Phenomenological consequences of enhanced bulk viscosity near the QCD critical point

In the proximity of the QCD critical point the bulk viscosity of quark-gluon matter is expected to be proportional to nearly the third power of the critical correlation length, and become significantly enhanced. This work is the first attempt to study the phenomenological consequences of enhanced bulk viscosity near the QCD critical point. For this purpose, we implement the expected critical behavior of the bulk viscosity within a non-boost-invariant, longitudinally expanding $1+1$ dimensional causal relativistic hydrodynamical evolution at nonzero baryon density. We demonstrate that the critically enhanced bulk viscosity induces a substantial nonequilibrium pressure, effectively softening the equation of state, and leads to sizable effects in the flow velocity and single-particle distributions at the freeze-out. The observable effects that may arise due to the enhanced bulk viscosity in the vicinity of the QCD critical point can be used as complementary information to facilitate searches for the QCD critical point.

Figure 1

Dependence of initial energy density, ${\epsilon }_I\left(\eta \right)$ (a), and initial baryon number density, $n_B^I\left(\eta \right)$ (b), normalized by their corresponding values at $\eta =0$, on the spatial rapidity, $\eta$.

Figure 2

Hydrodynamic evolution trajectories in the ${\mu }_B-T$ plane for different spatial rapidity, $\eta$, as well as with and without the presence of a critical point. The black solid curve plots the equal-$\xi$ contour, i.e., the critical region, with the red dot illustrating the position of the critical point; see text.

Figure 3

The ratios of bulk viscosity to entropy density $\zeta /s$ (a), bulk viscous pressure to equilibrium pressure $\mathrm{\Pi }/p$ (b), and the fluid velocity $v_{\eta }=u^{\eta }/u^{\tau }$ (c) along the hydrodynamic evolution trajectory corresponding to spatial rapidity $\eta =1.5$ and in presence of a critical point. Results for evolution with several values of the bulk relaxation time ${\tau }_{\mathrm{\Pi }}$ corresponding to $C_{\mathrm{\Pi }}=0.25$, 1, and 4 [see Eq. (8b)] are shown by red, blue, and green curves, respectively. The Navier-Stokes limit along the same trajectory in the presence of the critical point also is shown by the black dotted curve. The black dashed curves show results in the absence of a critical point and with $C_{\pi }=1$.

Figure 4

(a) Charge particle multiplicity per unit momentum rapidity, $d{N}_{\mathrm{ch}}/dY$, as a function of $Y$. The dashed black, solid red, and dashed blue curves, respectively, correspond to results for hydrodynamical evolution with (CP) without (no-CP) a critical point, as well as including the nonequilibrium $\delta f$ contribution to the freeze-out (CP+$\delta f$). (b) The relative change of $d{N}_{\mathrm{ch}}/dY$ with and without a critical point.

Figure 5

(a) Net-baryon multiplicity per unit momentum rapidity, $d{N}_{\mathrm{B}}/dY$, as a function of $Y$. The dashed black, solid red, and dashed blue curves, respectively, correspond to results for hydrodynamical evolution with (CP) without (no-CP) a critical point, as well as including the nonequilibrium $\delta f$ contribution to the freeze-out (CP+$\delta f$). (b) The relative change of $d{N}_{\mathrm{B}}/dY$ with and without a critical point.