Dilepton signature of a first-order phase transition

The search for a first-order phase transition in strongly interacting matter is one of the major objectives in the exploration of the phase diagram of quantum chromodynamics (QCD). In the present work we investigate dilepton radiation from the hot and dense fireballs created in Au-Au collisions at projectile energies of 1–2 $A\mathrm{GeV}$ for potential signatures of a first-order transition. Toward this end, we employ a hydrodynamic simulation with two different equations of state, with and without a phase transition. The latter is constrained by susceptibilities at vanishing chemical potential from lattice-QCD as well as neutron star properties, while the former is implemented via modification of the mean fields in the quark phase. We find that the latent heat involved in the first-order transition leads to a substantial increase in the low-mass thermal emission signal by about a factor of two above the crossover scenario.

Figure 1

Speed of sound for first-order EoS (left panel) and the crossover EoS (right panel) in the Frankfurt CMF model. For the first-order scenario the mechanically unstable region is shown in blue color, encompassed by the spinodal lines (dashed lines). The coexistence region, where metastable solutions of phases can exist, is indicated by the dashed lines. To illustrate the approximate dynamical evolution path in a HIC, the time evolution of the central cell (after $t=7$ fm/$c$) in the full fluid dynamical evolution is shown as a gray line with symbols in each scenario.

Figure 2

Pressure as a function of energy density along a line of constant entropy per baryon, $S/A$.

Figure 3

Comparison of the final pion transverse-mass spectrum from the three bulk evolution models used in this work for $b=2$ fm 1.23 $A\mathrm{GeV}$ Au-Au collision at midrapidity ($\left|y\right|<0.05$). The two fluid dynamical results are almost identical while the transport model shows a small deviation from those at small $m_T$.

Figure 4

Distributions of the four-volume weights in fireball temperature and baryon density in central $\text{Au}\text{−}\text{Au}$ collisions at 1.23 $A\mathrm{GeV}$ extracted from the coarse-grained UrQMD transport model (left panel) and ideal-hydro evolutions with crossover EoS (middle panel) and first-order EoS (right panel). Contributions from the first 7 fm/$c$ after initial impact are not included.

Figure 5

Time evolution of the fireball temperature (left panel) and density (middle panel) in $\text{Au}\text{−}\text{Au}$ collisions at 1.23 $A\mathrm{GeV}$ extracted from the coarse-grained UrQMD transport model simulation (blue curve), ideal hydrodynamics with either crossover (red curve) or first-order EoS (green curve). The bands correspond to the second moment of the corresponding distributions. The right panel shows fireball trajectories in the temperature-density plane, defined by the most probable value of $T$ and ${\rho }_B$ at a given time, as extracted from the three simulation models (same color code as in the other panels).

Figure 6

Invariant-mass spectrum of $e^{+}{e}^{-}$ radiated from central $\text{Au}\text{−}\text{Au}$ collisions at 1.23 $A\mathrm{GeV}$. The blue, red, and green curves show the results of the simulations with the coarse-grained UrQMD transport model, hydrodynamics with crossover EoS and with first-order EoS, respectively. The solid curves correspond to contributions from all cells while the dashed curves are calculated by accounting only for cells after 7 fm/$c$. The left and right panel correspond to results using the in-medium $\rho$-meson spectral function or the perturbative $q\overline{q}$ rate, respectively.

Figure 7

Left panel: Ratio of dilepton invariant-mass spectra from the hydro evolution with phase transition over the one without phase transition (here we only considered emission from cells after 7 fm/$c$). The result from using the in-medium vector-meson spectral functions (black line) is compared to the one using the $q\overline{q}$ rate. Right panel: Ratio of the 2-differential dilepton spectra in the plane of transverse pair momentum and invariant mass for the hydro with phase transition divided by the hydro without phase transition, using the in-medium hadronic emission rates.

Figure 8

Profile of the entropy per baryon, $S/A$, in the transverse plane ($x\text{−}y$ plane for $z=0)$ in the fluid-dynamical simulations with (left panel) and without (right panel) phase transition at a time of $t=8\mathrm{fm}/c$. Note the regions of maximal $S/A$ at the upper and lower edges (“caps”) of the hydrodynamic medium.

Figure 9

Left panel: Ratio of dilepton spectra from the hydro evolution with phase transition divided by the one without, for different $S/A$ cuts. Only cells from times $>$7 fm/$c$ are taken into account, and the in-medium vector-meson spectral functions are used. Right panel: Comparison of the $e^{+}{e}^{-}$ invariant-mass spectra from the hydro evolutions with $S/A<5$ (green and red line with and without phase transition, respectively) to the coarse-grained UrQMD transport simulation (blue line).