Vacuum stability of Standard Model++

Abstract

Abstract:The latest results of the ATLAS and CMS experiments point to a preferred narrow Higgs mass range (m H 124 − 126 GeV) in which the effective potential of the Standard Model (SM) develops a vacuum instability at a scale 10 9 − 10 11 GeV, with the precise scale depending on the precise value of the top quark mass and the strong coupling constant. Motivated by this experimental situation, we present here a detailed investigation about the stability of the SM ++ vacuum, which is characterized by a simple extension of the SM obtained by adding to the scalar sector a complex SU(2) singlet that has the quantum numbers of the right-handed neutrino, H , and to the gauge sector an U(1) that is broken by the vacuum expectation value of H . We derive the complete set of renormalization group equations at one loop. We then pursue a numerical study of the system to determine the triviality and vacuum stability bounds, using a scan of 10 4 random set of points to fix the initial conditions. We show that, if there is no mixing in the scalar sector, the top Yukawa coupling drives the quartic Higgs coupling to negative values in the ultraviolet and, as for the SM, the effective potential develops an instability below the Planck scale. However, for a mixing angle −0.35 α −0.02 or 0.01 α 0.35, with the new scalar mass in the range 500 GeV m h 8 TeV, the SM ++ ground state can be absolutely stable up to the Planck scale. These results are largely independent of TeV-scale free parameters in the model: the mass of the non-anomalous U(1) gauge boson and its branching fractions.

The Higgs mass and the scale of new physics

“…Several physical interpretations of this scale are possible: first, we can require that the Higgs potential be stable at all scales. New degrees of freedom would then have to appear below or at 10 10 GeV, changing the renormalization group evolution, and rendering the potential stable [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. We review one such approach based on a Higgs portal with a scalar dark matter candidate in the appendix [49,50].…”

Majorana dark matter through the Higgs portal under the vacuum stability lamppost

“…Since the stability condition of the electroweak vacuum is strongly sensitive to new physics, from the phenomenological point of view it is clear that beyond SM physics models have to pass a sort of "stability test" [21][22][23]. Indeed, only new physics models that reinforce the requirement of a stable or metastable (but with τ > T U ) electroweak vacuum can be accepted as a viable UV completion of the SM [24][25][26][27][28][29][30][31][32][33][34][35].…”

Refined partition functions for open superstrings with 4, 8 and 16 supercharges

“…We emphasize that, on the contrary to elliptic genera or other types of characters that are used in loop amplitude computations, the states that we trace over are not graded with a minus sign for spacetime fermions. 2 As a result, the partition functions we are considering in this paper do not exhibit a modular invariant property. 3 Open string states also carry Chan-Paton factors.…”

“…All partition functions computed in this paper allow for a straightforward inclusion of the Chan-Paton contributions; hence, we shall not discuss Chan-Paton factors in the subsequent. 2 To illustrate this point, let us look at the first mass level for a 10d theory with 16 supercharges, there are 256 states in total (see Table 1). This number comes from (a) 44 spin two degrees of freedom and 84 three-form degrees of freedom constituting the spacetime bosonic states, and (b) 128 spin 3/2 degrees of freedom constituting the spacetime fermonic states.…”

“…1 Four-dimensional superstrings subject to N 4d = 1 super-Poincaré invariance are especially worth to be studied, since N 4d = 1 compactifications with broken supersymmetry are expected to provide phenomenologically interesting string solutions at low energies with the spectrum of certain extensions of the supersymmetric Standard Model (see e.g. [2] for a stable low energy open string vacuum, the Standard Model ++ with two Higgs fields). In addition to the light states, the knowledge of the universal massive string spectrum is also important in order to compute string scattering amplitudes of massive open string states in N 4d = 1 string compactifications [3].…”