Abstract
Using extended mean field theory (EMFT) on the lattice, we study properties of the Higgs-Yukawa model as an approximation of the standard model Higgs sector, and the effect of higher dimension operators. We note that the discussion of vacuum stability is completely modified in the presence of a $\phi^6$ term, and that the Higgs mass no longer appears fine tuned. We also study the finite temperature transition. Without higher dimension operators the transition is found to be second order (crossover with gauge fields) for the experimental value of the Higgs mass $M_h=125$ GeV. By taking a $\phi^6$ interaction in the Higgs potential as a proxy for a UV completion of the standard model, the transition becomes stronger and turns first order if the scale of new physics, i.e. the mass of the lightest mediator particle, is around $1.5$ TeV. This implies that electroweak baryogenesis may be viable in models which introduce new particles around that scale.
Highlights
Even before the Higgs boson was discovered several studies where the standard model (SM) couplings were run to very large energies were conducted
In order to assess how well our extended mean field theory (EMFT) method works in the presence of fermions, we compare it to already existing full Monte Carlo results and results obtained using an analytic, approximate method, the constraint effective potential (CEP) [16]
It is clear that EMFT is a very good approximation and gives results close to the Monte Carlo results in all cases, in contrast to CEP which works acceptably well for small values of λ6 only
Summary
Even before the Higgs boson was discovered several studies where the standard model (SM) couplings were run to very large energies were conducted This resulted in both upper and lower bounds on the Higgs mass stemming from the triviality of the Higgs self-interaction and the electroweak (EW) vacuum stability, respectively. We may add higher-dimension operators, which may not directly be relevant for the low energy physics but which can, for example, play an important role for the stability of the EW vacuum or in the context of EW baryogenesis, in an effective field theory way This will drastically change the running of the SM coupling constants so the question of whether the Higgs mass puts the universe in a near critical state or not loses its relevance in this context.
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