Properties of the electroweak vacuum versus the QCD-vacuum in strong magnetic fields
Jos Van Doorsselaere
备注：
8 pages, 4 figures, Talk given at the International Workshop on QCD Green's Functions, Confinement and Phenomenology, 5-9 September 2011, Trento, Italy
In strongly magnetized backgrounds, electrically charged vector bosons can condense. When considering the rho-meson sector of QCD, this results in the existence of a superconducting state with Abrikosov vortices. As a next order effect, also the neutral mesons condense and one expects the resulting lattice to be a mix of neutral and charged condensates, opening a possibility to the existence of a superfluid property. We will show how the detailed structure of the vacuum can be calculated and which implications it has on the nature of the exotic superconducting state.
We show that, for all values of $Tan β$ and the light right-handed stop mass for which the electroweak phase transition is strong enough to avoid washout following electroweak baryogenesis, the electroweak vacuum is stable over the lifetime of the observed Universe. Cosmological stability of the electroweak vacuum is violated only if the light right-handed stop is lighter than 100-115GeV.
We make a change of variable in the standard model Higgs field by a fermion operator and show that the latter is responsible for the electroweak vacuum. By computing the vacuum expectation value of this fermion operator in the path integral formalism we determine a relation among the quark vacuum condensates, the quark masses and the intrinsic scale of the theory. We show that the heavy quark vacuum condensates do not justify the hypothesis of dynamical electroweak symmetry breaking with only standard model fermions.
We reveal a new source of CP-violation in the electroweak sector that is free of any experimental bounds, and we highlight the possible implications for baryogenesis.
Two different two-loop relations between the pole- and the MS-mass of the top quark have been derived in the literature which were based on different treatments of the tadpole diagrams. In addition, the limit M_W^2/m_t^2 \to 0 was employed in one of the calculations. It is shown that, after appropriate transformations, the results of the two calculations are in perfect agreement. Furthermore we demonstrate that the inclusion of the non-vanishing mass of the W-boson leads to small modifications only.
In the Standard Model (SM), the Higgs mass around 125 GeV implies that the electroweak vacuum is metastable since the quartic Higgs coupling turns negative at high energies. I point out that a tiny mixing of the Higgs with a heavy singlet can make the electroweak vacuum completely stable. This is due to a tree level correction to the Higgs mass-coupling relation, which survives in the zero-mixing/heavy-singlet limit. Such a situation is experimentally indistinguishable from the SM, unless the Higgs self-coupling can be measured. As a result, Higgs inflation and its variants can still be viable…
We use the two loop effective potential to study the first order electroweak phase transition in the minimial supersymmetric standard model. A global search of the parameter space is made to identify parameters compatible with electroweak baryogenesis. We improve on previous such studies by fully incorporating squark and Higgs boson mixing, by using the latest experimental constraints, and by computing the latent heat and the sphaleron rate. We find the constraints tan beta > 2.1, top squark mass < 172 GeV, and Higgs mass < 107 GeV (becoming more or less restrictive if the heavy stop has mass …
We extend the so-called singlet doublet dark matter model, where the dark matter is an admixture of a Standard Model singlet and a pair of electroweak doublet fermions, by a singlet scalar field. The new portal coupling of it with the dark sector not only contributes to the dark matter phenomenology (involving relic density and direct detection limits), but also becomes important for generation of dark matter mass through its vacuum expectation value. While the presence of dark sector fermions affects the stability of the electroweak vacuum adversely, we find this additional singlet is capable…
Whether the Standard Model electroweak vacuum is stable, metastable or unstable depends crucially on the top mass (and, to a lesser extent, on other measurable quantities). These topics are reviewed and updated by taking into account the most recent determination of the top and Higgs masses. Moreover, the correction to the vacuum decay due to Einstein gravity is described. This process is also discussed in a scenario, called softened gravity, which has been proposed as a solution of the Higgs mass hierarchy problem.
We analyse effective potential around the electroweak (EW) scale in the Standard Model extended with a heavy scalar doublet. We show that the additional scalars can have a strong impact on vacuum stability. Although the additional heavy scalars may improve the behaviour of running Higgs self-coupling at large field values, we prove that they can destabilise the vacuum due to EW-scale effects. A new EW symmetry conserving minimum of the effective potential can appear rendering the electroweak symmetry breaking minimum meta- or unstable. However, for the case of the inert doublet model (IDM) wit…
In models of dynamical electroweak symmetry breaking which sensitively involve the third generation, such as top quark condensation, the effects of the new dynamics can show up experimentally in Z->b\bar{b}. We compare the sensitivity of Z->b\bar{b} and top quark production at the Tevatron to models of the new physics. Z->b\bar{b} is a relatively more sensitive probe to new strongly coupled U(1) gauge bosons, while it is generally less sensitive a probe to new physics involving color octet gauge bosons as is top quark production itself. Nonetheless, to accomodate a significant excess in Z->b\b…
We investigate the electroweak vacuum stability in an extended version of the Standard Model which incorporates two additional singlet scalar fields and three right handed neutrinos. One of these extra scalars plays the role of dark matter while the other scalar not only helps in making the electroweak vacuum stable but also opens up the low mass window of the scalar singlet dark matter (< 500 GeV). We consider the effect of large neutrino Yukawa coupling on the running of Higgs quartic coupling. We have analyzed the constraints on the model and identify the range of parameter space which is c…
A composite Higgs boson of 125 GeV mass, only mildly fine-tuned, requires top partners with a semi-perturbative coupling and a mass not greater than about a TeV. We analyze the strong constraints on such picture arising from flavour and electroweak precision tests in models of partial compositeness. We consider different representations for the composite fermions and compare the case of an anarchic flavour structure to models with a U(3)^3 and U(2)^3 flavour symmetry. Although non trivially, some models emerge that look capable of accommodating a 125 GeV Higgs boson with top partners in an int…
In this paper we investigate the consequences of imposing an SO(4) symmetry both on the scalar field and on spacetime prior to any spontaneous symmetry breakdown in the electroweak model. First we argue that the local electroweak gauge symmetry is implied by the initial SO(4) symmetry of the scalar field. Then we parameterize the vacuum, in a slightly different way with respect to the conventional assignment in the electroweak model, around the ground state mainly in two different ways: Once over the local electroweak gauge transformations and once over the local $γ$ basis which generates the …
We have calculated the fermion contributions to the shift of the position of the poles of the massive gauge boson propagators at two-loop order in the Standard Model. Together with the bosonic contributions calculated previously the full two-loop corrections are available. This allows us to investigate the full correction in the relationship between MS and pole masses of the vector bosons Z and W. Two-loop renormalization and the corresponding renormalization group equations are discussed. Analytical results for the master-integrals appearing in the massless fermion contributions are given. A …
We study Coleman-De Luccia tunneling of the Standard Model Higgs field during inflation in the case when the electroweak vacuum is metastable. We verify that the tunneling rate is exponentially suppressed. The main contribution to the suppression is the same as in flat space-time. We analytically estimate the corrections due to the expansion of the universe and an effective mass term in the Higgs potential that can be present at inflation.
We consider singlet extensions of the standard model, both in the fermion and the scalar sector, to account for the generation of neutrino mass at the TeV scale and the existence of dark matter respectively. For the neutrino sector we consider models with extra singlet fermions which can generate neutrino mass via the so called inverse or linear seesaw mechanism whereas a singlet scalar is introduced as the candidate for dark matter. We show that although these two sectors are disconnected at low energy, the coupling constants of both the sectors get correlated at high energy scale by the cons…
We investigate the effect of fermionic electroweak multiplet dark matter models on the stability of the electroweak vacuum using two-loop renormalization group equations (RGEs) and one-loop matching conditions. Such a treatment is crucial to obtain reliable conclusions, compared with one-loop RGEs and tree-level matching conditions. In addition, we find that the requirement of perturbativity up to the Planck scale would give strong and almost mass-independent constraints on the Yukawa couplings in the dark sector. We also evaluate these models via the idea of finite naturalness for the Higgs m…
We examine the gauge dependence of lower bounds on the Higgs mass obtained from the requirement that the electroweak vacuum be the global minimum of the effective potential. We study a simple model, the spontaneously-broken Abelian Higgs model coupled to a chiral quark doublet in a two-parameter gauge and demonstrate that the lower bounds on the Higgs mass obtained in this model are dependent on the choice of gauge parameters. We discuss the significance of this result for calculations in the Standard Model.
Within the Standard Model, the current Higgs and top quark data favor metastability of the electroweak vacuum, although the uncertainties are still significant. The true vacuum is many orders of magnitude deeper than ours and the barrier separating the two is tiny compared to the depth of the well. This raises a cosmological question: how did the Higgs field get trapped in the shallow minimum and why did it stay there during inflation? The Higgs initial conditions before inflation must be fine--tuned to about one part in 10^8 in order for the Higgs field to end up in the right vacuum. In this …
The complex field $Φ$ containing the QCD axion has a natural portal coupling to the Higgs doublet of the form $λ_{h ϕ}|Φ|^2 |H|^2$. Here we consider the possibility that $λ_{h ϕ}$ has a natural magnitude for a dimensionless coupling, $λ_{h ϕ} \sim 0.1-1$. This is possible if the total mass squared parameter of the Higgs in the vacuum, including quadratic divergent and the $Φ$ vacuum expectation value contributions, is renormalized to reproduce the observed Higgs boson mass. It is then possible for the axion sector to stabilize the electroweak vacuum. We show the requirement of electroweak vacu…
The existence of a second Higgs doublet in Nature could lead to a cosmological first order electroweak phase transition and explain the origin of the matter-antimatter asymmetry in the Universe. We explore the parameter space of such a two-Higgs-doublet-model and show that a first order electroweak phase transition strongly correlates with a significant uplifting of the Higgs vacuum w.r.t. its Standard Model value. We then obtain the spectrum and properties of the new scalars $H_0$, $A_0$ and $H^{\pm}$ that signal such a phase transition, showing that the decay $A_0 \rightarrow H_0 Z$ at the L…
To avoid possible electroweak vacuum instability in the vector-like fermion model, we introduce a new singlet scalar to the model, which couples to the vector-like fermion, and also mixes with the Higgs boson after spontaneous symmetry breaking. We investigate the vector-like fermion predominantly coupled to the third generation quarks, and its mass is generated from the vacuum expectation value of the new scalar field in the model. In this setup, as running towards high energies, the new scalar provides positive contribution to the running of the higgs quartic coupling, and the matching on th…
We derive the QCD corrections to the electroweak gauge bosons vacuum polarization functions at high and zero--momentum transfer in the case of arbitrary internal quark masses. We then discuss in this general case (i) the connection between the $O(αα_S)$ calculations of the vector bosons self--energies using dimensional regularization and the one performed via a dispersive approach and (ii) the QCD corrections to the $ρ$ parameter for a heavy quark isodoublet.
We propose a modification to the standard hybrid inflation model \cite{Linde:1993cn}, that connects a successful hybrid inflation scenario to the standard model Higgs sector, via the electroweak vacuum stability. The proposed model results in an effective inflation potential of a hilltop-type, with both the trans-Planckian and sub-Planckian inflation regimes consistent with the recent Planck/BICEP combined results. Reheating via the inflation sector decays to right-handed neutrinos is considered. An upper bound on the reheating temperature $T_{\rm R} \lsim 2\times 10^{11}~(1\times 10^{13})$ Ge…
Recently, both ATLAS and CMS collaborations at the CERN Large Hadron Collider (LHC) have announced their observations of an excess of diphoton events around the invariant mass of $750~{\rm GeV}$ with a local significance of $3.6σ$ and $2.6σ$, respectively. In this paper, we interpret the diphoton excess as the on-shell production of a real singlet scalar in the $pp \to S \to γγ$ channel. To accommodate the observed production rate, we further introduce a vector-like fermion $F$, which is carrying both color and electric charges. The viable regions of model parameters are explored for this simp…
We perform a precise calculation of the decay rate of the electroweak vacuum in the standard model as well as in models beyond the standard model. We use a recently-developed technique to calculate the decay rate of a false vacuum, which provides a gauge invariant calculation of the decay rate at the one-loop level. We give a prescription to take into account the zero modes in association with translational, dilatational, and gauge symmetries. We calculate the decay rate per unit volume, $γ$, by using an analytic formula. The decay rate of the electroweak vacuum in the standard model is estima…
We explore the connection between tree-level Dirac neutrino masses and axion physics in a scenario where the PQ symmetry enforces lepton number conservation perturbatively. Requiring that the PQ scale $f_a$ is the only heavy scale to play a role in neutrino mass generation, we are led to the construction of a KSVZ-type model where Dirac neutrino masses are inversely proportional to $f_a$, provided a real scalar triplet (zero hypercharge) is added to the SM scalar sector. We analyse this extended scalar sector, focusing on the stabilisation of the electroweak vacuum. The contribution of the tri…
We study the stability of neutral electroweak vacua in two Higgs doublet models, and calculate the lifetime of these states when the parameters are such that they are false vacua. As the two Higgs doublet model is invariant under a sign change of both doublets, degenerate true vacua exist. It is shown that this degeneracy, despite the fact that each of these minima locally describes the same physics, can immensely affect their lifetime. We apply these calculations to the parameter space of the models which is allowed by recent LHC searches, and infer combinations of parameters which should be …
There is a newly emerging tension between determinations of $V_{us}$ from different sources (known as the Cabibbo anomaly), which is clearly demonstrated by the new $R(V_{us})$ observable. We explore this observable from the perspective of the Standard Model Effective Field Theory and show there is a discrepancy between $R(V_{us})$ and existing electroweak precision observables (EWPO) in a simple single operator dominated scenario. We explore all possible single particle extensions of the Standard Model that can generate the Cabibbo anomaly effect and show how they cannot reconcile the current…
We demonstrate that the dispersive computation of the threshold enhancements to heavy quark vacuum polarizations is unstable. Because of the slow convergence of the dispersion relations the result critically depends on the intermediate energy region where the non-relativistic approximation, intrinsic to threshold calculations, is invalid. We discuss other ambiguities precluding a reliable calculation of the threshold contribution to the vacuum polarizations. In the absence of a solution prudence should force one to assign an error to the radiative corrections not far below the level of the per…
[Talk presented at the International Seminar Quarks `92, Zvenigorod, Russia, May 11-17, 1992.] The electroweak vacuum need not be absolutely stable. For certain top and Higgs masses in the Minimal Standard Model, it is instead metastable with a lifetime exceeding the present age of the Universe. The decay of our vacuum may be nucleated at low temperature by quantum tunneling or at high temperature in the early Universe by thermal excitation. I briefly review the constraints on top and Higgs masses from requiring that the electroweak vacuum be sufficiently stable to have survived to the present…
We study a scalar singlet dark matter (DM) having mass in sub-TeV regime by extending the minimal scalar singlet DM setup by additional vector like fermions. While the minimal scalar singlet DM satisfies the relic and direct detection constraints for mass beyond TeV only, presence of its portal coupling with vector like fermions opens up additional co-annihilation channels. These vector like fermions also help in achieving electroweak vacuum stability all the way up to Planck scale. We find that for one generation of vector like quarks consisting of a $SU(2)_L$ doublet and a singlet, scalar si…
Formation of a vacuum like domain of the strong-interaction chiral condensate misaligned with respect to the electroweak symmetry breaking arguably modifies the mass spectrum of electroweak gauge bosons and their interactions in that domain in an observable manner. In particular,photon acquires the mass $m_γ\sim{1/2}f_π\sin2θ_{W}$.
A two-component scalar DM scenario comprising an additional scalar doublet and a $Y$ = 0 scalar triplet is proposed. Key features of the ensuing dark matter phenomenology are highlighted with emphasis on inter-conversion between the two dark matter components. For suitable choices of the model parameters, we show that such inter-conversion can explain the observed relic abundance when the doublet dark matter component has mass in the \emph{desert} region while the triplet component has sub-TeV mass. This finding is important in the context of such mass regions known to predict under-abundant r…
We study the minimal type-III seesaw model in which we extend the SM by adding two $SU(2)_L$ triplet fermions with zero hypercharge to explain the origin of the non-zero neutrino masses. We show that the naturalness conditions and the limits from lepton flavor violating decays provide very stringent bounds on the model parameters along with the constraints from the stability/metastability of the electroweak vacuum. We perform a detailed analysis of the model parameter space including all the constraints for both normal as well as inverted hierarchies of the light neutrino masses. We find that …
Electroweak vacuum transition processes (sphalerons) in the early Universe provide a possible explanation of the baryon asymmetry. Combining this physics with the anomalous commutators of Adler and Boulware and renormalization group invariance, we argue that electroweak baryon number violation also induces a ``topological condensate'' in the vacuum. QCD sphaleron processes act to distribute the baryon number violation between both left and right handed quarks and induce a spin independent component in this ``condensate''.
We study the stability of the electroweak vacuum in low-scale inflation models whose Hubble parameter is much smaller than the instability scale of the Higgs potential. In general, couplings between the inflaton and Higgs are present, and hence we study effects of these couplings during and after inflation. We derive constraints on the couplings between the inflaton and Higgs by requiring that they do not lead to catastrophic electroweak vacuum decay, in particular, via resonant production of the Higgs particles.
We propose a two component dark matter set-up by extending the Standard Model with a singlet and a hypercharge-less triplet scalars, each of them being odd under different $Z_2$ symmetries. We observe that the inter-conversion between the two dark matter components allow a viable parameter space where masses of both the dark matter candidates can be below TeV, even though their individual contribution to single component dark matter rules out any such sub-TeV dark matter. We find that a lighter mass of the neutral component of the scalar triplet, playing the role of one dark matter component, …
The inert scalar doublet model of dark matter can be valid up to the Planck scale. We briefly review the bounds on the model in such a scenario and identify parameter spaces that lead to absolute stability and metastability of the electroweak vacuum.
We study the electroweak vacuum stability in Type I seesaw models for 3 generations of neutrinos in scenarios where the right-handed neutrinos have explicit bare mass terms in the Lagrangian and where these are dynamically generated through the mechanism of spontaneous symmetry breaking. To best highlight the difference of the two cases we concentrate on the absolute stability of the scalar potential. We observe that for the first scenario, the scale at which the scalar potential becomes unstable is lower from that within the Standard Model. In addition the Yukawa couplings $\mathbf{Y}_ν$ are …
We discuss properties of the electroweak vacuum as a function of an external magnetic field. The interest in these properties arises due to possible existence of the electromagnetically superconducting phase of QCD in the background of a sufficiently strong magnetic field. In the electroweak theory, a superconducting vacuum exists for a well defined range of magnetic background fields, and the interest of the current paper is the behaviour near the upper critical magnetic field. We determine this critical field and calculate the vacuum condensates to leading order.
Vacuum stability in the Standard Model is problematic as the Higgs quartic self-coupling runs negative at a renormalization scale of about $10^{10}$ GeV. We consider a non-supersymmetric SO(10) grand unification model for which gauge coupling unification is made possible through an intermediate scale gauge group, $G_{\text{int}}=\text{SU}(3)_C\otimes \text{SU}(2)_L\otimes \text{SU}(2)_R \otimes \text{U}(1)_{B-L}$. $G_{\text{int}}$ is broken by the vacuum expectation value of a 126 of SO(10) which not only provides for neutrino masses through the seesaw mechanism but also preserves a discrete $…
We study several aspects of electroweak vacuum metastability when an extra gauge singlet scalar, a viable candidate for a dark matter particle, is added to the standard model of particle physics, which is assumed to be valid up to the Planck scale. Phase diagrams are drawn for different parameter spaces, and based on that, we graphically demonstrate how the confidence level, at which stability of electroweak vacuum is excluded, depends on such new physics parameters.
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 presence of right-handed neutrinos in the type I seesaw mechanism may lead to significant corrections to the RG evolution of the Higgs self-coupling. Compared to the Standard Model case, the Higgs mass window can become narrower, and the cutoff scale become lower. Naively, these effects decrease with decreasing right-handed neutrino mass. However, we point out that the unknown Dirac Yukawa matrix may impact the vacuum stability constraints even in the low scale seesaw case not far away from the electroweak scale, hence much below the canonical seesaw scale of 10^15 GeV. This includes situa…
The recent precise measurement of the $W$-mass by the CDF II collaboration is indicative of new physics beyond the Standard Model. On the other hand, a resolution of the longstanding muon $g-2$ anomaly also calls for additional dynamics. In this work, we accommodate the two aforementioned anomalies in an extension of the minimal Type-II seesaw model. That is, the minimal Type-II model is augmented with an additional doubly charged scalar and vector leptons. While a chirality-flip of the vector leptons can predict the observed value of muon $g-2$, the value of the recently reported $W$-mass can…
We investigate if the topology of pure gauge fields in the electroweak vacuum can play a role in classical dynamics at the electroweak phase transition. Our numerical analysis shows that magnetic fields are produced if the initial vacuum has non-trivial Chern-Simons number, and the fields are helical if the Chern-Simons number changes during the phase transition.
We briefly review a recently proposed scheme for a gauge-invariant treatment of tadpole corrections in spontaneously broken gauge theories called Gauge-Invariant Vacuum expectation value Scheme (GIVS). The tadpole scheme matters in higher-order predictions of observables if not all free parameters are fixed by renormalization conditions based on S-matrix elements, such as in MSbar renormalization. In contrast to previously used tadpole schemes, the GIVS unifies the properties of gauge invariance and perturbative stability. The application of the GIVS to the Standard Model, for instance, leads …
The renormalization of vacuum expectation value parameters, such as $v$ in the Standard Model (SM), is an important ingredient in electroweak renormalization, where this issue is connected to the treatment of tadpoles. Tadpole counterterms can be generated in two different ways in the Lagrangian: in the course of parameter renormalization, or alternatively via Higgs field redefinitions. The former typically leads to small corrections originating from tadpoles, but in general suffers from gauge dependences if MSbar renormalization conditions are used for mass parameters. The latter is free from…
We compare two methods of analyzing the finite-temperature electroweak phase transition in the minimal supersymmetric standard model: the traditional effective potential (EP) approach, and the more recently advocated procedure of dimensional reduction (DR). The latter tries to avoid the infrared instabilities of the former by matching the full theory to an effective theory that has been studied on the lattice. We point out a limitation of DR that caused a large apparent disagreement with the effective potential results in our previous work. We also incorporate wave function renormalization int…
We update instability and metastability bounds of the Standard Model electroweak vacuum in view of the recent ATLAS and CMS Higgs results. For a Higgs mass in the range 124--126 GeV, and for the current central values of the top mass and strong coupling constant, the Higgs potential develops an instability around $10^{11}$ GeV, with a lifetime much longer than the age of the Universe. However, taking into account theoretical and experimental errors, stability up to the Planck scale cannot be excluded. Stability at finite temperature implies an upper bound on the reheat temperature after inflat…
The light slepton-sneutrino scenario with non-universal scalar masses at the GUT scale is preferred by the electroweak precision data. Though a universal soft breaking mass at or below the Plank scale can produce the required non-universality at the GUT scale through running, such models are in conflict with the stability of the electroweak symmetry breaking vacuum. If the supergravity motivated idea of a common scalar mass at some high scale along with light sleptons is supported by future experiments that may indicate that we are living in a false vacuum. In contrast SO(10) D-terms, which ma…
The Georgi-Machacek model extends the standard model Higgs sector by adding two isospin triplet scalar fields and imposing global SU(2)$_R$ symmetry on them. A feature of the model is that the triplets can acquire a large vacuum expectation value without conflicting with the current experimental bound on the $ρ$ parameter. We investigate the electroweak phase transition in the Georgi-Machacek model by evaluating the finite-temperature effective potential of the Higgs sector. The electroweak phase transition can be sufficiently strong in a large parameter space when the triplets acquire a vacuu…
We study a model with an exotic new sector strongly coupled to the Higgs boson, in which supersymmetry is introduced to protect the quartic coupling from a large running and avoid potential vacuum stability problem. The fermionic components present vector like mass terms, through which the Higgs diphoton decay branching ratio can be tuned. The bosonic components trigger a strongly first order electroweak phase transition. We find a large parameter region of effective Yukawa coupling $y\gtrsim2$ and mass parameters $m_f\sim m_s$ of a few hundred GeV, that can simultaneously accommodate the diph…
In this proceedings we compare phenomenological predictions for differential distributions in top-quark pair production at the LHC. In particular we consider NNLO QCD fixed-order predictions and parton-level predictions based on NLO QCD multi-jet merging following the MEPS@NLO scheme. In both predictions NLO electroweak (EW) corrections are incorporated in different approximations. We focus on several transverse-momentum distributions and on the top-quark invariant mass distribution, both highly relevant for the ongoing physics program at the LHC. We discuss comparisons between the different c…
It is known that the present electroweak vacuum is likely to be metastable and it may lead to a serious instability during/after inflation. We propose a simple solution to the problem of vacuum instability during/after inflation. If there is a moduli field which has Planck-suppressed interactions with the standard model fields, the Higgs quartic coupling in the early universe naturally takes a different value from the present one. A slight change of the quartic coupling in the early universe makes the Higgs potential absolutely stable and hence we are free from the vacuum instability during/af…
Vacuum structure of the Babu-Nandi-Tavartkiladze model of neutrino mass generation
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of the Witwatersrand（威特沃特斯兰德大学）；Indian Institute of Science Education and Research Pune（印度科学教育与研究学院浦那分校）
