Vincenzo Branchina

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.

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.

Impact of New Physics on the EW vacuum stability in a curved spacetime background

A bstractIt has been recently shown that, contrary to an intuitive decoupling argument, the presence of new physics at very large energy scales (say around the Planck scale) can have a strong impact on the electroweak vacuum lifetime. In particular, the vacuum could be totally destabilized. This study was performed in a flat spacetime background, and it is important to extend the analysis to curved spacetime since these are Planckian-physics effects. It is generally expected that under these extreme conditions gravity should totally quench the formation of true vacuum bubbles, thus washing out the destabilizing effect of new physics. In this work we extend the analysis to curved spacetime and show that, although gravity pushes toward stabilization, the destabilizing effect of new physics is still (by far) the dominating one. In order to get model independent results, high energy new physics is parametrized in two different independent ways: as higher order operators in the Higgs field, or introducing new particles with very large masses. The destabilizing effect is observed in both cases, hinting at a general mechanism that does not depend on the parametrization details for new physics, thus maintaining the results obtained from the analysis performed in flat spacetime.

Effective potential and vacuum stability

By following previous work on this subject, we investigate the issue of the instability of the electroweak vacuum against the top loop corrections by performing an accurate analysis of a Higgs–Yukawa model. We find that when the physical cutoff is properly implemented in the theory the potential does not exhibit any instability. Moreover, contrary to recent claims, we show that this instability cannot be understood in terms of the very insightful work of Wu and Weinberg on the non-convexity of the one-loop effective potential of a scalar theory. Some of the theoretical and phenomenological consequences of our results are briefly discussed.

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.

Finite-momentum Bose-Einstein condensates in shaken two-dimensional square optical lattices

We consider ultracold bosons in a two-dimensional square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor-hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. Therefore, it is necessary to account for higher-order-hopping terms, which are renormalized differently by the shaking, and to introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentum condensates with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott insulator and the different superfluid phases and present the time-of-flight images expected to be observed experimentally. Our results open up possibilities for the realization of bosonic analogs of the Fulde, Ferrel, Larkin, and Ovchinnikov phase describing inhomogeneous superconductivity

Dark energy and Josephson junctions

It has been recently claimed that dark energy can be (and has been) observed in laboratory experiments by measuring the power spectrum SI(ω) of the noise current in a resistively shunted Josephson junction and that in new dedicated experiments, which will soon test a higher frequency range, SI(ω) should show a deviation from the linear rising observed in the lower frequency region because higher frequencies should not contribute to dark energy. Based on previous work on theoretical aspects of the fluctuation-dissipation theorem, we carefully investigate these issues and show that these claims are based on a misunderstanding of the physical origin of the spectral function SI(ω). According to our analysis, dark energy has never been (and will never be) observed in Josephson junctions experiments. We also predict that no deviation from the linear rising behavior of SI(ω) will be observed in forthcoming experiments. Our findings provide new (we believe definite) arguments which strongly support previous criticisms.

Mapping fermion and boson systems onto the Fock space of harmonic oscillators.

The fluctuation-dissipation theorem (FDT) is very general and applies to a broad variety of different physical phenomena in condensed matter physics. With the help of the FDT and following the famous work of Caldeira and Leggett, we show that, whenever linear response theory applies, any generic bosonic or fermionic system at finite temperature T can be mapped onto a fictitious system of free-harmonic oscillators. To the best of our knowledge, this is the first time that such a mapping is explicitly worked out. This finding provides further theoretical support to the phenomenological harmonic oscillator models commonly used in condensed matter. Moreover, our result helps in clarifying an interpretation issue related to the presence and physical origin of the Bose-Einstein factor in the FDT.