Theory HEP Seminar

Non-renormalizability of the classical-statistical approximation

Thomas Epelbaum

IPhT Saclay

In recent years, the classical-statistical approximation (CSA), that aims at (among other) describing out of equilibrium systems, has experienced great successes. In particular, in the framework of heavy-ion-collisions, its use gave [arXiv:1307.1765, arXiv:1307.2214] the first hints of a possible fast ~Shydrodynamization~T (isotropization of the pressure tensor, very low viscosity over entropy ratio) of the quark gluon plasma, in agreement with the early hydrodynamical description of the experimental outcomes.

But a recent study [arXiv:1312.5216] has triggered new interrogations on the range of validity of the CSA, showing a strong cutoff dependence in the numerical simulations of a scalar toy model. The question therefore lies down to the following one: is the CSA renormalizable? If the answer to this question was positive, then it would simply mean that the renormalization work was not done properly in previous studies (including [arXiv:1312.5216]). But as we will argue in this talk, the CSA is indeed non-renormalizable [arXiv:1402.0115]. The key reason behind this fact is that a vertex is missing in the CSA when compared to the full fledge quantum theory. This missing vertex forbids some non-trivial cancellations in one loop four point functions that do happen in the full theory.

In the present talk, after having recalled in a first part the recent uses and successes of the CSA, we will elaborate on its non-renormalizability. We will conclude by presenting a possible modification of the CSA in order to extend its range of validity.