2009/07/31 by Emil Mottola, Zs. Szép, Zsolt Szep
Mathematics · Physics and Astronomy · #Electron #Factorization #Gauge theory #High-Energy Particle Collisions Research #Loop (graph theory) #Mathematics #Particle physics theoretical and experimental studies #Perturbation theory (quantum mechanics) #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum electrodynamics #Quantum mechanics #Resummation #Self-energy #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.81.025014
published as Phys.Rev.D81:025014,2010 · 63 pages, 10 figures. Published version. Main differences from v1: (1) Gaudin method explained in more detail; (2) Full expression (3.9) for Two-Loop Bubble Self-Energy with no need to expand in M; (3) Appendix C eliminated and incorporated in Secs. 4 and 5; (4) Examples of the breakdown of HTL resummation added to summary and Discussion in Sec. 7
openalex publication_date 2010/01/21 · arxiv created 2010/02/09 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In order to investigate the systematics of the loop expansion in high temperature gauge theories beyond the leading order hard thermal loop (HTL) approximation, we calculate the two-loop electron proper self-energy \ensuremathΣ in high temperature QED. The two-loop bubble diagram of \ensuremathΣ contains a linear infrared divergence. Even if regulated with a nonzero photon mass M of order of the Debye mass, this infrared sensitivity implies that the two-loop self-energy contributes terms to the fermion dispersion relation that are comparable to or even larger than the next-to-leading order (NLO) contributions of the one-loop \ensuremathΣ. Additional evidence for the necessity of a systematic restructuring of the loop expansion comes from the explicit gauge-parameter dependence of the fermion damping rate at both one and two loops. The leading terms in the high temperature expansion of the two-loop self-energy for all topologies arise from an explicit hard-soft factorization pattern, in which one of the loop integrals is hard (p\ensuremath≃T), nested inside a second loop integral which is soft (0\ensuremath≤p\ensuremath\lesssimT for real parts; p\ensuremath≃eT for imaginary parts). There are no hard-hard contributions to the two-loop \ensuremathΣ at leading order at high T. Provided the same factorization pattern holds for arbitrary \ensuremathℓ loops, the NLO high temperature contributions to the electron self-energy come from \ensuremathℓ\ensuremath-1 hard loops factorized with one soft loop integral. This hard-soft pattern is a necessary condition for the resummation over \ensuremathℓ to coincide with the one-loop self-energy calculated with HTL dressed propagators and vertices, and to yield the complete NLO correction to \ensuremathΣ at scales \ensuremath∼eT, which is both infrared finite and gauge invariant. We employ spectral representations and the Gaudin method for evaluating finite temperature Matsubara sums, which facilitates the analysis of multiloop diagrams at high T.