Higgs mass implications on the stability of the electroweak vacuum

The issue of vacuum stability of standard model (SM) is discussed by embedding it within the TeV scale left–right quark see-saw model. The Higgs potential in this case has only two coupling parameters (λ1, λ2) and two mass parameters. There are only two physical neutral Higgs bosons (h,H), the lighter one being identified with the 126 GeV Higgs boson. We explore the range of values for (λ1, λ2) for which the vacuum is stable for all values of the Higgs fields till 1016 GeV. Combining with the further requirement that the scalar self-couplings remain perturbative till 1016 GeV, we find (i) an upper and lower limit on the second Higgs (H) mass to be within the range: 0.4 ≤ (MH/vR) ≤ 0.7, where vR is the parity breaking scale and (ii) the masses of heavy vector-like top, bottom and τ partner fermions (P3, N3,E3) have an upper bound ≤ vR. These predictions can be tested at LHC and future higher energy colliders.

We discuss a new family of multiquanta-bound states in the standard model which exist due to the mutual Higgs-based attraction of the heaviest members of the standard model, namely, gauge quanta $W$, $Z$, and (anti)top quarks, $\overline{t}$, $t$. We use a self-consistent mean-field approximation, up to a rather large particle number $N$. In this paper we do not focus on weakly bound, nonrelativistic bound states, but rather on ``bags'' in which the Higgs vacuum expectation value is significantly modified or depleted. The minimal number $N$ above which such states appear strongly depends on the ratio of the Higgs mass to the masses of $W$, $Z$, $\overline{t}$, $t$: For a light Higgs mass, ${m}_{H}\ensuremath{\sim}50\text{ }\text{ }\mathrm{GeV}$, bound states start from $N\ensuremath{\sim}O(10)$, but for a ``realistic'' Higgs mass, ${m}_{H}\ensuremath{\sim}100\text{ }\text{ }\mathrm{GeV}$, one finds metastable/bound $W$, $Z$ bags only for $N\ensuremath{\sim}O(1000)$. We also found that in the latter case pure top bags disappear for all $N$, although top quarks can still be well bound to the $W$ bags. Anticipating the cosmological applications (discussed in the following Article [Phys. Rev. D 82, 073019]) of these bags as ``doorway states'' for baryosynthesis, we also consider here the existence of such metastable bags at finite temperatures, when standard-model parameters such as Higgs, gauge, and top masses are significantly modified.

The possibility that new physics beyond the Standard Model (SM) appears only at the Planck scale $M_P$ is often considered. However, it is usually argued that new physics interactions at $M_P$ do not affect the SM stability phase diagram, so the latter is obtained neglecting these terms. According to this diagram, for the current experimental values of the top and Higgs masses, our universe lives in a metastable state (with very long lifetime), near the edge of stability. Contrary to these expectations, however, we show that the stability phase diagram strongly depends on new physics and that, despite claims to the contrary, a more precise determination of the top (as well as of the Higgs) mass will not allow to discriminate between stability, metastability or criticality of the electroweak vacuum. At the same time, we show that the conditions needed for the realization of Higgs inflation scenarios (all obtained neglecting new physics) are too sensitive to the presence of new interactions at $M_P$. Therefore, Higgs inflation scenarios require very severe fine tunings that cast serious doubts on these models.

Top quark and Higgs boson masses: Interplay between infrared and ultraviolet physics

If the Standard Model is valid up to very high energies it is known that the Higgs potential can develop a local minimum at field values around 10^15−10^17 GeV, for a narrow band of values of the top quark and Higgs masses. We show that in a scalar-tensor theory of gravity such Higgs false vacuum can give rise to viable inflation if the potential barrier is very shallow, allowing for tunneling and relaxation into the electroweak scale true vacuum. The amplitude of cosmological density perturbations from inflation is directly linked to the value of the Higgs potential at the false minimum. Requiring the top quark mass, the amplitude and spectral index of density perturbations to be compatible with observations, selects a narrow range of values for the Higgs mass, mH=126.0±3.5 GeV, where the error is mostly due to the theoretical uncertainty of the 2-loop RGE. This prediction could be soon tested at the Large Hadron Collider. Our inflationary scenario could also be further checked by better constraining the spectral index and the tensor-to-scalar ratio.

In the framework of the two-loop renormalization group, the restrictions on the Higgs mass from the electroweak vacuum stability and from the absence of the strong coupling are refined, while the more precise value of the top mass is taken into account. When the SM cutoff is equal to the Planck scale, the Higgs mass must be $M_{\mathrm H} = (161.3 \pm 20.6)^{+4}_{-10}$ GeV and $M_{\mathrm H}\ge 140.7^{+10}_{-10}$ GeV, where the $M_{\mathrm H}$ corridor is the theoretical one and the errors are due to the top-mass uncertainty. The SM two-loop $\beta$ functions are generalized to the case with massive neutrinos from extra families. The requirement of self-consistency of the perturbative SM as an underlying theory up to the Planck scale excludes a fourth chiral family. Under the precision-experiment restriction $M_{\mathrm H}\leq 215$ GeV, the fourth chiral family, if alone, is excluded even when the SM is regarded as an effective theory. Nevertheless a pair of chiral families constituting a vector-like one could exist.

In supersymmetric models with minimal particle content and without large left-right squarks mixing, the conventional knowledge is that the Higgs Boson mass around 125 GeV leads to top squark masses O(10) TeV, far beyond the reach of colliders. Here, we pointed out that this conclusion is subject to several theoretical uncertainties. We find that electroweak symmetry breaking and evaluation of Higgs mass at a scale far away from the true electroweak symmetry breaking scale introduce a large uncertainty in Higgs mass calculation. We show that the electroweak symmetry breaking at the scale near the true vacuum expectation value of Higgs field can increase the Higgs Boson mass about 4–5 GeV and can lower the bounds on squarks and slepton masses to 1 TeV. Here we pointed out that the Higgs mass even with inclusion of radiative corrections can vary with electroweak symmetry breaking scale. We calculate it at two loop level and show that it varies substantially. We argue that Higgs mass like other coupling parameters can vary with energy scale and the Higgs potential with all orders loop corrections is scale invariant. This uncertainty to the Higgs mass calculation due to electroweak symmetry breaking around the supersymmetry breaking scale, normally taken as mt˜Lmt˜R, to minimize the 1-loop radiative corrections can be removed if one considers all significant radiative contributions to make Higgs potential renormalization group evolution scale invariant and evaluates electroweak symmetry breaking at the scale near the electroweak symmetry breaking scale. A large parameter space becomes allowed when one considers electroweak symmetry breaking at its true scale not only for producing correct values of the Higgs masses, but also for providing successful breaking of this symmetry in more parameter spaces.

We present the first complete next-to-next-to-leading order analysis of the Standard Model Higgs potential. We computed the two-loop QCD and Yukawa corrections to the relation between the Higgs quartic coupling (λ) and the Higgs mass (M h ), reducing the theoretical uncertainty in the determination of the critical value of M h for vacuum stability to 1 GeV. While λ at the Planck scale is remarkably close to zero, absolute stability of the Higgs potential is excluded at 98 % C.L. for M h < 126 GeV. Possible consequences of the near vanishing of λ at the Planck scale, including speculations about the role of the Higgs field during inflation, are discussed.

We refine and update the metastability constraint on the standard model (SM) top and Higgs masses by analytically including gravitational corrections to the vacuum decay rate. Present best-fit ranges of the top and Higgs masses mostly lie in the narrow metastable region. Furthermore, we show that the SM potential can be fine-tuned in order to be made suitable for inflation. However, SM inflation results in a power spectrum of cosmological perturbations not consistent with observations.

We revisited the scenario of electroweak baryogenesis in the presence of large Yukawa couplings, in which it was found previously that a strongly first order electroweak phase transition can occur with the Higgs mass at its observed value of 125 GeV. Given the sensitivity of the running of the Higgs quartic coupling on the Yukawa coupling constants, we find that the addition of order one Yukawa couplings beyond the top quark drastically lowers the scale at which the Higgs potential becomes unstable. Specifically, even with only one additional order one Yukawa coupling, the scalar potential becomes unstable already at the TeV scale, assuming the Standard Model values for the Higgs sector parameters at the electroweak scale. Furthermore, by assuming the Standard Model values for the Higgs sector parameters at the TeV scale, the quartic coupling constant is driven to be larger than its Standard Model value at the electroweak scale. This in turn predicts a much lighter Higgs mass than the measured value of 125 GeV. In this scenario, the strength of the electroweak phase transition is also significantly weakened.

We compute the one loop corrections to the CP-even Higgs mass matrix in the supersymmetric inverse seesaw model to single out the different cases where the radiative corrections from the neutrino sector could become important. It is found that there could be a significant enhancement in the Higgs mass even for Dirac neutrino masses of O(30) GeV if the left-handed sneutrino soft mass is comparable or larger than the right-handed neutrino mass. In the case where right-handed neutrino masses are significantly larger than the supersymmetry breaking scale, the corrections can utmost account to an upward shift of 3 GeV. For very heavy multi TeV sneutrinos, the corrections replicate the stop corrections at 1-loop. We further show that general gauge mediation with inverse seesaw model naturally accommodates a 125 GeV Higgs with TeV scale stops.

We consider the minimal seesaw model in which two gauge singlet right-handed neutrinos with opposite lepton numbers are added to the Standard Model. In this model, the smallness of the neutrino mass is explained by the tiny lepton number violating coupling between one of the singlets with the standard left-handed neutrinos. This allows one to have the right-handed neutrino mass at the TeV scale as well as appreciable mixing between the light and heavy states. This model is fully reconstructible in terms of the neutrino oscillation parameters apart from the overall coupling strengths. We show that the overall coupling strength ${y}_{\ensuremath{\nu}}$ for the Dirac-type coupling between the left-handed neutrino and one of the singlets can be restricted by consideration of the (meta)stability bounds on the electroweak vacuum. In this scenario the lepton flavor violating decays of charged leptons can be appreciable, which can put further constraint on ${y}_{\ensuremath{\nu}}$ for right-handed neutrinos at TeV scale. We discuss the combined constraints on ${y}_{\ensuremath{\nu}}$ for this scenario from the process $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and from the consideration of vacuum (meta)stability constraints on the Higgs self-coupling. We also briefly discuss the implications for neutrinoless double beta decay and possible signatures of the model that can be expected at colliders.

Extrapolating the Standard Model Higgs potential at high energies, we study the barrier between the electroweak and Planck scale minima. The barrier arises by taking the central values of the relevant experimental inputs, that is the strong coupling constant and the top quark and Higgs masses. We then extend the Standard Model by including a non-minimal coupling to gravity, and explore the phenomenology of the Higgs inflation model. We point out that even configurations that would be metastable in the Standard Model, become viable for inflation if the non-minimal coupling is large enough to flatten the Higgs potential at field values below the barrier; we find that the required value of the non-minimal coupling is smaller than the one needed for the conventional Higgs inflation scenario (which relies on a stable Standard Model Higgs potential, without any barrier); in addition, values of the top mass which are larger than those required in the conventional scenario are allowed.

The null results of the LHC searches have put strong bounds on new physics scenarios such as supersymmetry (SUSY). With the latest values for the top quark mass and strong coupling, we study the upper bounds on the sfermion masses in split SUSY from the observed Higgs boson mass and electroweak (EW) vacuum stability. To be consistent with the observed Higgs mass, we find that the largest values of supersymmetry breaking scales $M_{S}$ for $\tan\beta=2$, $\tan\beta=4$, and $\tan\beta=50$ are $10^{6.2}$, $10^{4.5}$, and $10^{4.3}\, {\rm GeV}$, respectively. In particular, split SUSY with $\tan\beta \gtrsim 4$ can be probed in future 100 TeV proton–proton colliders such as FCC-hh and SppC. In addition, the Higgs quartic coupling becomes negative at about $10^{8.2}$, $10^{8.7}$, and $10^{9.6}\, {\rm GeV}$ respectively for $m_h =$ 123, 125, and 127 GeV from EW vacuum stability. These bounds are about one order smaller than the Standard Model due to the extra Higgs–Higgsino–gaugino couplings. We briefly comment on the lifetime of gluinos in our study and compare it with the current LHC observations. Additionally, we comment on the prospects of the discovery of prompt gluinos at the FCC-hh and SppC.

If the Standard Model is valid up to scales near the Planck mass, and if the cosmological constant and Higgs mass parameters scan on a landscape of vacua, it is well known that the observed orders of magnitude of these quantities can be understood from environmental selection for large-scale structure and atoms. If in addition the Higgs quartic coupling scans, with a probability distribution peaked at low values, environmental selection for a phase having a scale of electroweak symmetry breaking much less than the Planck scale leads to a most probable Higgs mass of 106 GeV. While fluctuations below this are negligible, the upward fluctuation is 25/p GeV, where p measures the strength of the peaking of the a priori distribution of the quartic coupling. If the top Yukawa coupling also scans, the most probable top quark mass is predicted to lie in the range (174--178) GeV, providing the standard model is valid to at least 10^{17} GeV. The downward fluctuation is 35 GeV/ \sqrt{p}, suggesting that p is sufficiently large to give a very precise Higgs mass prediction. While a high reheat temperature after inflation could raise the most probable value of the Higgs mass to 118 GeV, maintaining the successful top prediction suggests that reheating is limited to about 10^8 GeV, and that the most probable value of the Higgs mass remains at 106 GeV. If all Yukawa couplings scan, then the e,u,d and t masses are understood to be outliers having extreme values induced by the pressures of strong environmental selection, while the s, \mu, c, b, \tau Yukawa couplings span only two orders of magnitude, reflecting an a priori distribution peaked around 10^{-3}. Extensions of these ideas allow order of magnitude predictions for neutrino masses, the baryon asymmetry and important parameters of cosmological inflation.