Benchmarking a nonequilibrium approach to photon emission in relativistic heavy-ion collisions

In this work, the production of photons through binary scattering processes is investigated for equilibrated hadronic systems. More precisely, a nonequilibrium hadronic transport approach to describe relativistic heavy-ion collisions is benchmarked with respect to photon emission. Cross sections for photon production in $\pi +\rho \to \pi +\gamma$ and $\pi +\pi \to \rho +\gamma$ scattering processes are derived from an effective chiral field theory and implemented into the hadronic transport approach, SMASH (Simulating Many Accelerated Strongly-interacting Hadrons). The implementation is verified by systematically comparing the thermal photon rate to theoretical expectations. Further, the impact of form factors is discussed, scattering processes mediated by $\omega$ mesons are found to contribute significantly to the total photon production. Several comparisons of the yielded photon rates are performed: to parametrizations of the very same rates as used in hydrodynamic simulations, to previous works relying on different cross sections for the production of direct photons from the hadronic stage, and to partonic rates. Finally, the impact of considering the finite width of the $\rho$ meson is investigated, where a significant enhancement of photon production in the low-energy region is observed. This benchmark is the first step toward a consistent treatment of photon emission in hybrid $\mathrm{hydrodynamics}+\mathrm{transport}$ approaches and toward a genuine dynamical description.

Figure 1

Cross sections of ($\pi$, $\rho$, $a_1$)-mediated $\pi +\pi \to \rho +\gamma$ processes (upper panel), ($\pi$, $\rho$, $a_1$)-mediated (center panel) and ($\omega$)-mediated (lower panel) $\pi +\rho \to \pi +\gamma$ processes as a function of $\sqrt{s}$.

Figure 2

Comparison of thermal photon rates for ($\pi$, $\rho$, $a_1$)-mediated processes, (6a)–(6e), as determined with SMASH (thin lines) to theoretical expectations (bands) in an infinite matter simulation at a temperature of $T=150\mathrm{MeV}$.

Figure 3

Comparison of thermal photon rates for $\omega$-mediated processes, (6f)—(6h), as determined with SMASH (thin lines) to theoretical expectations (bands) in an infinite matter simulation at a temperature of $T=150\mathrm{MeV}$.

Figure 4

Thermal photon rates of combined $\pi +\pi \to (\pi ,\rho ,a_1)\to \rho +\gamma$ (red), $\pi +\rho \to (\pi ,\rho ,a_1)\to \pi +\gamma$ (blue) and $\pi +\rho \to \omega \to \pi +\gamma$ (orange) production channels without form factors (dashed lines) and with form factors (solid lines) at $T=150\mathrm{MeV}$. The upper plot shows the resulting photon rates with form factors for all three contributions.

Figure 5

Thermal photon rates of combined ($\pi$, $\rho$, $a_1$)-mediated and $\omega$-mediated processes at a temperature of $T=150\mathrm{MeV}$ from an infinite matter simulation, carried out with SMASH. Form factors are included.

Figure 6

Temperature scaling of the thermal photon rate for $\pi +\pi \to \rho +\gamma$ processes (upper panel), for $\pi +\rho \to \pi +\gamma$ processes (center panel), and the total contribution (lower panel). Form factors are included. The y-axis is cut since the rates are growing rapidly at small energies.

Figure 7

Comparison of thermal photon rates within SMASH (dashed lines) to parametrizations of these rates (solid lines), taken from [37], at $T=150\mathrm{MeV}$.

Figure 8

Comparison of thermal photon rates from SMASH following the logic in [37, 38] (dashed line) to parametrization of the photon rates used in other transport models, provided in [34] (solid line). The parametrizations are taken from [50].

Figure 9

Comparison of thermal hadronic photon rates from SMASH (dashed) to partonic photon rates (solid) described within the AMY framework [21] at a temperature of $T=150\mathrm{MeV}$. For the AMY parametrizations, ${\alpha }_{\mathrm{s}}=0.2$ and 2-flavor QCD are applied.

Figure 10

Effect of considering finite-width $\rho$ mesons on the thermal photon rate in $\pi +\pi \to \rho +\gamma$ processes (red) and $\pi +\rho \to \pi +\gamma$ processes (blue). Computations with stable $\rho$ mesons are displayed with solid lines, those with finite $\rho$ mesons with dashed lines.

Figure 11

Differential cross section of $\pi +\pi \to \rho +\gamma$ processes as a function of Mandelstam $t$ (upper) and the scattering angle $\theta$ (lower).

Figure 12

Differential cross sections of ($\pi$, $\rho$, $a_1$)-mediated and ($\omega$)-mediated $\pi +\rho \to \pi +\gamma$ processes as a function of Mandelstam $t$ (upper plots) and of the scattering angle $\theta$ (lower plots).

Figure 13

Thermal photon rates as from SMASH (lines) in comparison to theoretical expectations (bands) at a temperature of $T=200\mathrm{MeV}$. See Sec. 3b1 for further details.

Figure 14

Average value of the current conservation breaking term, $\mathrm{\Delta }$, as a function of the temperature. $M_{\rho }=0.776\mathrm{GeV}$ is assumed while $m_{\rho }$ and $u$ are extracted from SMASH.

Figure 15

Thermal photon rate for process (6d), ${\pi }^0+{\rho }^{\pm }\to {\pi }^{\pm }+\gamma$, with (solid) and without (dashed) considering an additional contact term to restore current conservation in the case of broad $\rho$ mesons at $T=150\mathrm{MeV}$.