Abstract
We investigate the impact of operators of higher canonical dimension on the lower Higgs-mass consistency bound by means of generalized Higgs–Yukawa interactions. Analogously to higher-order operators in the bare Higgs potential in an effective field theory approach, the inclusion of higher-order Yukawa interactions, e.g., phi ^3bar{psi }psi , leads to a diminishing of the lower Higgs-mass bound and thus to a shift of the scale of new physics towards larger scales by a few orders of magnitude without introducing a metastability in the effective Higgs potential. We observe that similar renormalization group mechanisms near the weak-coupling fixed point are at work in both generalizations of the microscopic action. Thus, a combination of higher-dimensional operators with generalized Higgs as well as Yukawa interactions does not lead to an additive shift of the lower mass bound, but it relaxes the consistency bounds found recently only slightly. On the method side, we clarify the convergence properties of different projection and expansion schemes for the Yukawa potential used in the functional renormalization group literature so far.
Highlights
The usual perturbative treatment of the lower Higgs-mass bound is based on the assumption that the high energy behavior of particle physics is dominated only by standard-model degrees of freedom as well as by perturbatively renormalizable operators
This is in agreement with the extended mean-field analysis: the renormalization group (RG) flow originating from the second projection scheme can overrate the impact of the neglected higher-order Yukawa couplings which leads to larger Higgs masses in the gauged model
We have investigated the impact of a generalized Yukawa function H (ρ) rather than a simple coupling on the lower Higgs-mass consistency bound from a functional RG perspective
Summary
The usual perturbative treatment of the lower Higgs-mass bound is based on the assumption that the high energy behavior of particle physics is dominated only by standard-model degrees of freedom as well as by perturbatively renormalizable operators. Recent studies based on general RG arguments in an effective field theory approach demonstrate that higher-dimensional operators at some UV cutoff scale can exert an influence on the Higgs-mass stability bound In these studies, based on the functional RG [48,49,50,51] as well as nonperturbative lattice simulations [52,53,54,55,56], a lower Higgs-mass bound emerges naturally from the RG flow itself and is primarily connected with a consistency condition on the bare action rather than with the stability of the effective Higgs potential which is a resulting long-range property. The aim of this work is to investigate the impact of further higher-dimensional operators by means of a generalized Yukawa interaction term This goes beyond the class of polynomially stable bare potentials (e.g., of φ6-type) with a unique minimum studied so far.
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