies $\epsilon_2=0.60$ (a) and $\epsilon_2=0.88$ (b) due to initial fluctuations.
• Figure 4: (Color online) Initial transverse-plane temperature profiles of the hot deconfined medium. The Gaussian width of each hot spot is $a_x = 1$ fm. In panels (a) and (b), the distance between hot spots is set to $a_y=1$ fm ($\epsilon_2=0.23$) and $2$ fm ($\epsilon_2=0.51$), respectively.
• Figure 5: (Color online) Nuclear modification factor $R_{pPb}$ at $\sqrt{s_{NN}} = 5.02$ TeV and elliptic flow $v_2$ at $\sqrt{s_{NN}} = 8.16$ of $D$ mesons in $p$-Pb collisions. Results shown in panels (a) and (b) correspond to initial energy densities of the bulk medium proportional to an elliptical Gaussian: $\exp[-x^2/\sigma_x^2 - y^2/\sigma_y^2]$. Panels (c) and (d) depict results for initial conditions consisting of two Gaussian hot spots with separation distances given by $a_y$. Experimental data are from CMS:2018loeALICE:2019fhe