OSEFT or how to go beyond hard thermal loops

¹ Instituto de Ciencias del Espacio (IEEC/CSIC) C. Can Magrans s.n., 08193 Cerdanyola del Vallès, Catalonia, Spain
² Departament de Fisica Quàntica i Astrofisica and Institut de Ciències del Cosmos, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Catalonia, Spain.
³ Institute for Nuclear Theory, University of Washington, Seattle, WA 98195, USA

^a e-mail: cmanuel@ice.cat

Published online: 22 March 2017

Abstract

We show that effective field theory techniques can be applied in the high temperature T regime of plasmas to improve the accuracy of the physics of the hard scales (or scales of order T), and as a by-product, also that of the soft scales (or scales of order gT). At leading order in the coupling constant the hard scales of the plasma can be viewed as on-shell classical particles. Based on this observation, and without any reference to the state of the system, 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 thermal equilibrium, where 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. For the soft scales the first non-vanishing power correction turns out to be a perturbative correction to the HTL result.