Uncertainty quantification of holographic transport and energy loss for the hot and baryon-dense QGP

Abstract

We investigate several transport coefficients across the phase diagram of a holographic Einstein-Maxwell-Dilaton (EMD) model of hot and dense QCD with $N_f=2+1$ flavors. Our results are obtained from an open-source implementation of this model in C++, publicly available as a module within the MUSES Framework. This code includes a new numerical method to extract thermodynamic quantities from near-boundary asymptotics in holographic models, introduced here for the first time, which greatly improves numerical stability and performance in comparison to earlier implementations. Thanks to this improved technique, we are able to compute results for many realizations of our holographic model, sampled from a Bayesian posterior distribution constrained by lattice QCD results at zero chemical potential. This allows us to propagate lattice QCD error bars to predictions of transport coefficients in a wide window of temperature and baryon chemical potential, covering the crossover region, the neighborhood of the predicted critical point, and the line of first-order phase transition. The physical observables include baryon and thermal conductivities, baryon diffusion, shear and bulk viscosities, the jet-quenching parameter, the heavy-quark drag force, and Langevin diffusion coefficients. At vanishing baryon density, we compare our results to estimates extracted by the JETSCAPE Collaboration from heavy-ion data, with which we find good agreement.

Figures (20)

• Figure 1: Left panel: A constant $\phi_0$-line starting at $(T,\mu_B)= (60,0)$ MeV, computed with a prefactor $\phi_A$ extracted by different means. The dot-dashed blue curve shows results obtained using the methods presented in Ref. Grefa:2021qvt, while the solid red curve represents results extracted with the present relaxational approach. Right panel: Ultraviolet scaling coefficient $\phi_A$, obtained from Eq. \ref{['eq:relaxsol']}, with $\Gamma_{C}/\Lambda = 10$ (dashed blue curves) and $\Gamma_{C}/\Lambda = 5$ (magenta dot-dashed curves), for ramdomly selected values of $115$ MeV$\leq T\leq 250$ MeV and $\mu_{B} \leq 3.5 \,T$.
• Figure 2: Left panel: Lines of constant $\phi_0$ are displayed as thin solid lines across the phase diagram, colored according to the value of $\phi_0$. Stable, metastable and unstable states are realized as different dual black holes corresponding to the same value of $(\mu_{B}, T)$. Thick dashed lines correspond to the spinodal lines, where metastable solutions become unstable. The star marks the position of the critical endpoint, where these lines end. Right panel: The process of finding the critical point at which constant $\phi_0$-lines cross each other. Parabolas interpolating previously found values of $(\mu_B,T)$ on a constant $\phi_0$ line are used to find the critical point.
• Figure 3: Comparison between the Equation of State at finite density obtained from the best fit to lattice results at zero chemical potential for the PHA Ansatz, and the state-of-the-art lattice QCD results from Borsanyi:2021sxv. For detailed comparison between the lattice results and PA, PHA models, see Ref. Hippert:2023bel.
• Figure 4: The left panel shows posterior bands at 95% confidence level, and corresponding best-fit curves (solid lines) of $\sigma_B/T$ as a function of $T$ for different values of $\mu_B$ while the right panel displays the $\sigma_B/T$ as a function of $T$ and $\mu_B$ computed from the best-fit parameterization.
• Figure 5: The left panel shows posterior bands at 95% confidence level, and corresponding best-fit curves (solid lines) for $\chi^{B}_{2}$ as a function of $T$ for different values of $\mu_B$ while the right panel displays the $\chi^{B}_{2}$ as a function of $T$ and $\mu_B$ computed from the best-fit parameterization.