Emanuele Messina

Stability, Higgs Boson Mass and New Physics

Assuming that the particle with mass ∼126  GeV discovered at LHC is the standard model Higgs boson, we find that the stability of the electroweak (EW) vacuum strongly depends on new physics interaction at the Planck scale MP, despite of the fact that they are higher-dimensional interactions, apparently suppressed by inverse powers of MP. In particular, for the present experimental values of the top and Higgs boson masses, if τ is the lifetime of the EW vacuum, new physics can turn τ from τ≫TU to τ≪TU, where TU is the age of the Universe, thus, weakening the conclusions of the so called metastability scenario.

Lifetime of the electroweak vacuum and sensitivity to Planck scale physics

If the Standard Model (SM) is valid up to extremely high energy scales, then the Higgs potential becomes unstable at approximately 1 0 11 GeV . However, calculations of the lifetime of the SM vacuum have shown that it vastly exceeds the age of the Universe. It was pointed out by two of us (V. B., E. M.) that these calculations are extremely sensitive to effects from Planck scale higher-dimensional operators and, without knowledge of these operators, firm conclusions about the lifetime of the SM vacuum cannot be drawn. The previous paper used analytical approximations to the potential and, except for Higgs contributions, ignored loop corrections to the bounce action. In this work, we do not rely on any analytical approximations and consider all contributions to the bounce action, confirming the earlier result. It is surprising that the Planck scale operators can have such a large effect when the instability is at 1 0 11 GeV . There are two reasons for the size of this effect. In typical tunneling calculations, the value of the field at the center of the critical bubble is much larger than the point of the instability; in the SM case, this turns out to be numerically within an order of magnitude of the Planck scale. In addition, tunneling is an inherently nonperturbative phenomenon and may not be as strongly suppressed by inverse powers of the Planck scale. We include effective Φ 6 and Φ 8 Planck-scale operators and show that they can have an enormous effect on the tunneling rate.

Top mass determination, Higgs inflation, and vacuum stability

A bstractThe possibility that new physics beyond the Standard Model (SM) appears only at the Planck scale MP is often considered. However, it is usually assumed that new physics interactions at MP do not affect the electroweak vacuum lifetime, so the latter is obtained neglecting these terms. According to the resulting stability phase 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. 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 MP . Therefore, Higgs inflation scenarios require very severe fine tunings that cast serious doubts on these models.

Stability and UV completion of the Standard Model

The knowledge of the stability condition of the electroweak (EW) vacuum is of the greatest importance for our understanding of beyond Standard Model (BSM) physics. It is widely believed that new physics that lives at very high energy scales should have no impact on the stability analysis. This expectation has been recently challenged, but the results were controversial as new physics was given in terms of non-renormalizable higher order operators. Here we consider for the first time a renormalizable (toy) UV completion of the SM, and definitely show that such a decoupling does not take place. This result has important phenomenological consequences, providing a very useful test for BSM theories. In particular, it shows that speculations based on the so called “criticality” do not appear to be well founded.

Impact of gravity on vacuum stability

In a pioneering paper on the role of gravity on false vacuum decay, Coleman and De Luccia showed that a strong gravitational field can stabilize the false vacuum, suppressing the formation of true vacuum bubbles. This result is obtained for the case when the energy density difference between the two vacua is small, the so called thin wall regime, but is considered of more general validity. Here we show that when this condition does not hold, however, {\it a strong gravitational field (Planckian physics) does not necessarily induce a total suppression of true vacuum bubble nucleation}. Contrary to common expectations then, gravitational physics at the Planck scale {\it does not stabilize the false vacuum}. These results are of crucial importance for the stability analysis of the electroweak vacuum and for searches of new physics beyond the Standard Model.

Ordinary versus PT-symmetric

A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.

\phi^3

around the fixed point is examined and it is shown that the corresponding phase transition is related to the existence of a nontrivial solution of the gap equation. The theory is studied first in the mean-field approximation and the critical exponents are calculated. Then, it is examined beyond the mean-field approximation by using renormalization-group techniques, and the critical exponents for 6−ǫ dimensions are calculated to order ǫ. It is shown that because of its stability the PT -symmetric iφ 3 theory has a higher predictive power than the conventional φ 3 theory. A comparison of the iφ 3 model with the Lee-Yang model is given.

quantum field theory

around the fixed point is examined and it is shown that the corresponding phase transition is related to the existence of a nontrivial solution of the gap equation. The theory is studied first in the mean-field approximation and the critical exponents are calculated. Then, it is examined beyond the mean-field approximation by using renormalization-group techniques, and the critical exponents for 6−ǫ dimensions are calculated to order ǫ. It is shown that because of its stability the PT -symmetric iφ 3 theory has a higher predictive power than the conventional φ 3 theory. A comparison of the iφ 3 model with the Lee-Yang model is given.

Critical behavior of the PT-symmetric iϕ3 quantum field theory

around the fixed point is examined and it is shown that the corresponding phase transition is related to the existence of a nontrivial solution of the gap equation. The theory is studied first in the mean-field approximation and the critical exponents are calculated. Then, it is examined beyond the mean-field approximation by using renormalization-group techniques, and the critical exponents for 6−ǫ dimensions are calculated to order ǫ. It is shown that because of its stability the PT -symmetric iφ 3 theory has a higher predictive power than the conventional φ 3 theory. A comparison of the iφ 3 model with the Lee-Yang model is given.

Critical behavior of the P T -symmetric i ϕ 3 quantum field theory

The longitudinal susceptibility χL of the O(N) theory in the broken phase is analyzed by means of three different approaches, namely the leading contribution of the 1/N expansion, the Functional Renormalization Group flow in the Local Potential approximation and the improved effective potential via the Callan–Symanzik equations, properly extended to d = 4 dimensions through the expansion in powers of ϵ = 4-d. The findings of the three approaches are compared and their agreement in the large N limit is shown. The numerical analysis of the Functional Renormalization Group flow equations at small N supports the vanishing of in d = 3 and d = 3.5 but is not conclusive in d = 4, where we have to resort to the Callan–Smanzik approach. At finite N as well as in the limit N→∞, we find that vanishes with J as Jϵ/2 for ϵ> 0 and as (ln(J))-1 in d = 4.