Abstract
Understanding the Higgs potential at large field values corresponding to scales in the range above 1010GeV is important for questions of vacuum stability, particularly in the early universe where survival of the Higgs vacuum can be an issue. In this paper we show that the Higgs potential can be derived in away which is independent of the choice of conformal frame for the spacetime metric. Questions about vacuum stability can therefore be answered unambiguously. We show that frame independence leads to new relations between the beta functions of the theory and we give improved limits on the allowed values of the Higgs curvature coupling for stability.
Highlights
Metastable minimum if ξR is positive, and has the opposite effect when ξR is negative, making Higgs stability sensitive to the value of ξ
Understanding the Higgs potential at large field values corresponding to scales in the range above 1010GeV is important for questions of vacuum stability, in the early universe where survival of the Higgs vacuum can be an issue
We finish of with the top quark as an example of a fermion field. It is far from clear how the covariant approach generalises to fermion fields, so we take the minimalist approach and leave off any extra contributions to the effective action
Summary
The aim of this section is to introduce the field-covariant effective action and to give two methods for evaluating the action to one loop order, by taking the Landau gauge-fixing limit and by decomposition into gauge-fixed and pure gauge modes, leading to the results quoted in the introduction. At one-loop, the contribution to the covariant effective action obtained from a geodesic expansion of the fields in the path integral is. [41], it was shown that the expansion coefficients remain polynomial for some classes of non-Laplacian operators relevant to the covariant effective action. In these cases, we can use b2(A) to read off the rescaling behaviour of the terms in the effective potential or the effective Lagrangian using the renormalisation group equation (1.2). We can combine the terms at one loop order into dΓ(n1c)[φ] dμR dΓ(E1)[φ + f dμR ln μR] Note that this does not imply that the approaches are equivalent, because the covariant action is covariant not invariant under field redefinitions. The Landau gauge result eq (2.15) is equal to eq (2.25) which is equal to the gauge decomposition eq (2.14)
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