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Heavy quark collisional energy loss in a nonextensive quark-gluon plasma

Bing-feng Jiang, Jun Chen, De-fu Hou

TL;DR

This work studies how nonextensive statistics, quantified by the parameter $q$, modify heavy-quark collisional energy loss in a quark-gluon plasma. By incorporating nonextensive distribution functions into the gluon polarization tensor, the authors derive modified longitudinal and transverse dielectric functions through a nonextensive Debye mass $m_{DE}$ and evaluate the energy loss using two established frameworks: the Thoma–Gyulassy plasma-physics formula and the Kirzhnits–Thoma thermal-field-theory approach via Leontovich relations. They find that increasing $q$ enhances the collisional energy loss, with a stronger effect at higher quark momenta and for lighter masses, and that the Kirzhnits–Thoma results are typically larger than the Thoma–Gyulassy ones, with weaker mass suppression in the former. The results demonstrate that nonextensive statistics can meaningfully alter jet-quenching-related observables and motivate further study of radiative losses and experimental implications in nonextensive QGP models.

Abstract

In this study, we derive the longitudinal and transverse gluon self-energies and the corresponding dielectric functions for a nonextensive QGP, based on nonextensive statistical mechanics and a kinetic theory framework. The nonextensive parameter $q$ enters these quantities primarily through the modification of the Debye mass. Utilizing the derived dielectric functions, we then calculate the collisional energy loss for a heavy quark using two established formalisms: the plasma physics-based Thoma-Gyulassy formula and the thermal field theory-originated Kirzhnits-Thoma formula. Our results show that for both formalisms, the collisional energy loss increases with the nonextensive parameter $q$ with this enhancement being more significant at higher incident quark momenta and suppressed for a heavier quark mass. The energy loss predicted from the Kirzhnits-Thoma formula is substantially larger than that from the Thoma-Gyulassy formula, and the nonextensive effect on the energy loss is more pronounced in the former. Furthermore, the mass suppression of the nonextensive effect on the energy loss is weaker in the Kirzhnits-Thoma approach. These calculations demonstrate that nonextensive statistics can significantly alter the energy loss in the QGP.

Heavy quark collisional energy loss in a nonextensive quark-gluon plasma

TL;DR

This work studies how nonextensive statistics, quantified by the parameter , modify heavy-quark collisional energy loss in a quark-gluon plasma. By incorporating nonextensive distribution functions into the gluon polarization tensor, the authors derive modified longitudinal and transverse dielectric functions through a nonextensive Debye mass and evaluate the energy loss using two established frameworks: the Thoma–Gyulassy plasma-physics formula and the Kirzhnits–Thoma thermal-field-theory approach via Leontovich relations. They find that increasing enhances the collisional energy loss, with a stronger effect at higher quark momenta and for lighter masses, and that the Kirzhnits–Thoma results are typically larger than the Thoma–Gyulassy ones, with weaker mass suppression in the former. The results demonstrate that nonextensive statistics can meaningfully alter jet-quenching-related observables and motivate further study of radiative losses and experimental implications in nonextensive QGP models.

Abstract

In this study, we derive the longitudinal and transverse gluon self-energies and the corresponding dielectric functions for a nonextensive QGP, based on nonextensive statistical mechanics and a kinetic theory framework. The nonextensive parameter enters these quantities primarily through the modification of the Debye mass. Utilizing the derived dielectric functions, we then calculate the collisional energy loss for a heavy quark using two established formalisms: the plasma physics-based Thoma-Gyulassy formula and the thermal field theory-originated Kirzhnits-Thoma formula. Our results show that for both formalisms, the collisional energy loss increases with the nonextensive parameter with this enhancement being more significant at higher incident quark momenta and suppressed for a heavier quark mass. The energy loss predicted from the Kirzhnits-Thoma formula is substantially larger than that from the Thoma-Gyulassy formula, and the nonextensive effect on the energy loss is more pronounced in the former. Furthermore, the mass suppression of the nonextensive effect on the energy loss is weaker in the Kirzhnits-Thoma approach. These calculations demonstrate that nonextensive statistics can significantly alter the energy loss in the QGP.
Paper Structure (9 sections, 37 equations, 6 figures)

This paper contains 9 sections, 37 equations, 6 figures.

Table of Contents

  1. Introduction
  2. The theoretical frameworks for the collisional energy loss
  3. The plasma physics method: Thoma-Gyulassy formula
  4. The Leontovich relations in thermal field theory: Kirzhnits-Thoma formula
  5. The gluon self-energies and the dielectric functions in a nonextensive QGP
  6. The nonextensive distribution functions
  7. The gluon self-energies and the dielectric functions
  8. Numerical results
  9. Conclusion and Discussion

Figures (6)

  • Figure 1: Feynman diagram for the heavy quark self-energy $\Sigma(P)$ with the resummaiton gluon propagator.
  • Figure 2: (color online) The scaled square of the Debye mass with respect to the nonextensive parameter $q$.
  • Figure 3: (color online) The collisional energy loss of a heavy quark in a nonextensive QGP in the Thoma-Gyulassy formula. The solid-black, red, green, blue and dashed-black curves are for the cases of $q=1, 1.05, 1.1, 1.15, 1.2$ respectively. Top panel: charm quark, Bottom panel: bottom quark.
  • Figure 4: (color online) The collisional energy loss of a heavy quark in a nonextensive QGP in the Kirzhnits-Thoma formula. The solid-black, red, green, blue and dashed-black curves are for the cases of $q=1, 1.05, 1.1, 1.15, 1.2$ respectively. Top panel: charm quark, Bottom panel: bottom quark.
  • Figure 5: (color online) The collisional energy loss in a nonextensive QGP in the Thoma-Gyulassy formula (T-G) and in the Kirzhnits-Thoma formula (K-T). The solid curves are for the case of T-G, while the dashed curves are for the case of K-T. Top panel: charm quark, Bottom panel: bottom quark.
  • ...and 1 more figures