Abstract
Motivated by the boost-invariant Glasma state in the initial stages in heavy-ion collisions, we perform classical-statistical simulations of SU(2) gauge theory in 2+1 dimensional space-time both with and without a scalar field in the adjoint representation. We show that irrespective of the details of the initial condition, the far-from-equilibrium evolution of these highly occupied systems approaches a unique universal attractor at high momenta that is the same for the gauge and scalar sectors. We extract the scaling exponents and the form of the distribution function close to this non-thermal fixed point. We find that the dynamics are governed by an energy cascade to higher momenta with scaling exponents $\alpha = 3\beta$ and $\beta = -1/5$. We argue that these values can be obtained from parametric estimates within kinetic theory indicating the dominance of small momentum transfer in the scattering processes. We also extract the Debye mass non-perturbatively from a longitudinally polarized correlator and observe an IR enhancement of the scalar correlation function for low momenta below the Debye mass.
Highlights
A characteristic feature of many highly occupied systems is that they often approach universal self-similar attractors, referred to as nonthermal fixed points (NTFP) [1,2]
While we focus here on the dynamics of hard modes, questions concerning hard (thermal) loop (HL) and quasiparticle descriptions of soft momentum modes p ∼ mD will be studied with unequal-time correlation functions in classical-statistical simulations in a forthcoming work
In order to constitute a universal nonthermal fixed point, the scaling exponents α, β and the scaling function fsðpÞ in Eq (13) must be the same for different initial conditions
Summary
A characteristic feature of many highly occupied systems is that they often approach universal self-similar attractors, referred to as nonthermal fixed points (NTFP) [1,2]. A kinetic theory description of the underlying theory is often a natural way to explain the existence and properties of such fixed points [1,14,23–27] These NTFPs appear because the interaction rate of the initial conditions is faster than that of the final equilibrium state. The hard (thermal) loop (HL) treatment used to regulate the Coulomb divergence of elastic scatterings in 3D is insufficient in the two-dimensional case It is a priori not obvious whether or to what extent quasiparticle descriptions are applicable and whether the system can exhibit self-similar behavior. Apart from these theoretical questions, this uncertainty has conceptual consequences for our understanding of the thermalization (hydrodynamization) process in ultrarelativistic heavy-ion collisions In this context, nonlinear interactions of gluons produced at central rapidities have been argued to lead to a transverse momentum scale Qs ≫ ΛQCD up to which gluonic fields are of order A ∼ 1=g [29], where g is the gauge coupling.
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