Off-equilibrium corrections to energy and conserved charge densities in the relativistic fluid in heavy-ion collisions

Dissipative processes in relativistic fluids are known to be important in analyses of the hot QCD matter created in high-energy heavy-ion collisions. In this work, I consider dissipative corrections to energy and conserved charge densities, which are conventionally assumed to be vanishing but could be finite. Causal dissipative hydrodynamics is formulated in the presence of these dissipative currents. The relation between hydrodynamic stability and transport coefficients is discussed. I then study their phenomenological consequences on the observables of heavy-ion collisions in numerical simulations. It is shown that particle spectra and elliptic flow can be visibly modified.

Figure 1

The entropy distribution at $y={\eta }_s=0$ and $\tau =5\mathrm{fm}/c$ for the ideal fluid (solid line) and for dissipative fluids with $(C_{\mathrm{\Pi }},C_w)=(2,6)$ (dotted line), (2,0) (dashed line), and $(2,-6)$ (dash-dotted line). $C_v$ is set to vanishing.

Figure 2

$p_T$ spectra of ${\pi }^{+}$ (a) without and (b) with $\delta f$ correction for the ideal fluid (solid line) and for dissipative fluids with $(C_{\mathrm{\Pi }},C_w)=(2,6)$ (dotted line), (2,0) (dashed line), and $(2,-6)$ (dash-dotted line). $C_v$ is set to vanishing.

Figure 3

Differential elliptic flow $v_2\left(p_T\right)$ of ${\pi }^{+}$ (a) without and (b) with $\delta f$ correction for the ideal fluid (solid line) and for dissipative fluids with $(C_{\mathrm{\Pi }},C_w)=(2,6)$ (dotted line), (2,0) (dashed line), and $(2,-6)$ (dash-dotted line). $C_v$ is set to vanishing.