Thermal photon, dilepton production, and electric charge transport in a baryon rich strongly coupled QGP from holography

We obtain the thermal photon and dilepton production rates in a strongly coupled quark-gluon plasma (QGP) at both zero and nonzero baryon chemical potentials using a bottom-up Einstein-Maxwell-dilaton holographic model that is in good quantitative agreement with the thermodynamics of ($2+1$)-flavor lattice QCD around the crossover transition for baryon chemical potentials up to 400 MeV, which may be reached in the beam energy scan at RHIC. We find that increasing the temperature $T$ and the baryon chemical potential ${\mu }_B$ enhances the peak present in both spectra. We also obtain the electric charge susceptibility, the dc and ac electric conductivities, and the electric charge diffusion as functions of $T$ and ${\mu }_B$. We find that electric diffusive transport is suppressed as one increases ${\mu }_B$. At zero baryon density, we compare our results for the dc electric conductivity and the electric charge diffusion with the latest lattice data available for these observables and find reasonable agreement around the crossover transition. Therefore, our holographic results may be used to constraint the magnitude of the thermal photon and dilepton production rates in a strongly coupled QGP, which we found to be at least 1 order of magnitude below perturbative estimates.

Figure 1

Speed of sound squared $c_s^2$ and normalized pressure $p/T^4$ as functions of the temperature $T$ at different fixed values of the baryon chemical potential ${\mu }_B$. The points with error bars correspond to lattice data for ($2+1$)-flavor QCD with physical quark masses from Ref. [75].

Figure 2

Normalized baryon susceptibility at zero baryon chemical potential as a function of the temperature. The points with error bars correspond to lattice data for ($2+1$)-flavor QCD with physical quark masses from Ref. [76].

Figure 3

Normalized electric charge susceptibility as a function of the temperature $T$ obtained in the present EMD holographic model at (a) ${\mu }_B=0$ compared to lattice data for ($2+1$)-flavor QCD with physical quark masses from Ref. [76] and the $\mathcal{N}=4$ SYM result obtained in Ref. [61]; (b) different fixed values of ${\mu }_B$.

Figure 4

Normalized electric dc conductivity as a function of the temperature $T$ obtained in the present EMD holographic model at (a) ${\mu }_B=0$ compared to lattice data for ($2+1$)-flavor QCD from Ref. [95] and the $\mathcal{N}=4$ SYM result obtained in Ref. [61]; we also show other lattice estimates from Refs. [98] (blue squares), [99] (red triangle), [100] (green inverted triangle), [101] (purple diamond), and [102] (brown star); (b) different fixed values of ${\mu }_B$.

Figure 5

Real part of the normalized ac electric conductivity as a function of frequency for several fixed values of the temperature $T$ at (a) ${\mu }_B=0$ and (b) ${\mu }_B=400\mathrm{MeV}$.

Figure 6

Normalized electric charge diffusion constant as a function of the temperature $T$ obtained in the present EMD holographic model at (a) ${\mu }_B=0$ compared to lattice data for ($2+1$)-flavor QCD from Ref. [95] and the $\mathcal{N}=4$ SYM result obtained in Ref. [103]; (b) different fixed values of ${\mu }_B$.

Figure 7

Normalized thermal photon production rate as a function of frequency for several fixed values of the temperature $T$ at (a) ${\mu }_B=0$ and (b) ${\mu }_B=400\mathrm{MeV}$.

Figure 8

Normalized thermal photon production rate as a function of frequency for several fixed values of the baryon chemical potential ${\mu }_B$ at $T=150\mathrm{MeV}$.

Figure 9

Normalized thermal dilepton production rate as a function of the invariant mass $M$ of the dilepton pair for several values of the temperature $T$ and momentum $k$. In the left panel, we show the results at ${\mu }_B=0$ and (a) $k=0.25\mathrm{GeV}$, (c) $k=0.5\mathrm{GeV}$, and (e) $k=1\mathrm{GeV}$. In the right panel, we display the results at ${\mu }_B=400\mathrm{MeV}$ and (b) $k=0.25\mathrm{GeV}$, (d) $k=0.5\mathrm{GeV}$, and (f) $k=1\mathrm{GeV}$.

Figure 10

Normalized thermal dilepton production rate as a function of the invariant mass $M$ of the dilepton pair for several values of the baryon chemical potential ${\mu }_B$ at the fixed temperature $T=150\mathrm{MeV}$ with (a) $k=0.25\mathrm{GeV}$, (b) $k=0.5\mathrm{GeV}$, and (c) $k=1\mathrm{GeV}$.