85. Hard thermal loops: what is it?

Suppose that you are a person studying non-equilibrium diagrammatic methods. At some point you realize that in many situations (such as at the time scale of prethermalization in the quark-gluon plasma or soon after the end of preheating) brute-force perturbation theory breaks down, as breaks the description of the dynamics by means of a single kinetic equation (in such case, the whole BBGKY chain of equations is necessary to take into account). In order to describe your strongly coupled plasma and deal with full BBGKY chain, you need to develop some non-perturbative methods, and very soon you figure out that not so many of them are currently on the market.

One of such non-perturbative methods is hard thermal loop effective field theory . So, what is it all about? If plasma of massless paricles is in thermal equilibrium, the only scale that appears in the theory is the temperature , corresponding to the mean energy of particles in the plasma. The Debye screening mass is determined in turn by the scale , where is the self-interaction coupling for plasma particles. There are no propagating modes in plasma below the Debye scale.

The term “hard thermal loops” takes its origin from the fact that Debye screening is given by loop contributions with the highest power of loop momentum. The latter is cut off by the temperature , i.e., these loops are hard thermal loops. If we want to determine what happens at scales softer than (and time scales longer than ), we have to correspondingly resum propagators and vertices; this resummation gives rise to the hard thermal loop (HTL) effective field theory.

There are other important scales in the theory where not only naive perturbation theory, but also the resummed HTL effective QFT  cease to work. One such scale is , where magnetostatic sector becomes involved, and another is – the scale related to inverse shear viscosity in plasma. Nevertheless, HTL analysis may be sufficient if one considers dynamics of plasma far from the equilibrium. The reason is that this dynamics is almost completely determined by instabilities in plasma, and the latter are seen already in collisionless limit (recall, say, physics of repeating), i.e., at the level of HTL masses.