2017/09/07 by Stephen P. Martin · 1 citation
Physics and Astronomy · #hep-ph
paper · pdf · doi:10.1103/physrevd.96.096005
published as Phys. Rev. D 96, 096005 (2017) · 48 pages, 8 ancillary files
arxiv created 2017/09/07 · arxiv updated 2017/11/22
I present the effective potential at three-loop order for a general renormalizable theory, using the \MSbar renormalization scheme and Landau gauge fixing. As applications and illustrative points of reference, the results are specialized to the supersymmetric Wess-Zumino model and to the Standard Model. In each case, renormalization group scale invariance provides a consistency check. In the Wess-Zumino model, the required vanishing of the minimum vacuum energy yields an additional check. For the Standard Model, I carry out the resummation of Goldstone boson contributions, which provides yet more opportunities for non-trivial checks, and obtain the minimization condition for the Higgs vacuum expectation value at full three-loop order. An infrared divergence due to doubled photon propagators appears in the three-loop Standard Model effective potential, but it does not affect the minimization condition or physical observables and can be eliminated by resummation.