Photon and dilepton production at the Facility for Antiproton and Ion Research and beam-energy scan at the Relativistic Heavy-Ion Collider using coarse-grained microscopic transport simulations

We present calculations of dilepton and photon spectra for the energy range $E_{\text{lab}}=2A\text{to}35A\mathrm{GeV}$ which will be available for the Compressed Baryonic Matter (CBM) experiment at the future Facility for Antiproton and Ion Research (FAIR). The same energy regime will also be covered by phase II of the beam-energy scan at the Relativistic Heavy-Ion Collider (RHIC-BES). Coarse-grained dynamics from microscopic transport calculations of the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model is used to determine temperature and chemical potentials, which allows for the use of dilepton and photon-emission rates from equilibrium quantum-field-theory calculations. The results indicate that nonequilibrium effects, the presence of baryonic matter, and the creation of a deconfined phase might show up in specific manners in the measurable dilepton invariant-mass spectra and in the photon transverse-momentum spectra. However, as the many influences are difficult to disentangle, we argue that the challenge for future measurements of electromagnetic probes will be to provide a high precision with uncertainties much lower than in previous experiments. Furthermore, a systematic study of the whole energy range covered by CBM at FAIR and RHIC-BES is necessary to discriminate between different effects, which influence the spectra, and to identify possible signatures of a phase transition.

Figure 1

Time evolution of (a) temperature $T$ and (b) baryochemical potential ${\mu }_{\text{B}}$ for the central cell of the coarse-graining grid for different beam energies $E_{\text{lab}}=2A\text{–}35A\mathrm{GeV}$. The results are obtained for the 0%–10% most central collisions in $\text{Au}+\text{Au}$ reactions.

Figure 2

Thermal four-volume in units of ${\mathrm{fm}}^4$ from the coarse-grained transport calculations as a function of temperature $T$ and baryochemical potential ${\mu }_{\mathrm{B}}$. Results are shown for (a) $E_{\text{lab}}=4A\mathrm{GeV}$ and (b) $35A\mathrm{GeV}$ in central $\text{Au}+\text{Au}$ collisions.

Figure 3

Average values of the pion chemical potential ${\mu }_{\pi }$ (blue lines) and the kaon chemical potential ${\mu }_K$ (green lines) as a function of the cell temperature. Results are shown for central $\text{Au}+\text{Au}$ collisions at three different collision energies, $E_{\text{lab}}=4A,15A,\text{and}35A\mathrm{GeV}$.

Figure 4

Dilepton invariant-mass spectra for $\text{Au}+\text{Au}$ reactions at different energies $E_{\text{lab}}=2A\text{–}35A\mathrm{GeV}$ within the centrality class of 0%–10% most central collisions. The resulting spectra include thermal contributions from the coarse-graining of the microscopic simulations (CG of UrQMD) and the nonthermal contributions directly extracted from the transport calculations (UrQMD). The hadronic thermal contributions are only shown for vanishing pion chemical potential, while the total yield is plotted for both cases, ${\mu }_{\pi }=0$ and ${\mu }_{\pi }\ne 0$.

Figure 5

High-mass region of the dilepton $M_{e^{+}{e}^{-}}$ spectrum for central $\text{Au}+\text{Au}$ collisions at (a) $E_{\text{lab}}=8A\mathrm{GeV}$ and (b) $35A\mathrm{GeV}$, assuming different emission scenarios. The baseline calculation assumes hadronic emission up to 170 MeV with vanishing ${\mu }_{\pi }$ and partonic emission for higher temperatures (full line). Besides the results with a five-times-enhanced emission around the critical temperature (dashed line) and for a pure hadron-gas scenario with emission at all temperatures from hadronic sources (dashed-triple-dotted line) are shown. Again, we also depict the baseline result including finite pion chemical potential (dashed-dotted line).

Figure 6

Transverse-momentum spectra of the dilepton yield in central $\text{Au}+\text{Au}$ reactions $E_{\text{lab}}=4A\mathrm{GeV}$ (red) and $35A\mathrm{GeV}$ (blue). The results are shown for four different invariant-mass bins: (a) $M_{e^{+}{e}^{-}}<0.2\text{GeV}/c^2$, (b) $0.2<M_{e^{+}{e}^{-}}<0.6\mathrm{GeV}/c^2$, (c) $0.6<M_{e^{+}{e}^{-}}<0.9\mathrm{GeV}/c^2$, and (d) $M_{e^{+}{e}^{-}}>1.1\mathrm{GeV}/c^2$.

Figure 7

(a) Temperature dependence of dilepton emission $dN/dT$ from thermal sources for central $\text{Au}+\text{Au}$ at $E_{\mathrm{lab}}=35A$ GeV, i.e., the lepton pairs directly extracted from the hadronic cocktail as calculated with UrQMD are not included. The results are shown for four different invariant-mass bins: $M_{e^{+}{e}^{-}}<0.2\mathrm{GeV}/c^2,0.2<M_{e^{+}{e}^{-}}<0.6\mathrm{GeV}/c^2,0.6<M_{e^{+}{e}^{-}}<0.9\mathrm{GeV}/c^2$, and $M_{e^{+}{e}^{-}}>1.1\mathrm{GeV}/c^2$. (b) Time evolution $dN/dt$ of thermal dilepton emission for $2A$ GeV (green) and $35A$ GeV (blue). The dashed line shows the emission from the QGP for the top FAIR energy.

Figure 8

Thermal photon yield at midrapidity in dependence on (a) temperature, $d{N}_{\gamma }/dT$, and (b) baryochemical potential, $d{N}_{\gamma }/d{\mu }_{\text{B}}$, for central $\text{Au}+\text{Au}$ collisions at different beam energies $E_{\text{lab}}=2A\text{–}35A\mathrm{GeV}$. The results are shown for the case of vanishing ${\mu }_{\pi }$ and ${\mu }_{\text{K}}$.

Figure 9

Transverse-momentum spectra at midrapidity $\left(|y_{\gamma }|<0.5\right)$ of the thermal photon yield for central $\text{Au}+\text{Au}$ reactions at (a) $E_{\text{lab}}=2A\mathrm{GeV}$, (b) $8A\mathrm{GeV}$, (c) $15A\mathrm{GeV}$ and (d) $35A\mathrm{GeV}$. The total yields are plotted for both cases ${\mu }_{\pi }=0$ (full black line) and ${\mu }_{\pi }\ne 0$ (dashed line). The single hadronic contributions from the $\rho$ spectral function (red, long dashed), the meson gas (green, dashed-double-dotted), and the $\pi \text{−}\rho \text{−}\omega$ complex (beige, dashed-dotted) are only shown for vanishing pion chemical potential. The partonic contribution from the QGP is plotted as orange short-dashed line.

Figure 10

Comparison of the transverse-momentum spectra at midrapidity $\left(|y_{\gamma }|<0.5\right)$ of the thermal photon yield for central $\text{Au}+\text{Au}$ reactions resulting from different emission scenarios. In panel (a) the effect of a finite baryon chemical potential ${\mu }_{\mathrm{B}}$ on the transverse momentum spectrum for the $\rho$ contribution and the total yield is shown for $2A\mathrm{GeV}$ (lower results) and $35A\mathrm{GeV}$ (upper results), comparing the standard scenario with ${\mu }_{\mathrm{B}}\ne 0$ (full lines) with the results for ${\mu }_{\mathrm{B}}=0$ (dashed lines). Panel (b) shows the results for a purely hadronic scenario, i.e., for emission from the hadron gas also for $T>170\mathrm{MeV}$ and no partonic contribution. The single contributions are plotted as in Fig. 9; for comparison the total yield for the standard result including hadronic + partonic emission is shown (black dashed).

Figure 11

(b) Comparison of the overall photon transverse-momentum spectra and (b) the thermal dilepton invariant-mass spectra at midrapidity $\left|y\right|<0.5$ for different energies in the range $E_{\text{lab}}=2A\text{–}35A\mathrm{GeV}$. The results are shown for vanishing meson chemical potentials ${\mu }_{\pi }={\mu }_K=0$.

Figure 12

(a) Energy dependence of the thermal photon and dilepton yield in different invariant-mass or transverse-momentum bins, respectively. The yields are normalized to the result at $E_{\text{lab}}=2A\mathrm{GeV}$. (b) Fraction of thermal QGP emission in relation to the total thermal yield of photons or dileptons in different $M_{e^{+}{e}^{-}}$ and photon-$p_{\mathrm{t}}$ bins. All results in this figure are shown for midrapidity and vanishing meson chemical potentials.

Figure 13

Energy dependence for the ratio of thermal photon yield $N_{\gamma }^{\text{thermal}}$ at midrapidity $\left(\left|y\right|<0.5\right)$ to the overall number $N_{{\pi }^0}$ of neutral pions. The results are shown for two different regions of the photon transverse momenta: $0.5<p_{\mathrm{t}}<1.0\mathrm{GeV}/c$ (green) and $p_{\mathrm{t}}>1.0$ GeV/$c$ (red). The baseline calculation assumes hadronic emission up to 170 MeV with vanishing ${\mu }_{\pi }$ and ${\mu }_K$ and partonic emission for higher temperatures (full line). In addition, the results are shown with a five-times-enhanced emission around the critical temperature (dashed-dotted line), for a pure-hadron-gas scenario with emission at all temperatures from hadronic sources (short dashed line), and including meson chemical potentials (dashed line).