Abstract
We explore the transition to hydrodynamics in a weakly-coupled model of quark-gluon plasma given by kinetic theory in the relaxation time approximation with conformal symmetry. We demonstrate that the gradient expansion in this model has a vanishing radius of convergence due to the presence of a transient (nonhydrodynamic) mode, in a way similar to results obtained earlier in strongly-coupled gauge theories. This suggests that the mechanism by which hydrodynamic behaviour emerges is the same, which we further corroborate by a novel comparison between solutions of different weakly and strongly coupled models. However, in contrast with other known cases, we find that not all the singularities of the analytic continuation of the Borel transform of the gradient expansion correspond to transient excitations of the microscopic system: some of them reflect analytic properties of the kinetic equation when the proper time is continued to complex values.
Highlights
AND SUMMARYHeavy-ion collisions at the Relativistic Heavy Ion Collider and LHC provide an outstanding opportunity to test our understanding of QCD
We explore the transition to hydrodynamics in a weakly coupled model of quark-gluon plasma given by kinetic theory in the relaxation-time approximation with conformal symmetry
There are two approaches to the study of the transition to hydrodynamics in non-Abelian gauge theories like QCD: a weakly coupled description based on effective kinetic theory (EKT) [3] and a strongly coupled plasma paradigm based on
Summary
The reason for the divergence turns out to be the same as in the case of holographic plasma: the presence of fast-decaying (nonhydrodynamic) modes [20,21,22,23] of which the relaxation controls the emergence of hydrodynamic behavior (and, in particular, its applicability to the physics of heavy-ion collisions [24,25,26]). We demonstrate below that these singularities are instead a manifestation of analytic properties of the evolution equations in complexified time This feature is related to what has been observed in other contexts where large-order behavior of perturbative series expansions is used to draw conclusions about nonperturbative effects As a byproduct of this analysis, we present a new and effective way of visualizing (see Fig. 2) the correlation between the hydrodynamization time and the value of the η=s ratio noted in Ref. [46]
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