Causal electric charge diffusion and balance functions in relativistic heavy-ion collisions

Abstract

We study the propogation and diffusion of electric charge fluctuations in high energy heavy ion collisions using the Cattaneo form for the dissipative part of the electric current. As opposed to the ordinary diffusion equation this form limits the speed at which charge can propagate. Including the noise term in the current, which arises uniquely from the fluctuation-dissipation theorem, we calculate the balance functions for charged hadrons in a simple 1+1 dimensional Bjorken hydrodynamical model. Limiting the speed of propogation of charge fluctuations increases the height and reduces the width of these balance functions when plotted versus rapidity. We also estimate the numerical value of the associated diffusion time constant from AdS/CFT theory.

Evolving charge correlations in a hybrid model with both hydrodynamics and hadronic Boltzmann descriptions

“…Secondly, the random walk never violates causality. Invoking causal diffusion in differential equations can also be applied [31][32][33]. Non-diagonal elements of the diffusion constant, or equivalently of the conductivity, were ignored here, which is reasonable for a QGP, but might become questionable if the hydrodynamic description were to be applied for large portions of the hadronic stage.…”

Dynamics of critical fluctuations: Theory -- phenomenology -- heavy-ion collisions

“…Here, η, ζ and σ denote the relevant transport coefficients shear viscosity, bulk viscosity and charge conductivity for the conserved charge, respectively. The local approximation of white noise, given by the Dirac δ-function is an approximation of more complicated noise kernels, that can be obtained from microscopic calculations [56,57] or causality arguments [58]. The discretization of this Dirac-δ function leads to stochastic terms, which diverge δ ∼ 1 ∆t∆V with decreasing grid spacing.…”

On Resonance Contribution to Balance Functions

“…For instance, in thermal models, the higher the transverse velocity of particles at the freeze-out surface, the closer the distance between balancing charges in rapidity and azimuth [4]. In the balance function, an interplay between the magnitude of the radial flow of the "bulk" and boosted neutral resonances may, in principle, be resolved with analytical procedure (2).…”

“…This problem is relevant also for other types of balance functions, for example, the BF between pions and protons may contain a contribution from Λ 0 → πp decays. Such "parasitic" contributions from weak decays can be eliminated with the neutral source removal procedure (2), provided that the proper simulation of detector response exists and fractions of secondary particles are known.…”

“…Balance functions are typically characterized by their shape, widths in ∆y and ∆ϕ, and by the integral that is the total probability to find the balancing charge within an experimental acceptance. The width of the balance function in rapidity could indicate the time of production of the pair of opposite charges and provide information about their subsequent transport in the hadronic medium [1,2,3], being affected, however, by multiple effects like radial flow [4] quantum statistics [5], etc.…”