TH Heavy Ion Coffee
# On-shell effective field theory: a new tool in thermal field theory

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4/2-037 - TH meeting room (CERN)

Description

It is well-known that at high temperature T naive perturbation in QFT breaks down. Both in QED and QCD for momenta of order gT, where g is the coupling constant, there are one loop thermal corrections, the so called hard thermal loops (HTLs), which are as relevant as tree amplitudes and have to be resummed in effective propagators and vertices. HTLs arise in one-loop diagrams from the so called hard scales, or scales of order T, in the loop. The HTL resummed perturbation theory has been successfully used in a variety of computations of different physical properties of the QED and QCD, but little is known on how to push these computations to higher orders. On the other hand, it was shown that the hard scales in the plasmas in the system can be viewed as classical on-shell particles, described by simple classical transport equations, which correctly describe the HTLs. Based on this observation, and first for QED, we derive an effective field theory describing the quantum fluctuations around an on-shell fermion with energy p, described as a set of high dimension operators over the on-shell energy p. When applied to systems close to equilibrium, when for most on-shell particles p ~ T, we show that the on-shell effective field theory (OSEFT) properly describes the HTL photon polarization tensor of QED, and its 1/T corrections. These represent perturbative corrections to the HTLs for soft momenta. We also show how with the OSEFT one can derive quantum corrections to classical transport equations.