Universal parametrization of thermal photon rates in hadronic matter

Electromagnetic (EM) radiation off strongly interacting matter created in high-energy heavy-ion collisions (HICs) encodes information on the high-temperature phases of nuclear matter. Microscopic calculations of thermal EM emission rates are usually rather involved and not readily accessible to broad applications in models of the fireball evolution which are required to compare with experimental data. An accurate and universal parametrization of the microscopic calculations is thus key to honing the theory behind the EM spectra. Here we provide such a parametrization for photon emission rates from hadronic matter, including the contributions from in-medium $\rho$ mesons (which incorporate effects from baryons and antibaryons), as well as bremsstrahlung from $\pi \pi$ scattering. Individual parametrizations for each contribution are numerically determined through nested fitting functions for photon energies from 0.2 to 5 GeV in chemically equilibrated matter of temperatures 100–180 MeV and baryon chemical potentials 0–400 MeV. Special care is taken to extent the parametrizations to chemical off-equilibrium as encountered in HICs after chemical freeze-out. This provides a functional description of thermal photon rates within a 20% variation of the microscopically calculated values.

Figure 1

Photon emission rates (vs photon energy) calculated from in-medium $\rho$ mesons (points) compared with their parametrization, Eq. (4) (curves), at ${\mu }_B=0$ (upper panel) and $T=150$ MeV (middle panel). (bottom panel) Ratio of parametrization over calculated rates.

Figure 2

(upper panel) Calculated thermal photon rates from $\pi \pi$ bremsstrahlung (symbols) compared to their parametrization (colored lines). (middle panel) Ratio of the parametrized over calculated bremsstrahlung rates. (bottom panel) Comparison of rates at $T=150$ MeV from bremsstrahlung (blue curve) [28], $\pi K\rho K^{*}{a}_1$ interactions (green curve) [23], $\pi \rho \to \pi \gamma$ with $\omega t$-channel exchange (red curve) [23], and in-medium $\rho$ decays (black curve).

Figure 3

Photon emission rates calculated from in-medium $\rho \mathrm{s}$ (points) compared to the parametrization of Eq. (4) evaluated with ${\mu }_B^{\mathrm{eff}}$ from Eq. (11) and an overall fugacity of $z_{\pi }^3$.