Rapidity correlation structure in nuclear collisions

We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time ${\tau }_{\pi }$ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity $\nu =\eta /sT$. We formulate methods for computing these correlations using second-order dissipative hydrodynamics with noise. Current data are consistent with ${\tau }_{\pi }/\nu \sim 10$, but targeted measurements can improve this precision.

Figure 1

Rapidity width as a function of the number of participants for second-order momentum diffusion calculations (solid curve) compared to first-order results. Data (solid circles) from STAR include a shaded area to denote the systematic uncertainty in the fit procedure [22].

Figure 2

Second-order momentum diffusion calculations (solid curve) compared to the rapidity dependence of the measured covariance (73). First-order calculations are also compared for best fit to these data (dashed curves) and best fit to $\sigma$ in Fig. 1 (dash-dotted curves). Data are from Ref. [22] (open stars) and Ref. [23] (solid circles). Percentages of the cross section indicate centrality, with each panel corresponding to a width measurement in Fig. 1.

Figure 3

Time dependence of the rapidity covariance in second-order diffusion.

Figure 4

The sensitivity of the rapidity width to the second-order relation time ${\tau }_{\pi }$ illustrated using initial conditions with no initial flow. The different values of $\beta$ change ${\tau }_{\pi }=\beta \nu$ for fixed kinematic viscosity $\nu$ relative to first order $\beta =0$. Data are the same as in Fig. 2.

Figure 5

The sensitivity of the rapidity profile of correlations to the second-order relation time ${\tau }_{\pi }$. The different values of $\beta$ change ${\tau }_{\pi }=\beta \nu$ for fixed kinematic viscosity $\nu$ relative to first order $\beta =0$. The top panel uses the no-flow initial condition (84) so that each curve has the same integrated width $\sigma$. The bottom panel uses near-equilibrium initial conditions (79), with $\sigma$ that follows Eq. (81).

Figure 6

Measured rapidity profile compared to the characteristic evolution of second-order diffusion from single peak to plateau. Same as Fig. 2, but with no initial flow.