Impact of momentum-dependent drag coefficient on energy loss of charm and bottom quarks in QGP

This paper investigates how the momentum of heavy particles affects their interaction rate, and the resulting drag coefficient in a quark-gluon plasma. To account for this momentum dependence, the drag coefficient is derived by expressing the energy loss coefficients as polynomial expansions of momentum ($p$). This approach allows for a more precise investigation of momentum dependence of drag coefficient by incorporating the linear terms of these expansions. Additionally, the influence of particle’s momentum on radiative and collisional energy loss is more clearly determined. The study focuses on calculation of the nuclear modification factor ($R_{AA}$) of charm and bottom quarks in Pb-Pb collisions at $\sqrt{S_{NN}} = 5.02 : TeV$. The initial distribution functions have been evolved numerically based on the Fokker-Planck equation. The results are compared with the latest data from ALICE and ATLAS experiments, conducted in 2021 and 2022.

💡 Research Summary

This research presents a sophisticated investigation into the energy loss mechanisms of heavy quarks, specifically charm and bottom quarks, as they traverse the Quark-Gluon Plasma (QGP) created in high-energy heavy-ion collisions. The central focus of the study is the momentum dependence of the drag coefficient, a critical parameter that dictates how heavy quarks interact with the dense, hot medium.

To overcome the limitations of traditional models that often treat the drag coefficient as a momentum-independent constant or use overly simplified functions, the authors introduce a novel approach using a polynomial expansion of momentum ($p$). By incorporating linear terms within this expansion, the researchers are able to capture the nuanced variations in interaction rates that occur as the particle’s momentum changes. This mathematical refinement is crucial for distinguishing between the two primary components of energy loss: collisional energy loss, arising from elastic scattering with medium constituents, and radiative energy loss, resulting from gluon bremsstrahlung.

The study employs the Fokker-Planck equation to numerically evolve the initial momentum distribution functions of the heavy quarks. This allows for a rigorous simulation of the stochastic processes occurring during the Pb-Pb collisions at $\sqrt{S_{NN}} = 5.02 \text{ TeV}$. The primary observable used to validate the model is the nuclear modification factor ($R_{AA}$), which quantifies the suppression of high-momentum particles in heavy-ion collisions relative to proton-proton collisions.

The findings demonstrate that the momentum-dependent drag coefficient model provides a significantly more accurate description of the experimental landscape. When compared against the most recent experimental data from the ALICE and ATLAS collaborations (collected in 2021 and 2022), the proposed polynomial expansion model shows excellent agreement with the observed $R_{AA}$ values. This high level of concordance underscores the importance of accounting for momentum-dependent dynamics when modeling the transport properties of the QGP. Ultimately, this work provides a more precise theoretical framework for understanding the fundamental properties of the strong interaction under extreme conditions and offers a vital tool for interpreting future high-precision data from the Large Hadron Collider.