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

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.

💡 Research Summary

This paper investigates how strong magnetic fields influence thermal photon production from the quark‑gluon plasma (QGP) created in relativistic heavy‑ion collisions. The authors adopt a 1+1 dimensional ideal magnetohydrodynamic (MHD) description based on the Bjorken boost‑invariant flow. The external magnetic field is assumed to decay with proper time τ according to a power law
( \mathbf{B}(\tau)=\mathbf{B}_0 (\tau_0/\tau)^a ),
where the exponent a controls the decay speed and the dimensionless parameter σ (through (B_0=\sqrt{\sigma},T_0^2)) sets the initial field strength.

Using the non‑resistive limit (infinite electrical conductivity) the electric field vanishes, and the energy‑momentum tensor reduces to the ideal MHD form. With a conformal equation of state (ε = 3p, p = a₁ T⁴) the energy‑conservation equation yields a first‑order differential equation for the temperature T(τ). An analytic solution is obtained (Eq. 14), which consists of the usual Bjorken cooling term ((\tau_0/\tau)^{1/3}) plus a magnetic correction that depends on a and σ.

Three limiting cases are examined in detail:

• a = 1 (frozen‑flux limit) – the magnetic correction disappears and the temperature follows the standard Bjorken law.
• a → 2/3 – a logarithmic term appears; for τ > τ₀ the logarithm is negative, accelerating the cooling. Larger σ makes the cooling even faster.
• a → ∞ (super‑fast decay) – the magnetic field deposits its energy instantaneously, giving a constant offset ((1+\sigma/6a_1)^{1/4}) to the Bjorken temperature. This slows the cooling and provides an upper bound on the temperature for a given σ.

The authors then compute thermal photon emission rates for three dominant QCD processes: Compton scattering plus quark‑antiquark annihilation (C+A), bremsstrahlung (Brems), and annihilation with additional scattering (A+S). The rates, which depend on the local temperature, are integrated over the full space‑time volume of the QGP (proper time τ, transverse area, and space‑time rapidity η_s) to obtain the transverse‑momentum spectrum dN/d²p_T dy.

Key findings:

1. Effect of the decay exponent a – Increasing a universally enhances photon yields at all p_T. The limit a → ∞ yields the largest spectrum, reflecting the fact that a rapid magnetic‑field decay injects energy early, keeping the medium hotter for a longer period.

2. Effect of the initial field strength σ – The influence of σ depends on a. For the slow‑decay case a = 2/3, larger σ accelerates cooling (through the negative logarithmic term) and therefore suppresses photon production. In contrast, in the super‑fast decay limit a → ∞, larger σ raises the constant temperature offset, prolonging the hot phase and enhancing photon yields.

3. Momentum dependence – Low‑p_T photons (p_T ≲ 1 GeV) receive sizable contributions from the entire evolution (early, middle, and late stages). High‑p_T photons (p_T ≳ 3 GeV) are dominated by the earliest times (τ ≲ 1 fm/c) when the temperature is highest.

4. Rapidity distribution – The central rapidity region (y = 0) dominates the total photon yield, consistent with the boost‑invariant assumption.

The study extends previous viscous‑hydrodynamics photon calculations by incorporating magnetic‑field dynamics in an analytically tractable MHD framework. It demonstrates that the magnetic‑field decay rate and initial strength are crucial knobs that can modify thermal photon observables, potentially offering a new avenue to infer early‑time electromagnetic fields from experimental photon spectra.

Nevertheless, the analysis has several limitations: it is restricted to 1+1 dimensions (no transverse expansion), assumes ideal (non‑resistive) MHD, neglects magnetization effects and viscous terms, and uses a simple conformal equation of state rather than lattice‑QCD‑based temperature‑dependent sound speed. Future work should incorporate finite electrical conductivity, shear and bulk viscosities, realistic 3+1 dimensional expansion, and a magnetized equation of state to assess how robust the present conclusions are under more realistic conditions.