We study the instability of the Higgs vacuum caused by a cloud of strings. By catalysis, the decay rate of the vacuum is highly enhanced and, when the energy density of the cloud is larger than the critical value, a semi-classical vacuum decay occurs. We also discuss the relation between the string cloud and observational constraints on the cosmic strings from the viewpoint of the catalysis, which are converted into bounds on the parameters of the Higgs potential.
We argue that the rate of Standard Model vacuum or thermal decay seeded by primordial black holes is negligible (because non-perturbatively suppressed by the small quartic Higgs coupling) and independent of the non-minimal coupling of the Higgs to gravity.
This talk reviews our recent work showing how tiny black holes can act as nucleation sites for the decay of the metastable Higgs vacuum. We start by discussing the formation of thin wall bubbles of true vacuum inside a false vacuum, and show how adding a black hole lowers the action of the Euclidean tunneling solution, thus strongly enhancing the probability of vacuum decay. We then review numerical results for the Higgs vacuum showing that the decay rate is even higher for these "thick wall" bubbles. The results imply either tiny black holes are not a component of our universe, or BSM correct…
We study the stability of the Electroweak (EW) vacuum in a scale-invariant extension of the Standard Model and General Relativity, known as a Higgs-Dilaton theory. The safety of the EW vacuum against possible transition towards another vacuum is a necessary condition for the model to be phenomenologically acceptable. We find that, within a wide range of parameters of the theory, the decay rate is significantly suppressed compared to that of the Standard Model. We also discuss properties of a tunneling solution that are specific to the Higgs-Dilaton theory.
The issue of electroweak vacuum stability is studied in presence of a scalar field which participates in modifying the minimal chaotic inflation model. It is shown that the threshold effect on the Higgs quartic coupling originating from the Higgs-inflaton sector interaction can essentially make the electroweak vacuum stable upto the Planck scale. On the other hand we observe that the new physics parameters in this combined framework are enough to provide deviation from the minimal chaotic inflation predictions so as to keep it consistent with recent observation by Planck 2015.
The problem of vacuum instability and creation of pairs by external fields SU(2) is studied. The effective mass operator has complex eigenvalues implying decay and pair creation. We consider a constant external chromoelectric field and a region in the parameter space where the vaccum becomes unstable and decays in pairs. Although the calculation is done in SU(2) color group it is also valid for SU(3).
After reviewing the calculation of the Standard Model one-loop effective potential in a class of linear gauges, we discuss the physical observables entering the vacuum stability analysis. While the electroweak-vacuum-stability bound on the Higgs boson mass can be formally proven to be gauge independent, the field value at which the effective potential turns negative (the so-called instability scale) is a gauge dependent quantity. By varying the gauge-fixing scheme and the gauge-fixing parameters in their perturbative domain, we find an irreducible theoretical uncertainty of at least two orders…
We show how a heavy scalar singlet with a large vacuum expectation value can evade the potential instability of the Standard Model electroweak vacuum. The quartic interaction between the heavy scalar singlet and the Higgs doublet leads to a positive tree-level threshold correction for the Higgs quartic coupling, which is very effective in stabilizing the potential. We provide examples, such as the see-saw, invisible axion and unitarized Higgs inflation, where the proposed mechanism is automatically implemented in well-defined ranges of Higgs masses.
The cosmological Higgs vacuum stability has been an attractive research subject and it is crucial to accurately follow the development of the Higgs fluctuations. In this work, we thoroughly investigate how the vacuum fluctuations of the Higgs field affect the stability of the electroweak vacuum in Friedmann-Lemaitre-Robertson-Walker (FLRW) background. Adopting adiabatic (WKB) approximation or adiabatic regularization methods, we clearly show that vacuum fluctuations of the Higgs field in the FLRW background depend on the curvature and also masses of the Higgs or other scalar fields. The Higgs …
The current central experimental values of the parameters of the Standard Model give rise to a striking conclusion: metastability of the electroweak vacuum is favoured over absolute stability. A metastable vacuum for the Higgs boson implies that it is possible, and in fact inevitable, that a vacuum decay takes place with catastrophic consequences for the Universe. The metastability of the Higgs vacuum is especially significant for cosmology, because there are many mechanisms that could have triggered the decay of the electroweak vacuum in the early Universe. We present a comprehensive review o…
We reconsider gravitational corrections to vacuum decay, confirming and simplifying earlier results and extending them by allowing for a non-minimal coupling of the Higgs to gravity. We find that leading-order gravitational corrections suppress the vacuum decay rate. Furthermore, we compute minor corrections to thermal vacuum decay in the SM by adding one-loop contributions to the Higgs kinetic term, two-loop contributions to the Higgs potential and allowing for time-dependent bounces.
We examine the effect of large extra dimensions on black hole seeded vacuum decay using the Randall-Sundrum model as a prototype for warped extra dimensions. We model the braneworld black hole by a tidal solution, and solve the Higgs equations of motion for the instanton on the brane. Remarkably, the action of the static instanton can be shown to be the difference in the bulk areas of the seed and remnant black holes, and we estimate these areas assuming the black holes are small compared to the bulk AdS radius. Comparing to the Hawking evaporation rate shows that small black hole seeds prefer…
We discuss the effect of gravitational interactions on the lifetime of the Higgs vacuum where generic quantum gravity corrections are taken into account. We show how small black holes can act as seeds for vacuum decay, spontaneously nucleating a new Higgs phase centered on the black hole with a lifetime measured in millions of Planck times rather than billions of years. The constraints on parameter space of corrections to the Higgs potential are outlined, and implications for collider black holes discussed.
The possible violation of the conventional lower Higgs mass stability bound by the discovered Higgs boson has far reaching consequences within particle physics and cosmology. We discuss the possibility that nonpolynomial bare interactions seeded at some high-momentum scale can considerably diminish the lower Higgs mass bound without introducing a metastability in the Higgs effective potential. For this, we classify various deformations of the usual quartic bare potential regarding their impact on stable IR physics. We perform the analysis in a large $N_{\mathrm{f}}$ expansion, addressing the c…
We show that for the simplest models of gauge mediated supersymmetry breaking, including all existing models, the true vacuum will not preserve QCD if it communicates supersymmetry breaking to the visible sector. We show that the desired supersymmetry breaking color preserving vacuum can nonetheless be stable cosmologically, but only if certain couplings are sufficiently small. We also present simple modifications to the sector which communicates supersymmetry breaking in which the true vacuum is acceptable, suggesting desirable properties to be sought in dynamical models of supersymmetry brea…
In the present paper we develop the self-consistent $Spin(4,4)$-invariant model of the unification of gravity with weak $SU(2)$ interactions in the assumption of the existence of visible and invisible sectors of the Universe. It was shown that the consequences of the multiple point principle predicting two degenerate vacua in the Standard Model (SM) suggest a theory of Inflation, in which the inflaton field $σ$ starts trapped in a cold coherent state in the "false vacuum" of the Universe at the value of the Higgs field's VEV $v\sim 10^{18}$ GeV (in the visible world). Then the inflations of th…
We study the inflationary evolution of a scalar field $h$ with an unstable potential for the case where the Hubble parameter $H$ during inflation is larger than the instability scale $Λ_I$ of the potential. Quantum fluctuations in the field of size $δh \sim \frac{H}{2 π}$ imply that the unstable part of the potential is sampled during inflation. We investigate the evolution of these fluctuations to the unstable regime, and in particular whether they generate cosmological defects or even terminate inflation. We apply the results of a toy scalar model to the case of the Standard Model (SM) Higgs…
In this paper, we discuss the vacuum structure of the gauge-Higgs unification theory, which is one of the attractive candidates of physics beyond the standard model. This scenario has a remarkable feature, namely it has infinitely degenerate vacua due to the characteristic periodic potential of the Higgs filed, to be identified with the extra space component of the higher dimensional gauge field. We address a question, whether to form the superposition of such degenerate vacua, like the $θ$-vacuum in QCD, is necessary or not, in order to realize the true vacuum state of the theory. We derive g…
The Standard Model Higgs potential becomes unstable at large field values. After clarifying the issue of gauge dependence of the effective potential, we study the cosmological evolution of the Higgs field in presence of this instability throughout inflation, reheating and the present epoch. We conclude that anti-de Sitter patches in which the Higgs field lies at its true vacuum are lethal for our universe. From this result, we derive upper bounds on the Hubble constant during inflation, which depend on the reheating temperature and on the Higgs coupling to the scalar curvature or to the inflat…
In this paper, we discuss the Higgs vacuum stability around evaporating black holes. We provide a new approach to investigate the false vacuum decay around the black hole and clearly show how vacuum fluctuations of the Higgs induce a gravitational collapse of the vacuum. Furthermore, we point out that the backreaction of the Hawking radiation can not be ignored and the gravitational vacuum decay is exponentially suppressed. However, a large number of the evaporating (or evaporated) primordial black holes threaten the existence of the Universe and we obtain a new upper bound on the evaporating …
For the current central values of the Higgs and top masses, the Standard Model Higgs potential develops an instability at a scale of the order of $10^{11}$ GeV. We show that a cosmological signature of such instability could be dark matter in the form of primordial black holes seeded by Higgs fluctuations during inflation. The existence of dark matter might not require physics beyond the Standard Model.
We have recently suggested that tiny black holes can act as nucleation seeds for the decay of the metastable Higgs vacuum. Previous results applied only to the nucleation of thin-wall bubbles, and covered a very small region of parameter space. This paper considers bubbles of arbitrary profile and reaches the same conclusion: black holes seed rapid vacuum decay. Seeded and unseeded nucleation rates are compared, and the gravitational back reaction of the bubbles is taken into account. The evolution of the bubble interior is described for the unseeded nucleation. Results are presented for the r…
We develop the formalism for computing gravitational corrections to vacuum decay from de Sitter space as a sub-Planckian perturbative expansion. Non-minimal coupling to gravity can be encoded in an effective potential. The Coleman bounce continuously deforms into the Hawking-Moss bounce, until they coincide for a critical value of the Hubble constant. As an application, we reconsider the decay of the electroweak Higgs vacuum during inflation. Our vacuum decay computation reproduces and improves bounds on the maximal inflationary Hubble scale previously computed through statistical techniques.
Using a physical renormalisation scheme we derive mass-dependent renormalisation group equations for the running of the Higgs quartic coupling within the Standard Model. Subsequently, we accurately take into account weak scale thresholds, resulting in a reduction of the error in the determination of the maximum $M_t$ required for absolute stability of the vacuum to 0.28 GeV. For the first time, we conclusively establish the fate of the electroweak vacuum, finding that absolute stability of the Higgs vacuum state is excluded at 99.98% C.L. We also discuss the consequences when this new result i…
So far, the experiments at the Large Hadron Collider (LHC) have shown no sign of new physics beyond the Standard Model. Assuming the Standard Model is correct at presently available energies, we can accurately extrapolate the theory to higher energies in order to verify its validity. Here we report the results of new high precision calculations which show that absolute stability of the Higgs vacuum state is now excluded. Combining these new results with the recent observation of primordial gravitational waves by the BICEP Collaboration, we find that the Higgs vacuum state would have quickly de…
In this work, we investigated the electroweak vacuum instability during or after inflation. In the inflationary Universe, i.e., de Sitter space, the vacuum field fluctuations $\left< {δϕ}^{ 2 } \right>$ enlarge in proportion to the Hubble scale $H^{2}$. Therefore, the large inflationary vacuum fluctuations of the Higgs field $\left< {δϕ}^{ 2 } \right>$ are potentially catastrophic to trigger the vacuum transition to the negative-energy Planck-scale vacuum state and cause an immediate collapse of the Universe. However, the vacuum field fluctuations $\left< {δϕ}^{ 2 } \right>$, i.e., the vacuum …
The measured values of the Standard Model (SM) parameters favors a shallow metastable electroweak (EW) vacuum surrounded by a deep global AdS or a runaway Minkowski minimum. Furthermore, fine-tuning is the only explanation for the Higgs relaxing in its present local minimum. In this paper, assuming no new physics beyond the SM, we study the universal effect of gravity on the Higgs dynamics in the early universe. A generic two-parameter model is considered in which the Higgs is non-minimally coupled to a higher-curvature theory of gravity. The coupling between the Higgs field and the Weyl field…
Stability of the Higgs vacuum during early universe inflation is dependent on how the Higgs couples to the spacetime curvature. Limits on the curvature coupling parameter at the electroweak scale $ξ_{EW}$ are shown to be consistent only when quantum gravity effects are included and a covariant quantisation procedure, such as Vilkovisky-DeWitt, is adopted. Stability requires $ξ_{EW}>-0.03$ for a top quark mass $M_t=173.34\,{\rm GeV}$.
The recently suggested Festina-Lente (FL) bound provides a lower bound on the masses of ${\rm U(1)}$ charged particles in terms of the positive vacuum energy. Since the charged particle masses in the Standard Model (SM) are generated by the Higgs mechanism, the FL bound provides a testbed of consistent Higgs potentials in the current dark energy-dominated universe as well as during inflation. We study the implications of the FL bound on the UV behavior of the Higgs potential for a miniscule vacuum energy, as in the current universe. We also present values of the Hubble parameter and the Higgs …
We consider an ultra-light scalar coupled to the Higgs in the presence of heavier new physics. In the electroweak broken phase the Higgs gives a tree-level contribution to the light-scalar potential, while new physics contributes at loop level. Thereby, the theory has a cosmologically meta-stable phase where the light scalar is around the top of its potential, and the Higgs is a loop factor lighter than new physics. Such regions with precarious naturalness are anthropically and environmentally selected, as regions with heavier Higgs crunch quickly. We expect observable effects of rolling in th…
The Standard Model Higgs potential becomes unstable at large Higgs field values where its quartic coupling becomes negative. While the tunneling lifetime of our current electroweak vacuum is comfortably longer than the age of the universe, quantum fluctuations during inflation might push the Higgs over the barrier, forming patches which might be lethal for our universe. We study the cosmological evolution of such regions and find that, at least in the thin wall approximation, they may be harmless as they collapse due to the backreaction of the Higgs itself. The presence of the Standard Model H…
We give a description of open strings stretched between N parallel D-branes in VSFT. We show how higgsing is generated as the branes are displaced: the shift in the mass formula for on-shell states stretched between different branes is due to a twist anomaly, a contribution localized at the midpoint.
Standard Model Higgs Peaks: a Note on the Vacuum Instability during Inflation
Università degli Studi di Padova（帕多瓦大学）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；National Technical University of Athens（雅典国立技术大学）；Université de Genève（日内瓦大学）
The abundance of the QCD axion is known to be suppressed if the Hubble parameter during inflation, $H_{\rm inf}$, is lower than the QCD scale, and if the inflation lasts sufficiently long. We show that the tight upper bound on the inflation scale can be significantly relaxed if the eternal old inflation is driven by the standard-model Higgs field trapped in a false vacuum at large field values. Specifically, $H_{\rm inf}$ can be larger than $100\,$GeV if the false vacuum is located above the intermediate scale. We also discuss the slow-roll inflation after the tunneling from the false vacuum t…
We argue that $(0,1)$ heterotic string models with 4 non-heterotic spacetime dimensions may provide an instability of the vacuum to gravitational polarization in globally strong gravitational fields. This instability would be triggered during gravitational collapse by a non-local quantum switching process, and lead to the formation of regions of a high temperature broken symmetry phase which would be the equivalent in these string models of conventional black holes.
We have recently proposed the idea that dark matter in our universe is formed by primordial black holes generated by Standard Model Higgs fluctuations during inflation and thanks to the fact that the Standard Model Higgs potential develops an instability at a scale of the order of $10^{11}$ GeV. In this sense, dark matter does not need any physics beyond the Standard Model, although the mechanism needs fine-tuning to avoid the overshooting of the Higgs into the dangerous AdS vacuum. We show how such fine-tuning can be naturally avoided by coupling the Higgs to a very heavy scalar with mass $\g…
The running of the Higgs self coupling may lead to numerous phenomena in early universe cosmology. In this paper we introduce a scenario where the Higgs running induces turns in the trajectory passing a region with tachyonic mass, leading to a temporal tachyonic growth in the curvature power spectrum. This effect induced by the Higgs leaves phenomena in the form of primordial black holes and stochastic gravitational waves, where proposed GW observatories will be able to probe in the near future.
The measured (central) values of the Higgs and top quark masses indicate that the Standard Model (SM) effective potential develops an instability at high field values. The scale of this instability, determined as the Higgs field value at which the potential drops below the electroweak minimum, is about $10^{11}$ GeV. However, such a scale is unphysical as it is not gauge-invariant and suffers from a gauge-fixing uncertainty of up to two orders of magnitude. Subjecting our system, the SM, to several probes of the instability (adding higher order operators to the potential; letting the vacuum de…
Based on the current experimental data, the Standard Model predicts that the current vacuum state of the Universe is metastable, leading to a non-zero rate of vacuum decay through nucleation of bubbles of true vacuum. Our existence implies that there cannot have been any such bubble nucleation events anywhere in our whole past lightcone. We consider a minimal scenario of the Standard Model together with Starobinsky inflation, using three-loop renormalization group improved Higgs effective potential with one-loop curvature corrections. We show that the survival of the vacuum state through infla…
We consider the noncommutative Abelian-Higgs theory and construct new types of exact multi-vortex solutions that solve the static equations of motion. They in general do not follow from the BPS equations; only for some specific values of parameters, they satisfy the BPS equations saturating the Bogomol'nyi bound. We further consider the Abelian-Higgs theory with more complicated scalar potential allowing unstable minima and construct exact solutions of noncommutative false vacuum bubble with integer magnetic flux. The classical stability of the solutions is discussed.
The measurements of the Higgs mass and top Yukawa coupling indicate that we live in a very special Universe, at the edge of the absolute stability of the electroweak vacuum. If fully stable, the Standard Model (SM) can be extended all the way up to the inflationary scale and the Higgs field, non-minimally coupled to gravity with strength $ξ$, can be responsible for inflation. We show that the successful Higgs inflation scenario can also take place if the SM vacuum is not absolutely stable. This conclusion is based on two effects that were overlooked previously. The first one is associated with…
We find the critical charge for a topologically massive gauge theory for any gauge group, generalising our earlier result for SU(2). The relation between critical charges in TMGT, singular vectors in the WZNW model and logarithmic CFT is investigated.
A Higgs description for the QCD vacuum in the limit of two quark flavors is proposed. Complete ``spontaneous breaking'' of color symmetry is realized by condensation of an adjoint quark-antiquark and a quark-quark pair. The vacuum is invariant under isospin symmetry applying color and flavor transformations simultaneously. All elementary excitations acquire integral charges. The dressed microscopic quark and gluon degrees of freedom can be identified with the macroscopic baryon and vector meson degrees of freedom. In addition to the nucleons we find soliton--type fermions with integer isospin.…
In the absence of new physics around $10^{10}$ GeV, the electroweak vacuum is at best metastable. This represents a major challenge for high scale inflationary models as, during the early rapid expansion of the universe, it seems difficult to understand how the Higgs vacuum would not decay to the true lower vacuum of the theory with catastrophic consequences if inflation took place at a scale above $10^{10}$ GeV. In this paper we show that the non-minimal coupling of the Higgs boson to curvature could solve this problem by generating a direct coupling of the Higgs boson to the inflationary pot…
We numerically study string production by evolving classical Abelian-Higgs gauge field wavepackets. Initial conditions are constructed for the propagation of a single wavepacket and for the collision of two wavepackets. We identify regions of parameter space that lead to prompt production of strings from a single wavepacket. The collision of two sub-critical wavepackets can also lead to the production of strings in certain regions of parameter space.
Recent analysis shows that if the 125-126 GeV LHC resonance turns out to be the Standard Model Higgs boson, the electroweak vacuum would be a metastable state at 98% C.L. In this paper we argue that, during inflation, the electroweak vacuum can actually be very short-lived, contrary to the conclusion that follows from the flat spacetime analysis. Namely, in the case of a pure Higgs potential the electroweak vacuum decays via the Hawking-Moss transition, which has no flat spacetime analogue. As a result, the Higgs vacuum is unstable, unless the rate of inflation is low enough: $H_{\rm inf}\less…
The vacuum diagram is calculated at second order for theories with self-interacting massless fields in the framework of finite causal perturbation theory. It is pointed out that the infrared behaviour of the vacuum diagram leads to unstable Fock vacua for QCD or massless QED, but not for quantum gravity. Therefore a radical rearrangement of the physical system must take place for such theories. Conversely, stability of the Fock vacuum for massless interacting fields is another hint at the possibility that quantum gravity should be treated as an effective theory.
The spacetime dependent lagrangian formalism of references [1-2] is used to obtain a classical solution of Yang-Mills theory. This is then used to obtain an estimate of the vacuum expectation value of the Higgs field, viz. $ϕ_{a}=A/e$, where $A$ is a constant and $e$ is the Yang-Mills coupling (related to the usual electric charge). The solution can also accommodate non-commuting coordinates on the boundary of the theory which may be used to construct D-brane actions. PACS:11.15.-q ; 11.27+d ; 11.10.Ef
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,…
We derive lower bounds for the Higgs-curvature coupling from vacuum stability during inflation in three inflationary models: quadratic and quartic chaotic inflation, and Starobinsky-like power-law inflation. In contrast to most previous studies we take the time-dependence of the Hubble rate into account both in the geometry of our past light-cone and in the Higgs effective potential, which is approximated with three-loop renormalisation group improvement supplemented with one-loop curvature corrections. We find that in all three models, the lower bound is $ξ\gtrsim 0.051\ldots 0.066$ depending…
We investigate the vacuum instability in the presence of dilaton field in a holographic set up. Although the dilaton is a bulk field, it leads to the vacuum instability on the boundary. We show that the whole process crucially depends on the probe brane position and as well on the radial coordinate. So that the effects of dilaton scale parameter in different regions of the bulk or for different probe brane positions are different. We also observe that in our study the temperature can strengthen the effect of scale parameter in reducing the potential barrier. Finally, we show that this Schwinge…
