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Medium-Induced Quarkonium Dissociation at Finite Chemical Potential and Weak Magnetic Field

Indrani Nilima, Mujeeb Hasan, Mohammad Yousuf Jamal, Salman Ahamad Khan, B. K. Singh

TL;DR

The paper addresses how a hot QCD medium with finite quark chemical potential and a weak magnetic field modifies heavy quarkonium. It constructs a complex heavy-quark potential from a HTL-resummed gluon propagator augmented by a dimension-two gluon condensate to obtain a complex dielectric permittivity, enabling binding energy calculations from the real part and thermal widths from the imaginary part. Using a resonance-melting criterion, it reveals a sequential suppression pattern where binding energies decrease and widths grow with temperature, with finite density and weak magnetic fields providing subleading shifts. The results underscore temperature as the dominant factor in quarkonium dissociation in the QGP and bear on heavy-ion phenomenology, while outlining avenues for future work on stronger fields and real-time dynamics.

Abstract

We investigate the in-medium modification and dissociation of heavy quarkonium in a hot QCD medium at finite quark chemical potential and in the weak magnetic-field regime. Starting from the one-loop resummed gluon propagator in the imaginary-time formalism, and incorporating non-perturbative effects through a phenomenological correction to the HTL description, we compute the real and imaginary parts of the dielectric permittivity. This, in turn, leads to a complex heavy-quark potential: the real part is used to determine binding energies by solving the nonrelativistic Schrödinger equation, while the imaginary part generates thermal decay widths, dominated by Landau damping. Within the explored parameter range, temperature has the greatest control over Debye screening, potential modification, and quarkonium stability, whereas finite density and weak magnetic fields introduce comparatively smaller quantitative changes. As the temperature increases, binding energies decrease and thermal widths grow, giving rise to the expected hierarchy between ground and excited states and a sequential suppression pattern in the dissociation temperatures. Overall, our results indicate that while finite chemical potential and weak magnetic fields can shift quarkonium properties in a measurable way, thermal effects remain the primary driver of dissociation, with direct relevance for heavy-ion collision phenomenology.

Medium-Induced Quarkonium Dissociation at Finite Chemical Potential and Weak Magnetic Field

TL;DR

The paper addresses how a hot QCD medium with finite quark chemical potential and a weak magnetic field modifies heavy quarkonium. It constructs a complex heavy-quark potential from a HTL-resummed gluon propagator augmented by a dimension-two gluon condensate to obtain a complex dielectric permittivity, enabling binding energy calculations from the real part and thermal widths from the imaginary part. Using a resonance-melting criterion, it reveals a sequential suppression pattern where binding energies decrease and widths grow with temperature, with finite density and weak magnetic fields providing subleading shifts. The results underscore temperature as the dominant factor in quarkonium dissociation in the QGP and bear on heavy-ion phenomenology, while outlining avenues for future work on stronger fields and real-time dynamics.

Abstract

We investigate the in-medium modification and dissociation of heavy quarkonium in a hot QCD medium at finite quark chemical potential and in the weak magnetic-field regime. Starting from the one-loop resummed gluon propagator in the imaginary-time formalism, and incorporating non-perturbative effects through a phenomenological correction to the HTL description, we compute the real and imaginary parts of the dielectric permittivity. This, in turn, leads to a complex heavy-quark potential: the real part is used to determine binding energies by solving the nonrelativistic Schrödinger equation, while the imaginary part generates thermal decay widths, dominated by Landau damping. Within the explored parameter range, temperature has the greatest control over Debye screening, potential modification, and quarkonium stability, whereas finite density and weak magnetic fields introduce comparatively smaller quantitative changes. As the temperature increases, binding energies decrease and thermal widths grow, giving rise to the expected hierarchy between ground and excited states and a sequential suppression pattern in the dissociation temperatures. Overall, our results indicate that while finite chemical potential and weak magnetic fields can shift quarkonium properties in a measurable way, thermal effects remain the primary driver of dissociation, with direct relevance for heavy-ion collision phenomenology.
Paper Structure (22 sections, 58 equations, 8 figures, 1 table)

This paper contains 22 sections, 58 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Complex Heavy Quarkonium Potential
  3. Complex permittivity in a hot QCD medium with weak magnetic field
  4. Real and imaginary parts of the resummed propagator
  5. Debye mass and running coupling
  6. Non-perturbative correction and $\epsilon(q)$
  7. Real and imaginary parts of the $Q\bar{Q}$ potential
  8. Properties and Dissociation of Heavy Quarkonia
  9. Binding energy
  10. Thermal width
  11. Medium-induced dissociation criterion
  12. Results
  13. Running coupling
  14. Debye screening mass
  15. Real part of the potential
  16. ...and 7 more sections

Figures (8)

  • Figure 1: Variation of coupling with magnetic field (left panel) and with temperature (right panel).
  • Figure 2: Variation of Debye mass with magnetic field (left panel), with chemical potential (middle panel), and with temperature (right panel).
  • Figure 3: Real part of the potential for different strengths of magnetic field (right panel), different strengths of chemical potential (middle panel), and for different strengths of temperature (left panel).
  • Figure 4: Imaginary part of the potential for different strengths of temperature (right panel), different strengths of chemical potential (middle panel) and for different strengths of magnetic field (left panel).
  • Figure 5: Variation of BE for charmonium 1s (left panel) and for bottomium 1s(right panel) at magnetic field $0.04~{\rm GeV}^2$.
  • ...and 3 more figures