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 in the Einstein frame has genuine predictions. In a broad region in the parameter space, the effective Higgs mass is large and it initially takes over through fast oscillations. This epoch is followed by the Weyl field slowly rolling a plateau-like potential. This framework generically predicts that the Higgs self-coupling in the EW vacuum is enhanced, compared to the SM predictions, through couplings to the gravity sector. Moreover, when the Higgs is settled in the EW vacuum, all other scalar flat directions would be lifted via gravitational effects mediated by the Weyl field.
In the present paper, we discuss gravitational relaxation models for the electroweak hierarchy problem. We show that modified gravity can naturally relax the electroweak hierarchy problem where conformal transformation provides a crucial rule about what modified gravity theories are favored to relax the electroweak hierarchy. The conformal transformation connects different gravitational theories and rescaling the metric changes the dimensional parameters like the Higgs mass or the cosmological constant in different frames drastically. When the electroweak scale is naturally realized by dynamic…
The first model of Foot, Kobakhidze and Volkas described in their work in arXiv:0704.1165 [hep-ph] is a tailored version of our model on broken scale invariance in the standard model presented in hep-th/0403039.
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 current electroweak data and the constraints on the Higgs mass are discussed. Within the context of the Standard Model the data prefer a relatively light Higgs mass.
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 …
We analyze the electroweak phase transition at finite temperature in a model of gauge-Higgs unification where the fermion mass hierarchy including top quark mass, a viable electroweak symmetry breaking and an observed Higgs mass are successfully reproduced. To study the phase transition, we derive the general formula of the 1-loop effective potential at finite temperature by using the $ζ$ function regularization method. It is remarkable that the functions determining the Kaluza-Klein mass spectrum have only to be necessary in calculations. This potential can be applicable to any higher dimensi…
It is shown that, nonminimal coupling between the Standard Model (SM) Higgs field and spacetime curvature, present already at the renormalizable level, can be fine-tuned to stabilize the electroweak scale against power-law ultraviolet divergences. The nonminimal coupling acts as an extrinsic stabilizer with no effect on the loop structure of the SM, if gravity is classical. This novel fine-tuning scheme, which could also be interpreted within Sakharov's induced gravity approach, works neatly in extensions of the SM involving additional Higgs fields or singlet scalars.
We match the electroweak chiral Lagrangian with two singlet scalars to the next-to-minimal composite Higgs model with $ SO(6)/SO(5) $ coset structure and extract the scalar divergences to one loop. Assuming the additional scalar to be heavy, we integrate it out and perform a matching to the well-established electroweak chiral Lagrangian with one light Higgs.
The one-loop radiative correction in an ultraviolet (UV) complete electroweak (EW) model without a Higgs particle is calculated. The $ρ$ parameter determining the ratio of the charged to neutral currents is derived for the dominant top quark contribution with the result $ρ\sim 1.01$. This result is compared to the radiative correction to $ρ$ in the standard EW model with a Higgs particle. For the favored light Higgs particle mass from global fits to EW data: $114.4\,{\rm GeV} \leq m_H\leq 135\, {\rm GeV}$, the Higgs contribution up to three loops is negligible and the Higgless model is consist…
We present `twin Higgs models', simple realizations of the Higgs as a pseudo-Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5 - 10 TeV. In the ultra-violet these theories have a discrete symmetry which interchanges each Standard Model particle with a corresponding particle which transforms under a twin or mirror Standard Model gauge group. In addition, the Higgs sector respects an approximate global SU(4) symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo-Goldstone Higgs pot…
This lecture discusses the Higgs boson sector of the SM and the MSSM, including their connection to electroweak precision physics and the searches for SM and SUSY Higgs bosons at the LHC.
The mass spectra of the standard model particles are reproduced in the $SO(11)$ gauge-Higgs grand unification in the six-dimensional warped space without introducing exotic light fermions. Light neutrino masses are explained by the gauge-Higgs seesaw mechanism. We evaluate the effective potential of the 4d Higgs boson appearing as a fluctuation mode of the Aharonov-Bohm phase $θ_H$ in the extra-dimensioal space, and show that the dynamical electroweak symmetry breaking takes place with the Higgs boson mass $m_H \sim 125\,$GeV and $θ_H \sim 0.1$. The Kaluza-Klein mass scale in the fifth dimensi…
We derive electroweak Z-string solutions in the Glashow-Weinberg-Salam model with two Higgs doublets. The existence of such solutions in particular requires a specific relation between the ratio of the two Higgs vacuum expectation values, {\it i.e.} $\tanβ$, and the couplings in the Higgs potential.
The manner in which the parameters of a two-Higgs-doublet model can be chosen so that no Higgs boson is discovered at a $\sqrt{s}\leq 800\gev$ $\epem$ collider, while maintaining consistency with current precision electroweak measurements, is described. The importance of a Giga-$Z$ factory and higher collider energies for such a scenario is emphasized.
In the gauge-Higgs unification scenario 4D Higgs fields are unified with gauge fields in higher dimensions. The electroweak model is constructed in the Randall-Sundrum warped space. The electroweak symmetry is dynamically broken by the Hosotani mechanism due to the top quark contribution. The Higgs mass is predicted to be around 50 GeV with the vanishing ZZH and WWH couplings so that the LEP2 bound for the Higgs mass is evaded.
We calculate both the cubic and the quartic self-couplings of the lighter scalar Higgs boson without assuming the decoupling limit in the two-Higgs-doublet model (THDM). In some regions of parameter space of the THDM where the electroweak phase transition is strongly first order, it is possible that the quartic self-coupling of the lighter scalar Higgs boson might be deviated by at least 40 % from the standard model prediction.
These three lectures review the state of our understanding of electroweak interactions and the search for the agent of electroweak symmetry breaking. The themes of the lectures are (i) the electroweak theory and its experimental status, (ii) the standard-model Higgs boson, and (iii) aspects of electroweak theory beyond the standard SU(2)_L x U(1)_Y model.
The recent calculation of the next-to-leading order electroweak corrections to the decay of the Standard Model Higgs boson to two photons in the framework of the complex-mass scheme is briefly summarized.
The little Higgs idea is an alternative to supersymmetry as a solution to the gauge hierarchy problem. In this note, I review various little Higgs models and their phenomenology with emphases on the precision electroweak constraints in these models.
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 propose a new model of 5D $SU(3)\otimes U(1)_X$ gauge-Higgs unification with a successful electroweak symmetry breaking and a realistic Higgs boson mass. In our model, the representations of the fermions are very simple, the ${\bf 3}, \overline{\bf 3}$ and $\bf \overline{15}$ representations of $SU(3)$ gauge group. Employing the anti-periodic boundary conditions for $\bf \overline{15}$ reduces massless exotic fermions and simplifies the brane localized mass terms. We calculate the 1-loop Higgs potential in detail and find that a realistic electroweak symmetry breaking and the observed Higgs…
The electroweak radiative correction, which turned out to be marginal within the standard electroweak model having the minimal Higgs sector in view of the present experimental information, fits well the experiment when the Higgs sector is extended to have two Higgs doublets. We predict the range where the charged and CP odd Higgs boson masses would lie, taking the two CP even neutral Higgs boson masses to be degenerate which makes the analysis in multiparameter space feasible. It is shown that the mass of neutral Higgs doublet boson can arbitrarily be large consistently with the $W$ mass, if t…
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…
In this talk I discuss the interpretation of LHC Higgs measurements within the electroweak chiral Lagrangian, paying particular attention to the role of power counting.
The possibility of a strongly first-order electroweak phase transition by means of a dimension-six Higgs operator in the Higgs potential of the standard model is studied at finite temperature at the one-loop level. Exact calculation of the one-loop effective Higgs potential at finite temperature suggests that for the Higgs boson with its mass between 115 and 132 GeV the strongly first-order electroweak phase transition is possible if a dimension-six operator is present.
This review provides an elementary discussion of electroweak symmetry breaking in the minimal and the next-to-minimal supersymmetric models with the focus on the fine-tuning problem -- the tension between natural electroweak symmetry breaking and the direct search limit on the Higgs boson mass. Two generic solutions of the fine-tuning problem are discussed in detail: models with unusual Higgs decays; and models with unusual pattern of soft supersymmetry breaking parameters.
We calculate next-to-leading order (NLO) QCD corrections to electroweak Higgs plus three jet production. Both vector boson fusion (VBF) and Higgs-strahlung type contributions are included along with all interferences. The calculation is implemented within the Matchbox NLO framework of the Herwig++ event generator.
I present applications of a master formula for next-to-next-to-leading order soft and virtual QCD corrections to various electroweak, Higgs, and supersymmetric processes. They include Drell-Yan and charged Higgs production, single-top production in flavor-changing neutral-current processes, and squark and gluino production.
The status of various precisely measured electroweak parameters is reviewed. Natural relations among them are shown to constrain the Higgs mass, m_H, via quantum loop effects to relatively low values. A comparison with direct Higgs searches is made.
Little Higgs theories are a fascinating new idea to solve the little hierarchy problem by stabilizing the Higgs mass against one-loop quadratically divergent radiative corrections. In this talk I give a brief overview of the idea, focusing mainly on the littlest Higgs model, and present a sampling of the electroweak precision constraints.
We examine the prospects for discovering and elucidating the weakly-coupled Higgs sector at future collider experiments. The Higgs search consists of three phases: (i) discovery of a Higgs candidate, (ii) verification of the Higgs interpretation of the signal, and (iii) precision measurements of Higgs sector properties. The discovery of one Higgs boson with Standard Model properties is not sufficient to expose the underlying structure of the electroweak symmetry breaking dynamics. It is critical to search for evidence for a non-minimal Higgs sector and/or new physics associated with electrowea…
The framework of the electroweak chiral Lagrangian with a light Higgs is extended by an additional scalar and then generalized to N scalars in the Higgs sector. Divergences from scalar fluctuations are renormalized up to one loop using the background field method. The results are crosschecked against the case of one scalar. A subset of the divergences is demonstrated and crosschecked diagrammatically. Together with the complete one-loop renormalization of the electroweak chiral theory with one light Higgs conducted previously, this constitutes a renormalization framework of any pure scalar ext…
We explore the connection between the strength of the electroweak phase transition and the properties of the Higgs boson. Our interest is in regions of parameter space that can realize electroweak baryogenesis. We do so in a simplified framework in which a single Higgs field couples to new scalar fields charged under SU(3)_c by way of the Higgs portal. Such new scalars can make the electroweak phase transition more strongly first-order, while contributing to the effective Higgs boson couplings to gluons and photons through loop effects. For Higgs boson masses in the range 115 GeV < m_h < 130 G…
We perform an updated fit to LHC Higgs data and LEP electroweak precision tests in the framework of the Standard Model Effective Field Theory (SMEFT). We assume a generic structure of the SMEFT operators without imposing any flavour symmetries. The implementation is released as part of the public global SMEFT likelihood. This allows one to fit parameters of a broad class of new physics models to combined Higgs, electroweak, quark flavour, and lepton flavour observables.
We present an introduction to the basic concepts of electroweak symmetry breaking and Higgs physics within the Standard Model and its supersymmetric extensions. A brief overview will also be given on alternative mechanisms of electroweak symmetry breaking. In addition to the theoretical basis, the present experimental status of Higgs physics and prospects at the Tevatron, the LHC and e+e- linear colliders are discussed.
In this talk I will give a brief introduction to Little Higgs models in general, including an overview of all models in existence thus far. I then review some of the generic constraints on these models from electroweak precision measurements.
The electroweak symmetry is nonlinearly realized in an extension of the minimal supersymmetric standard model (MSSM) through an additional pair of constrained Higgs doublet superfields. The superpotential couplings of this constrained Higgs doublet pair to the MSSM Higgs doublet pair catalyze their vacuum expectation values. The Higgs and Higgsino-gaugino mass spectrum is presented for several choices of supersymmetry (SUSY) breaking and Higgs superpotential mass parameters. The additional vacuum expectation values provided by the constrained fields can produce a phenomenology quite different …
We present the computer code RECOLA2 along with the first NLO electroweak corrections to Higgs production in vector-boson fusion and updated results for Higgs strahlung in the Two-Higgs-Doublet Model and Higgs-Singlet extension of the Standard Model. A fully automated procedure for the generation of tree-level and one-loop matrix elements in general models, including renormalization, is presented. We discuss the application of the Background-Field Method to the extended models. Numerical results for NLO electroweak cross sections are presented for different renormalization schemes in the Two-H…
We investigate the region of restored electroweak symmetry around a superconducting cosmic string coupled to the Weinberg-Salam model with an extra Higgs doublet. We show that the presence of the extra Higgs fields, and in particular their CP violating relative phase, does not qualitatively affect the results of Perkins and Davis[1] obtained for the standard electroweak theory. This result is neccessary to ensure the validity of some recently proposed string-mediated electroweak baryogenesis scenarios.
`Little Higgs' models, in which the Higgs particle arises as a pseudo-Goldstone boson, have a natural mechanism of electroweak symmetry breaking associated with the large value of the top quark Yukawa coupling. The mechanism typically involves a new heavy SU(2)_{L} singlet top quark, T. We discuss the relationship of the Higgs boson and the two top quarks. We suggest experimental tests of the Little Higgs mechanism of electroweak symmetry breaking using the production and decay of the T at the Large Hadron Collider.
The first LHC run has confirmed the Standard Model as the correct theory at the electroweak scale, and the existence of a Higgs-like particle associated with the spontaneous breaking of the electroweak gauge symmetry. These lectures overview the present knowledge on the Higgs boson and discuss alternative scenarios of electroweak symmetry breaking which are already being constrained by the experimental data.
This lecture discusses the Higgs boson sectors of the SM and the MSSM, in particular in view of the recently discovered particle at \sim 125.5 GeV. It also covers their connection to electroweak precision physics and the implications for the consistency tests of the respective model.
In this work, we revisit the non-minimally coupled Higgs Inflation scenario and investigate its observational viability in light of the current Cosmic Microwave Background, Baryon Acoustic Oscillation and type Ia Supernovae data. We explore the effects of the Coleman-Weinberg approximation to the Higgs potential in the primordial universe, connecting the predictions for the Lagrangian parameters at inflationary scales to the electroweak observables through Renormalization Group methods at two-loop order. As the main result, we find that observations on the electroweak scale are in disagreement…
In this letter, we show that the electroweak symmetry is restored at high temperature for Little Higgs (LH), when including dominant higher order thermal corrections, that are consequence of the non-linear nature of the scalar sector. This leads us to suggest that the LH requires a UV completion above the scale $Λ\lesssim f$.
We propose a phenomenological solution to the Electroweak hierarchy problem. It predicts no new particles beyond those in the Standard Model. The Higgs is arbitrarily massive and slow-roll inflation can be implemented naturally. Loop corrections will be negligible even for large cutoffs.
We propose a simple five-dimensional extension of the Standard Model (SM) without any Higgs potential nor any extra fields. A Higgs doublet lives in the bulk of a flat line segment and its boundary condition is Dirichlet at the ends of the line, which causes the electroweak symmetry breaking without Higgs potential. The vacuum expectation value of the Higgs is induced from the Dirichlet boundary condition which is generally allowed in higher dimensional theories. The lightest physical Higgs has non-flat profile in the extra dimension even though the vacuum expectation value is flat. As a conse…
We study the dynamics of $SU(2)_L$ times $U(1)_Y$ electroweak gauge fields during and after Higgs inflation. In particular, we investigate configurations of the gauge fields during inflation and find the gauge fields remain topologically non-trivial. We also find that the gauge fields grow due to parametric resonances caused by oscillations of a Higgs field after inflation. We show that the Chern-Simons number also grows significantly. Interestingly, the parametric amplification gives rise to sizable magnetic fields after the inflation whose final amplitudes depend on the anisotropy survived d…
Electroweak scale active right-handed neutrinos such as those proposed in a recent model necessitate the enlargement of the SM Higgs sector to include Higgs triplets with doubly charged scalars. The search for and constraints on such Higgs sector has implications not only on the nature of the electroweak symmetry breaking but also on the possibility of testing the seesaw mechanism at colliders such as the LHC and the ILC.
We update our analysis of technicolour theories with techniquarks in higher dimensional representations of the technicolour gauge group in the light of the new electroweak precision data on the Z resonance.
Adding radion perturbations (up to second order) to the static (RS) metric allows us to calculate the general first and second order interactions of the radion field with the electroweak vector bosons. We use these interactions to compute precision electroweak observables in the case of Higgs-radion mixing and compare with experiment.
Cold electroweak baryogenesis was proposed as a scenario to bypass generic problems of electroweak baryogenesis within the Standard Model. In this scenario, baryogenesis takes place during an electroweak symmetry breaking transition, which is also responsible for preheating after inflation. In the simplest modelling of the scenario, only two parameters remain undetermined: The Higgs mass and the strength of CP violation. Using full real-time lattice simulations, we compute the dependence of the asymmetry on these parameters.
We use transport equations to compute the evolution of the quark plasma at the electroweak phase transition in the two-doublet Higgs model, obtaining in a more rigorous and quantitatively accurate way results consistent with previous work. We discuss the model in connection with the electroweak baryogenesis scenario, and claim that the observed baryon asymmetry of the universe can be obtained within this model with a suitable choice of parameters.
The minimal supersymmetric standard model (MSSM) is extended by including an additional pair of constrained Higgs doublet superfields through which the electroweak symmetry is nonlinearly realized. The superpotential couplings of this constrained Higgs doublet pair to the MSSM Higgs doublet pair catalyze the later nontrivial vacuum expectation values. The mass spectrum of the Higgs scalars and Higgsino-gaugino sector is presented for several choices of supersymmetry (SUSY) breaking and Higgs superpotential mass parameters. The effect of the the additional constrained fields and multiple vacuum…
The predictions for electroweak observables following from Higgs-Free Model for Fundamental Interactions are derived. It is shown that these predictions are close to the Standard Model predictions and they are in a surprising agreement with the experimental data. The analysis of electroweak observables at low and high energy suggests that the Higgs mass $m_H$ is just the ultraviolet cutoff which increases if the process energy scale increases. We propose several experimental tests which can discriminate between the Standard and the Higgs-Free Models.
Skyrmions are extended field configurations, initially proposed to describe baryons as topological solitons in an effective field theory of mesons. We investigate and confirm the existence of skyrmions within the electroweak sector of the Standard Model and study their properties. We find that the interplay of the electroweak sector with a dynamical Higgs field and the Skyrme term leads to a non-trivial vacuum structure with the skyrmion and perturbative vacuum sectors separated by a finite energy barrier. We identify dimension-8 operators that stabilise the electroweak skyrmion as a spatially…
An introduction to electroweak symmetry breaking and Higgs physics is presented for the Standard Model and its supersymmetric extensions. A brief overview will also be given on strong interactions of the electroweak gauge bosons in alternative scenarios. In addition to the theoretical basis, the present experimental status of Higgs physics and implications for future experiments at the LHC and $e^+e^-$ linear colliders are discussed.
