Enhancement of photon emission rate near QCD critical point

TL;DR

The paper addresses how near the QCD critical point electromagnetic probes, specifically on-shell photons, respond to universal nonequilibrium critical dynamics. By employing model H to capture slow diffusive and momentum-coupled modes, it derives a universal scaling function Φ(ν) that governs the photon spectrum, revealing a divergent ω^{-1/2} behavior in the scaling regime with a crossover at ω ∼ γ_η/ξ^2 and ν = ω ξ^2/γ_η. The main result is a one-loop determination showing critical enhancement of the soft-photon emission rate via the fluctuating critical mode ψ, with the dominant term scaling as a^{-1/2} (a = 1/ξ^2) and modulated by Φ(ν); the sound mode contributes subleading, non-singular corrections. The findings provide a robust theoretical signature of near-critical dynamics accessible through electromagnetic probes and point to future work incorporating RG effects and dilepton spectra to broaden phenomenological relevance.

Abstract

We compute photon emission rate enhancement near the QCD critical point using an effective theory of dynamic critical phenomena and derive a universal photon spectrum. The emission rate scales similarly to conductivity, increasing with the correlation length ($ξ$), diverging at the critical point. The spectrum exhibits $ωdN_γ/d^3k \propto ω^{-1/2}$ in the scaling regime, with the transition occurring at a frequency comparable to shear damping rate $ω\sim γ_η/ξ^2$, reflecting the nonequilibrium properties of the near-critical liquid.

Figures (3)

• Figure 1: Photon spectra from critical fluctuations near the critical point for various correlation length $\xi/\gamma_\eta$. The absolute magnitude is proportional to an unknown coefficient; see the later discussion around Eq. \ref{['eq:rate']}. We assume that bare transport coefficients satisfy $\bar{\lambda}\equiv K\lambda/\gamma_{\eta}^3=1$.
• Figure 2: $\Phi(\nu)$ is compared with Eq. \ref{['eq:PiT_oneloop']} calculated using Eq. \ref{['eq:GG']} with $\bar{a}\equiv a\gamma_{\eta}^2=0.01$ ($\xi/\gamma_{\eta}=10$) and $\bar{\lambda}\equiv K\lambda/\gamma_{\eta}^3 = 0.1, 1, 10$. This corresponds to comparing $\Phi(\nu)$ and $\frac{3\bar{a}^{1/2}}{4\pi}F(\nu,\bar{a},\bar{\lambda})$.
• Figure 3: Photon spectrum from sound mode loop is compared with that from model H calculation near the critical point $\bar{a}\equiv a\gamma_{\eta}^2=10^{-5}, 10^{-4}, 10^{-3}$. The absolute magnitude is proportional to an unknown coefficient; see the later discussion around Eq. \ref{['eq:rate']}. We assume that bare transport coefficients satisfy $\bar{\lambda}\equiv K\lambda/\gamma_{\eta}^3=1$ and $\gamma_{\eta}=\gamma_{\zeta}/2$, and that sound velocity is $c_s^2 = 1/3$.