Heavy quark diffusion coefficients in magnetized quark-gluon plasma

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Heavy quark diffusion coefficients in magnetized quark-gluon plasma

Aritra Bandyopadhyay

Phys. Rev. D 109, 034013 – Published 15 February 2024

Abstract

We evaluate the heavy quark momentum diffusion coefficients in a hot magnetized medium for the most general scenario of any arbitrary values of the external magnetic field. We choose to work with the systematic way of incorporating the effect of the magnetic field, by using the effective gluon and quark propagators, generalized for a hot and magnetized medium. To get gauge independent analytic form factors valid through all Landau levels, we apply the hard thermal loop technique for the resummed effective gluon propagator. The derived effective hard thermal loop gluon propagator and the generalized version of Schwinger quark propagator subsequently allow us to analytically evaluate the longitudinal and transverse momentum diffusion coefficients for charm and bottom quarks beyond the static limit. Within the static limit we also explore another way of incorporating the effect of the magnetic field, i.e. through the magnetized medium modified Debye mass and compare the results to justify the need for structural changes.

Received 23 July 2023
Revised 15 December 2023
Accepted 29 January 2024

DOI:https://doi.org/10.1103/PhysRevD.109.034013

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Jets & heavy flavor physics Quark-gluon plasma

Particles & Fields

Authors & Affiliations

Aritra Bandyopadhyay

Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany

Article Text

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Issue

Vol. 109, Iss. 3 — 1 February 2024

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Images

Figure 1
The equivalences of the $t$ -channel scatterings of heavy quarks due to thermally generated light quarks and gluons, $q H \to q H$ (left) and $g H \to g H$ (right) are shown, as they can also be expressed as the cut (imaginary) part of the HQ self-energy. An HTL resummed heavy quark self-energy with effective gluon propagator takes into account the diagrams for the hard process among others.
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Figure 2
A flow chart summarizing the calculational steps to be followed from Sec. 3.
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Figure 3
The magnetized medium modified exact results ( $κ$ ) has been scaled with respect to the $e B = 0$ result ( $κ_{0}$ ), variation of which with respect to $e B$ has been shown for longitudinal (solid lines) and transverse (dashed lines) HQ momentum diffusion coefficients within the static limit of both charm (red curves) and bottom (blue curves) quarks. Comparison has been done for two different values of temperatures, i.e. $T = 0.4 GeV$ (left panel) and $T = 0.6 GeV$ (right panel). Charm and bottom quark masses $M$ are specified in the text.
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Figure 4
Variation of the ratio between the Debye mass approximated results ( $κ^{'}$ ) and the exact results ( $κ$ ) with respect to $e B$ has been shown for longitudinal (solid lines) and transverse (dashed lines) HQ momentum diffusion coefficients within the static limit of both charm (red curves) and bottom (blue curves) quarks. Comparison has been done for two different values of temperatures i.e. $T = 0.4 GeV$ (left panel) and $T = 0.6 GeV$ (right panel). Charm and bottom quark masses $M$ are specified in the text.
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Figure 5
$\vec{v} ∥ \vec{B}$ case: variation of the longitudinal (solid curves) and transverse (dashed curves) momentum diffusion coefficients for charm (red curves) and bottom (blue curves) quarks with external magnetic field for two different values of temperatures, i.e. $T = 0.4 GeV$ (left panel) and $T = 0.6 GeV$ (right panel). The magnetized momentum diffusion coefficients are scaled with respect to their $e B = 0$ counterparts. Charm and bottom quark masses $M$ are specified in the text and HQ momentum $p$ is taken to be 1 GeV.
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Figure 6
$\vec{v} ⊥ \vec{B}$ case: variation of the transverse components $κ_{1}$ (solid curves), $κ_{2}$ (dashed curves) and longitudinal component $κ_{3}$ (dotted curves) of the momentum diffusion coefficient for charm (left panel) and bottom (right panel) quarks with external magnetic field for a fixed value of temperature, i.e. $T = 0.4 GeV$ . The magnetized momentum diffusion coefficients are scaled with respect to their $e B = 0$ counterparts. Charm and bottom quark masses $M$ are specified in the text and HQ momentum $p$ is taken to be 1 GeV.
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