The Higgs boson mass used to be the only unknown input parameter of the electroweak contributions to (g-2)_μ in the Standard Model. It enters at the two-loop level in diagrams with e.g. top loops, W- or Z-exchange. We re-evaluate these contributions, providing analytic expressions and exact numerical results for the Higgs boson mass recently measured at the LHC. Our final result for the full Standard Model electroweak contributions is (153.6\pm1.0)*10^{-11}, where the remaining theory error comes from unknown three-loop contributions and hadronic uncertainties.
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.
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.
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.
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…
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.
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 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.
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.
We study the electroweak phase transition and the critical bubble in the scale-invariant two Higgs doublet model taking the recent LHC data into account. The sphaleron energy in this model is evaluated for the first time. It is found that the strong first-order electroweak phase transition is the inevitable consequence to be consistent with the observed 125 GeV Higgs boson. In such a case, the signal strength of the Higgs decay to two gammas and the triple Higgs boson coupling could deviate from the SM values by $-10$% and $+82$%, respectively.
Contrary to common belief, the requirement that supersymmetry exists and that there are two Higgs doublets and no singlet at the electroweak energy scale does not necessarily result in the minimal supersymmetric standard model (MSSM). Two interesting alternatives are presented.
We evaluate dominant two-loop corrections to the triple Higgs coupling and strength of a first-order electroweak phase transition in the inert Higgs doublet model. It is found that sunset diagrams can predominantly enhance the former and reduce the latter. As a result, the triple Higgs coupling normalized by the standard model value at two-loop level is more enhanced than the corresponding one-loop value.
We present the Higgs mechanism in the context of the EW-scale $ν_R$ model in which electroweak symmetry is dynamically broken by condensates of mirror quark and right-handed neutrino through the exchange of one fundamental Higgs doublet and one fundamental Higgs triplet, respectively. The formation of these condensates is dynamically investigated by using the Schwinger-Dyson approach. The occurrence of these condensates will give rise to the rich Higgs spectrum. In addition, the VEVs of Higgs fields is also discussed in this dynamical phenomenon.
We study collider signatures of electroweak baryogenesis in the two Higgs doublet model and the minimal supersymmetric standard model. It is found that the trilinear coupling of the lightest Higgs boson receives large quantum corrections if the electroweak phase transition is strongly first order for successful baryogenesis. In the two Higgs doublet model, the magnitude of the deviation from the standard model value is shown to be larger than 10 percent. Such a deviation can be detected at a future electron-positron linear collider.
Higgs sector extensions beyond the Standard Model (BSM) provide additional sources of CP violation and further scalar states that help to trigger a strong first order electroweak phase transition (SFOEWPT) required to generate the observed baryon asymmetry of the Universe through electroweak baryogenesis. We investigate the CP-violating 2-Higgs-Doublet Model (C2HDM) and the Next-to-Minimal 2-Higgs-Doublet Model (N2HDM) with respect to their potential to generate an SFOEWPT while being compatible with all relevant and recent theoretical and experimental constraints. The implications of an SFOEW…
We analyze the bounds on the Higgs pseudo-observables following from electroweak constraints, under the assumption that the Higgs particle is the massive excitation of an $SU(2)_L$ doublet. Using such bounds, detailed predictions for $h\to 4\ell$ decay rates, dilepton spectra, and lepton-universality ratios are presented.
The detailed study of the Higgs boson is one of the main tasks of contemporary particle physics. Gluon fusion, the main production channel of Higgs bosons at the LHC, has been successfully modelled in QCD up to $\text{N}^3\text{LO}$. To fully exploit this unprecedented theoretical effort, sub-leading contributions, such as electroweak corrections, must be investigated. I will present the analytic calculations of the gluon- and quark-induced Higgs plus jet amplitudes in mixed QCD-electroweak corrections mediated by light quarks up to order $v α^2 α_S^{3/2}$.
In this paper, we try to construct an electroweak model which avoids using Higgs mechanism. We simultaneously introduce two sets of gauge bosons so as to keep the masses of gauge bosons $W^{\pm}$ and $Z$ non-zero without using Higgs mechanism. In order to introduce symmetry breaking, we need a vacuum potential. In a proper limit, this model will return to the standard model, except that there exists no Higgs particle and couplings between Higgs particle and fermions or gauge fields. The fundamental dynamical characteristics of this model are similar to those of the standard model.
We consider, in the context of the minimal supersymmetric standard model, the case where the gravitino weighs 10^6 GeV or more, which is preferred by various cosmological difficulties associated with unstable gravitinos. Despite the large Higgs mixing parameter B together with the little hierarchy to other soft supersymmetry breaking masses, a light higgsino with an electroweak scale mass leads to successful electroweak symmetry breaking, at the price of fine-tuning the higgsino mixing mu parameter. Furthermore the light higgsinos produced at the decays of gravitinos can constitute the dark ma…
We set constraints on the trilinear Higgs boson self-coupling, $λ_3$, by combining the information coming from the $W$ mass and leptonic effective Weinberg angle, electroweak precision observables, with the single Higgs boson analyses targeting the $γγ,\, ZZ^*,\, WW^*, \,τ^+ τ^-$ and $\bar{b} b$ decay channels and the double Higgs boson analyses in the $b\bar{b}b\bar{b}, \, b\bar{b}b τ^+ τ^-$ and $b\bar{b}b γγ$ decay channels, performed by the ATLAS collaboration. With the assumption that the new physics affects only the Higgs potential, values outside the interval $ -1.8\, λ_3^{\rm SM} < λ_3 …
We study the effects of the extended electroweak gauge sector on the signal strengths of the Higgs boson at the LHC. Extension of the Higgs sector associate with the extension of the electroweak gauge symmetry. In our setup, there are two neutral Higgs states ($h$, $H$) and three new gauge bosons ($W'^{\pm}$, $Z'$). We assume the lightest scalar, $h$, is what LHC found and its mass is 125 GeV. We find the enhancement of $μ(gg \to h \to γγ)$. On the other hand, other decay processes are same as or smaller than the SM expectation.
In this paper, applying general gauge field theory, we will construct an electroweak model. In this new electroweak model, Higgs mechanism is not used, so no Higgs particle exists in the model. In order to keep the masses of intermediate gauge bosons non-zero, we will introduce two sets of gauge fields. We need a vacuum potential to introduce symmetry breaking and to introduce the masses of all fields. Except for theose terms concern of Higgs particle, the fundamental dynamical properties of this model are similar to those of the standard model. And in a proper limit, this model will approxima…
Contrary to common belief, the requirement that supersymmetry exists and that there are two Higgs doublets and no singlet at the electroweak energy scale does not necessarily result in the minimal supersymmetric standard model (MSSM). An interesting alternative is presented.
We present standard model predictions for a four fermion reaction e+ e- -> mu+ mu- bar_b b being one of the best detection channels of a low mass Higgs boson produced through the Higgsstrahlung mechanism at a linear collider. We include leading virtual and real QED corrections to all the lowest order Feynman diagrams of e+ e- -> mu+ mu- bar_b b and the complete O(alpha) electroweak corrections to the Z-Higgs production and to the Z and Higgs boson decay widths in the double pole approximation.
A phenomenological consequence of electroweak baryogenesis is studied in connection with the Higgs physics. In a two Higgs double model, the first order phase transition can be strong enough to allow the electroweak baryogenesis due to the effect of extra Higgs bosons. We investigate the quantum correction to the triple coupling of the lightest Higgs boson in such a scenario, and find that the condition of the strong first order phase transition necessarily leads to the deviation of at least 10 percent from the standard model prediction. Such magnitude of the deviation can be identified in fut…
One-loop contributions to the Higgs potential at finite temperatures are discussed in the supersymmetric standard model with four Higgs doublet chiral superfields as well as a pair of charged singlet chiral superfields. The mass of the lightest Higgs boson $h$ is determined only by the D-term at the tree-level in this model, while the triple Higgs boson coupling for $hhh$ can receive a significant radiative correction. The same nondecoupling effect can also contribute to realize the sufficient first order electroweak phase transition, which is required for a successful scenario of electroweak …
We briefly review recent progress in the analysis of the Higgs sector of the Minimal R-symmetric Supersymmetric Standard Model. Importance of the interplay between W and Higgs boson masses in constraining the parameter space of the model is shown.
