We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time τπ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity ν = η/sT . We formulate methods for computing these correlations using second order dissipative hydrodynamics with noise. Current data are consistent with τπ/ν ∼ 10, but targeted measurements can improve this precision.
Correlations born before the onset of hydrodynamic flow can leave observable traces on the final state particles. Measurement of these correlations can yield important information on the isotropization and thermalization process. Starting from a Boltzmann-like kinetic theory in the presence of dynamic Langevin noise, we derive a new partial differential equation for the two-particle correlation function that respects the microscopic conservation laws. We illustrate how this equation can be used to study the effect of thermalization on long range correlations.
Viscous diffusion can broaden the rapidity dependence of two-particle transverse momentum fluctuations. Surprisingly, measurements at RHIC by the STAR collaboration demonstrate that this broadening is accompanied by the appearance of unanticipated structure in the rapidity distribution of these fluctuations in the most central collisions. Although a first order classical Navier-Stokes theory can roughly explain the rapidity broadening, it cannot explain the additional structure. We propose that the rapidity structure can be explained using the second order causal Israel-Stewart hydrodynamics with stochastic noise.
We show that measurements of the rapidity dependence of transverse momentum correlations can be used to determine the characteristic time τπ that dictates the rate of isotropization of the stress energy tensor, as well as the shear viscosity ν = η/sT . We formulate methods for computing these correlations using second order dissipative hydrodynamics with noise. Current data are consistent with τπ/ν ∼ 10 but targeted measurements can improve this precision.
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