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Dilepton Production in a Rotating Thermal Medium: The Rigid Rotation Approximation

Jorge David Castaño-Yepes, Enrique Muñoz

Abstract

We investigate dilepton production in a thermalized quark--gluon plasma subject to global rotation, in the rigid rotating approximation. We consider a generic process involving quark-antiquark annihilation followed by the emission of a highly energetic virtual photon decaying into a dilepton pair. For this process, we compute the dilepton emission rate from the imaginary part of the photon polarization tensor, at finite temperature and vorticity. Our results show that vorticity induces characteristic modifications in the light dilepton channel, namely $e^-e^+$ production, where the emission spectrum exhibits a suppression at low transverse mass together with a mild shift of the production threshold. This behavior originates from the role of vorticity as an effective spin-dependent chemical potential that alters the available phase-space distribution for the emission process. In contrast, the $μ^-μ^+$ channel is {\color{red}more weakly affected by} the rotational background, thus remaining dominated by its intrinsic mass threshold. The resulting channel dependence highlights a potential phenomenological handle for disentangling rotational effects in heavy-ion collisions: while light dilepton spectra encode the imprints of vorticity in the infrared sector, the muon channel provides a comparatively robust baseline.

Dilepton Production in a Rotating Thermal Medium: The Rigid Rotation Approximation

Abstract

We investigate dilepton production in a thermalized quark--gluon plasma subject to global rotation, in the rigid rotating approximation. We consider a generic process involving quark-antiquark annihilation followed by the emission of a highly energetic virtual photon decaying into a dilepton pair. For this process, we compute the dilepton emission rate from the imaginary part of the photon polarization tensor, at finite temperature and vorticity. Our results show that vorticity induces characteristic modifications in the light dilepton channel, namely production, where the emission spectrum exhibits a suppression at low transverse mass together with a mild shift of the production threshold. This behavior originates from the role of vorticity as an effective spin-dependent chemical potential that alters the available phase-space distribution for the emission process. In contrast, the channel is {\color{red}more weakly affected by} the rotational background, thus remaining dominated by its intrinsic mass threshold. The resulting channel dependence highlights a potential phenomenological handle for disentangling rotational effects in heavy-ion collisions: while light dilepton spectra encode the imprints of vorticity in the infrared sector, the muon channel provides a comparatively robust baseline.

Paper Structure

This paper contains 12 sections, 156 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Theory
  3. The Fermion propagator in a rotating frame
  4. The Photon Polarization Tensor
  5. Results
  6. Summary and Conclusions
  7. The Fermion propagator
  8. Computation of $g_{\mu\nu}\Pi^{\mu\nu}$
  9. Computation of the Dirac trace
  10. Matsubara sums
  11. Momentum integrals
  12. The limit $\Omega = 0$

Figures (5)

  • Figure 1: Coordinate system for the photon's momentum and the local vorticity in the nuclear collision region. Schematic generated using an AI model and Geogebra openai_chatgptgeogebra.
  • Figure 2: Feynman diagram and coordinates system for the process of dilepton emission by quark-antiquark annihilation mediated by a virtual photon $q \overline{q}\rightarrow\gamma\rightarrow l\overline{l}$.
  • Figure 3: Feynman diagram illustrating the the polarization tensor. The dashed arrows indicate the charge flow in the diagram.
  • Figure 4: Electron–positron production rate from Eq. \ref{['eq:Rate1']} for several values of the vorticity $\Omega$ (dashed line $\Omega = 0$, red $\Omega = 7$ MeV, $\Omega = 30$ MeV, $\omega = 50$ MeV) and transverse momentum $p_T$. The temperature is fixed at $T = 150$ MeV.
  • Figure 5: Muon–anti-muon production rates from Eq. \ref{['eq:Rate1']} for different values of the vorticity $\Omega$ (dashed line $\Omega = 0$, red $\Omega = 7$ MeV, $\Omega = 30$ MeV, $\omega = 50$ MeV) and transverse momentum $p_T$. The temperature is set to $T = 150$ MeV.