Effective potential at three loops

Abstract

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.

48 pages, 8 ancillary files

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• Three-loop QCD corrections to the electroweak boson masses
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
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• LSZ-reduction, resonances and non-diagonal propagators: fermions and scalars
• Three-loop effective potential of general scalar theory via differential equations
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• Numerator Seagull and Extended Symmetries of Feynman Integrals
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• Higgs Mass Predictions in the CP-Violating High-Scale NMSSM
• The Renormalization Group and the Effective Potential in the Wess-Zumino model
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