Systematics of High Temperature Perturbation Theory: The Two-Loop Electron Self-Energy in QED
Emil Mottola, Zsolt Szep
备注：
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
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 in high temperature QED. The two-loop bubble diagram contains a linear infrared divergence. Even if regulated with a non-zero 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 at one-loop. 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, nested inside a second loop integral which is soft. There are no hard-hard contributions to the two-loop Sigma at leading order at high T. Provided the same factorization pattern holds for arbitrary ell loops, the NLO high temperature contributions to the electron self-energy come from ell-1 hard loops factorized with one soft loop integral. This hard-soft pattern is both a necessary condition for the resummation over ell to coincide with the one-loop self-energy calculated with HTL dressed propagators and vertices, and to yield the complete NLO correction to the self-energy at scales ~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 multi-loop diagrams at high T.
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Three-loop helicity amplitudes of four-lepton scattering in QED
Higgs Centre for Theoretical Physics, School of Physics and Astronomy The University of Edinburgh（爱丁堡大学物理与天文学学院希格斯理论物理中心）；Department of Mathematical Sciences, University of Liverpool（利物浦大学数学科学系）；Dipartimento di Fisica e Astronomia, Universita di Padova（帕多瓦大学物理与天文系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）
We obtain analytical five-loop results for the renormalization group $β$-function of Quantum Electrodynamics with the single lepton in different renormalization schemes. The theoretical consequences of the results obtained are discussed.
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Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion
School of Physics and Technology, Nanjing Normal University（南京师范大学物理科学与技术学院）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）；School of Physics, Hubei University（湖北大学物理学院）
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