Neutrino masses and Higgs vacuum stability

Abstract

The Standard Model electroweak vacuum has been found to be metastable, with the true stable vacuum given by a large, phenomenologically unacceptable vacuum expectation value ≈ M P . Moreover, it may be unstable in an inflationary universe. Motivated by the necessity of physics beyond the Standard Model and to accommodate non-zero neutrino masses, we investigate vacuum stability within type-II seesaw and left-right symmetric models. Our analysis is performed by solving the renormalisation group equations, carefully taking into account the relevant threshold corrections. We demonstrate that a phenomenologically viable left-right symmetric model can be constructed by matching it with the SM at one-loop. In both models we demonstrate the existence of a large area of parameter space where the Higgs vacuum is absolutely stable. arXiv:1305.7283v1 [hep-ph] 31 May 2013The presence of new physics modifies the Higgs potential at higher energies by changing the β-functions for the couplings, since we now include new particles running in loops when calculating radiative corrections. New bosonic particles provide a positive contribution to the running of the Higgs quartic coupling, whist new fermionic particles contribute negatively. Examples of this effect, as applied to the Higgs potential, were given in [6,7] where the presence of an additional scalar singlet, introduced below µ I , was found to preserve positivity of the quartic coupling up to the Planck scale.Whilst one can construct many different ad hoc new physics models to resolve the vacuum stability problem [8][9][10][11][12][13][14], we believe that models addressing other SM problems deserve primary consideration. In fact, empirically, we have firmly established evidence for physics beyond the SM: neutrino oscillations (and hence neutrino masses), dark matter and matter-antimatter asymmetry. Additional theoretical considerations based on the naturalness principle, such as the strong CP problem and the gauge hierarchy problem, also provide a hint of new physics beyond the SM. Amongst this evidence, neutrino mass is perhaps the most compelling, from a purely phenomenological point of view. Therefore, in this paper we analyse the effect of some models of neutrino mass generation upon stability of the Higgs vacuum.The rest of the paper is organised as follows. In the next section we briefly discuss the running of the Higgs quartic coupling in the SM and possible new physics which may affect this running at high energies. In Sec. 3 and 4 we present a thorough study of vacuum stability in the type-II seesaw and left-right symmetric models. Finally, in Sec. 5 the reader can find our conclusions. In Appendix A we provide details of the matching between MS and pole masses for the Higgs boson and top quark and values of the gauge couplings at the electroweak scale, while the relevant RGEs and β-functions are collected in Appendices B, C and D.

(Higgs) vacuum decay during inflation

“…Therefore, a small 'probability' ℘ ∼ 1 of vacuum tunnelling during inflation needs a bounce action S > ∼ 3N . 9 The horizon of the visible universe corresponds to a minimal number of N ∼ 60 e-foldings of inflation.…”

“…A possible extra quartic scalar coupling of the inflaton to the Higgs would 9 Evading this bound trough anthropic selection would need a very special landscape of unstable vacua with no low-scale inflation.…”

“…The Higgs field can fluctuate towards values a few orders of magnitude below the Planck scale, for which its potential can be deeper than for the electroweak vacuum [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. If vacuum decay happens during inflation, the regions of true vacuum expand and engulf the whole space [2,18,24].…”

TeV scale universal seesaw, vacuum stability and heavy Higgs

“…1 1 After this work was completed, we came across ref. [14], which discusses vacuum stability in the exact parity symmetric left-right seesaw model with right handed scale as well as the mass of the vector like fermions near 10 10 GeV. The tree level potential in this model does not break the standard model gauge group, whereas in our case, as we discuss below, parity is softly broken, so that we get a minimum which breaks SM gauge group as well as the right handed SU(2)R at the tree level.…”

“…However another direction of physics which may be suggested by this and one that has received great deal of attention in recent months, is that this "near criticality" of the Higgs coupling is a signal of nearby new physics that would stabilize this vacuum. Many extensions of the standard model by enlarging the Higgs and/or the gauge sector have been proposed as a way to eliminate the deeper high scale minimum of the potential [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”