Thermal photon emission from quark-gluon plasma: 1+1D magnetohydrodynamics results

TL;DR

This work investigates thermal photon production from a magnetized quark-gluon plasma within a 1+1D ideal magnetohydrodynamic framework using a boost-invariant Bjorken flow. The magnetic field decays as $\mathbf{B}(\tau)=\mathbf{B}_0 (\tau_0/\tau)^a$, with the initial strength characterized by $\sigma$, and the QGP temperature evolution is obtained from an analytic Victor-Bjorken–MHD solution that incorporates magnetic-energy exchange. Photon emission is computed from HTL-resummed one-loop rates for Compton scattering, $q\bar{q}$ annihilation, bremsstrahlung, and annihilation with an additional scattering (C+A, Bre, A+S), and then integrated over the spacetime history to obtain the hard photon spectrum $dN/(d^2p_T dy)$. The results show that larger decay rate $a$ generally boosts photon yields, with distinct behavior for $a\to\infty$ and $a=2/3$ depending on $\sigma$, while low-$p_T$ photons sample all stages of evolution and high-$p_T$ photons probe the early, hot QGP. Central rapidity ($y\approx0$) dominates the total yield, highlighting how magnetic-field dynamics imprint electromagnetic signals in relativistic heavy-ion collisions.

Abstract

We investigate thermal photon production in the quark-gluon plasma (QGP) under strong magnetic fields using a magnetohydrodynamic (MHD) framework. Adopting the Bjorken flow model with power-law decaying magnetic fields $\mathbf{B}(τ) = \mathbf{B}_0 (τ_0/τ)^a$ (where $a$ controls the decay rate, $B_0 = \sqrtσ T_0^2$, and $σ$ characterizes the initial field strength), we employ relativistic ideal fluid dynamics under the non-resistive approximation. The resulting QGP temperature evolution exhibits distinct $a$- and $σ$-dependent behaviors. Thermal photon production rates are calculated for three dominant processes: Compton scattering with $q\bar{q}$ annihilation (C+A), bremsstrahlung (Brems), and $q\bar{q}$ annihilation with additional scattering (A+S). These rates are integrated over the space-time volume to obtain the photon transverse momentum $(p_T)$ spectrum. Our results demonstrate that increasing $a$ enhances photon yields across all $p_T$, with $a \to \infty$ (super-fast decay) providing an upper bound. For $a = 2/3$, larger $σ$ suppresses yields through accelerated cooling, whereas for $a \to \infty$, larger $σ$ enhances yields via prolonged thermal emission. Low-$p_T$ photons receive significant contributions from all QGP evolution stages, while high-$p_T$ photons originate predominantly from early times. The central rapidity region $(y=0)$ dominates the total yield. This work extends photon yield studies to the MHD regime under strong magnetic fields, elucidating magnetic field effects on QGP electromagnetic signatures and establishing foundations for future investigations of magnetization and dissipative phenomena.

Figures (12)

• Figure 1: (Color online) Evolution of temperature $T$ (Eq. (\ref{['T_mhd_1']})) for a magnetic field with as functions of proper time $\tau$ for different initial magnetic field (upper panel) and different magnetic field decay parameter $a$ (lower panel).
• Figure 2: (Color online) Evolution of temperature $T$ as functions of proper time $\tau$ for different initial magnetic field decay parameter $a$ and strength $\sigma$.
• Figure 3: (Color online) Evolution of temperature $T$ as a function of proper time $\tau$ for different limit of magnetic field decay parameter $a$ with $\sigma=2$.
• Figure 4: (Color online) Hard thermal photon rates as a function of energy $E$ for fixed temperatures $T=0.25$ GeV and $T=0.45$ GeV, showing contributions from Compton scattering + $q\bar{q}$ annihilation (C+A), bremsstrahlung (Bre), and annihilation with scattering (A+S).
• Figure 5: (Color online) Total hard thermal photon rates (Eq. (\ref{['f:cabsa-total']})) as a function of energy $E$ for $T=0.25$ GeV, $T=0.45$ GeV, and $T=0.65$ GeV, where "Total = (C+A) + Bre + (A+S)".