Higgs vacuum stability with vectorlike fermions

Abstract

We present the effects of vector-like fermions (VLF) on the stability of the Higgs electroweak vacuum, using the renormalization group improved Higgs effective potential. We review the calculation of the one-loop beta-functions of the standard model couplings paying particular attention to the fermion contributions. From this, we derive the VLF contributions to the betafunctions. We also include the significant two-loop contributions to the beta-functions. Using these beta-functions, we determine the scale at which the effective Higgs quartic-coupling becomes zero and goes negative, signaling vacuum instability. We find that for certain VLF masses and Yukawa couplings, the Higgs quartic stays positive for field values all the way up to the Planck scale, implying that the meta-stable vacuum of the standard model can be rendered absolutely stable if VLFs are present with certain parameters. For other values of VLF parameters, the Higgs vacuum is metastable as in the standard model. For cases where the vacuum is metastable, we compute the probability of quantum tunneling from the false electroweak vacuum into a deeper true vacuum in our Hubble volume by numerically solving for the bounce configuration in Euclidean space-time and computing the bounce action for it. We compare our numerical solution with the analytical approximation for the bounce action commonly used in the literature, and comment on when the latter may be used. * shri@imsc.res.in † arunprasath@imsc.res.in arXiv:1812.11303v3 [hep-ph] 13 Jul 2019Denoting the field value as h ≡ µ and denoting λ eff (µ) as just λ(µ), it can be shown (see for example Ref. [41]) that λ(µ) obeys a renormalization group equation (RGE) of the formThe RGE is interpreted now as an evolution with field value h = µ, and the β-function β λ is the usual β-function for the coupling λ, governed by the RGE. The λ(µ) obtained by integrating the RGE has the leading logs of the form log n (µ/M ) resummed. β λ is shown as a function of λ itself, and also of the other couplings that contribute significantly, which, in the SM, are the top Yukawa coupling y t and the SU (3), SU (2), U (1) gauge couplings g a = {g 3 , g 2 , g 1 }. All these couplings also evolve with µ via analogous RGE equations with their corresponding β-functions β yt , β ga . We neglect the contributions of the other SM couplings to the β-functions as they contribute insignificantly. From Eq.(3) we see that for h m h , the instability is signalled by the Higgs quartic effective coupling λ(µ) becoming negative.As we show explicitly later, β λ obtains a negative contribution from y t , while it obtains a positive contribution from λ(µ) itself and from gauge couplings. Thus, the top quark has the important effect of decreasing λ(µ), and for y t as large as in the SM, for the observed m h , it drives λ(µ) negative at higher energies, signaling vacuum instability. The effect of fermions coupled to the Higgs is generally to destabilize the electroweak vacuum, although in this work we show that this statement is not so definit...

Sub-TeV singlet scalar dark matter and electroweak vacuum stability with vectorlike fermions

“…We have already seen the important role of these VLQs in the present setup in making the otherwise disallowed parameter space (say in terms of mass) a viable one by providing additional contributions to DM effective annihilation cross section and in DD diagrams. Following the results of [39], these VLQs also help in achieving the electroweak vacuum stable up to a large scale. This can be understood if we look into their positive (additional) contribution to the beta function of the gauge couplings g 1;2;3 associated with SUð3Þ; SUð2Þ and Uð1Þ gauge group of the SM respectively (at one loop) given by…”

“…Note that a small value of y (significantly below 1) turns out to be quite natural from the point of view of maintaining perturbativity of y. It is also found in[39] that y above 0.3 can make the Higgs quartic coupling λ H negative at some high scale and thereby could be dangerous for vacuum stability.…”

“…where n F is the number of families of VLQ multiplets (both doublet and singlet) participating in the Yukawa interaction with SM Higgs. In fact, it has been shown in [39] that y > Oð0.3Þ can make λ H negative at the large scale. However in our analysis we have found that this coupling does not have a significant impact on the DM phenomenology and hence we can keep it rather small throughout.…”

“…Although phenomenological implications of such a setup have already been addressed elsewhere from different perspectives [26][27][28][29][30][31][32][33][34][35][36][37], here we have one more motivation and that is to ensure the stability of electroweak vacuum all the way up to the Planck scale. The idea emerges from a recent observation [39] that, though we know fermions coupling to the Higgs contribute negatively to the RG running of quartic coupling λ H in general, the presence of VLQs can actually affect the SUð3Þ gauge coupling in such a way which in turn is useful in keeping λ H positive at all scales. We show that the same idea can be extended to VLLs also which affect the SUð2Þ gauge coupling in a similar way to keep λ H positive at all scales, though more generations of doublet-singlet VLLs are required to include.…”

Flavoured gauge extension of singlet-doublet fermionic dark matter: neutrino mass, high scale validity and collider signatures

“…In the scalar sector, apart from the SM Higgs doublet H we have two more singlet scalars: S and Φ both charged under U (1) B−3Lτ . These scalars take 2 With VLF alone, it is possible to make the electroweak vacuum stable, if they have coloured charges, as shown in [55].…”