Higgs boson properties in the Standard Model and its supersymmetric extensions

We review the realization of the Brout–Englert–Higgs mechanism in the electroweak theory and describe the experimental and theoretical constraints on the mass of the single Higgs boson expected in the minimal Standard Model. We also discuss the couplings of this Higgs boson and its possible decay modes as functions of its unknown mass. We then review the structure of the Higgs sector in the minimal supersymmetric extension of the Standard Model (MSSM), noting the importance of loop corrections to the masses of its five physical Higgs bosons. Finally, we discuss some non-minimal models. To cite this article: J. Ellis et al., C. R. Physique 8 (2007).     

Direct search for the Standard Model Higgs boson

For twelve years, LEP revolutionized the knowledge of electroweak symmetry breaking within the standard model, and the direct discovery of the Higgs boson would have been the crowning achievement. Searches at the Z resonance and above the W⁺W⁻ threshold allowed an unambiguous lower limit on the mass of the standard model Higgs boson to set be at 114.1 GeV·c⁻². After years of efforts to push the LEP performance far beyond the design limits, hints of what could be the first signs of the existence of a 115 GeV·c⁻² Higgs boson appeared in June 2000, were confirmed in September, and were then confirmed again in November. An additional six-month period of LEP operation was enough to provide a definite answer, with an opportunity to make a fundamental discovery of prime importance. To cite this article: P. Janot, M. Kado, C. R. Physique 3 (2002) 1193–1202.     

The Higgs as a pseudo-Goldstone boson

The old idea of the Higgs as a pseudo-Goldstone boson has been revived and re-energized as a possible solution to the little hierarchy puzzle in the Standard Model. Its most natural implementation may be in the context of models with supersymmetry not far above the electroweak breaking scale. To cite this article: H. Georgi, C. R. Physique 8 (2007).     

First-order electroweak phase transition powered by additional F-term loop effects in an extended supersymmetric Higgs sector

We investigate the one-loop effect of new charged scalar bosons on the Higgs potential at finite temperatures in the supersymmetric standard model with four Higgs doublet chiral superfields as well as a pair of charged singlet chiral superfields. In this model, the mass of the lightest Higgs boson h is determined only by the D-term in the Higgs potential at the tree-level, while the triple Higgs boson coupling for hhh can receive a significant radiative correction due to nondecoupling one-loop contributions of the additional charged scalar bosons. We find that the same nondecoupling mechanism can also contribute to realize stronger first order electroweak phase transition than that in the minimal supersymmetric standard model, which is definitely required for a successful scenario of electroweak baryogenesis. Therefore, this model can be a new candidate for a model in which the baryon asymmetry of the Universe is explained at the electroweak scale.     

Non-minimal Coupling of the Higgs Boson to Curvature in an Inflationary Universe

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 potential thereby stabilizing the electroweak vacuum. For specific values of the Higgs field initial condition and of its non-minimal coupling, inflation can drive the Higgs field to the electroweak vacuum quickly during inflation.     

Modified Yang-Mills Theory and Electroweak Interactions

Since the Higgs boson of the standard electroweak model has not been detecteddespite many experimental attempts, nonstandard electroweak models notincluding the Higgs boson may be worthy of consideration; one of them isproposed here. This new model of electroweak interactions is based on theYang-Mills theory completed by a nontrivial condition at infinity for theYang-Mills potentials corresponding to the zero-field intensities. It is shown thatwithin the framework of this model the three vector potentials of the Yang-Millstheory allow one to describe both the Maxwell electromagnetic interactions andthe Fermi weak interactions and to obtain the known value of the Z ⁰ boson mass.     

Integrating out the standard Higgs field in the path integral

We integrate out the Higgs boson in the electroweak standard model at one loop and construct a low-energy effective Lagrangian assuming that the Higgs mass is much larger than the gauge-boson masses. Instead of applying diagrammatical techniques, we integrate out the Higgs boson directly in the path integral, which turns out to be much simpler. By using the background-field method and the Stueckelberg formalism, we directly find a manifestly gauge-invariant result. The heavy-Higgs effects on fermionic couplings are derived, too. At one loop the log M_H terms of the heavy-Higgs limit of the electroweak standard model coincide with the UV-divergent terms in the gauged non-linear σ-model, but vertex functions differ in addition by finite constant terms. Finally, the leading Higgs effects to some physical processes are calculated from the effective Lagrangian.     

Electroweak vacuum stability in classically conformal $$$$ extension of the standard model

We consider the minimal U(1)\(_{B-L}\) extension of the standard model (SM) with the classically conformal invariance, where an anomaly-free U(1)\(_{B-L}\) gauge symmetry is introduced along with three generations of right-handed neutrinos and a U(1)\(_{B-L}\) Higgs field. Because of the classically conformal symmetry, all dimensional parameters are forbidden. The \(B-L\) gauge symmetry is radiatively broken through the Coleman–Weinberg mechanism, generating the mass for the \(U(1)_{B-L}\) gauge boson (\(Z^\prime \) boson) and the right-handed neutrinos. Through a small negative coupling between the SM Higgs doublet and the \(B-L\) Higgs field, the negative mass term for the SM Higgs doublet is generated and the electroweak symmetry is broken. In this model context, we investigate the electroweak vacuum instability problem in the SM. It is well known that in the classically conformal U(1)\(_{B-L}\) extension of the SM, the electroweak vacuum remains unstable in the renormalization group analysis at the one-loop level. In this paper, we extend the analysis to the two-loop level, and perform parameter scans. We identify a parameter region which not only solve the vacuum instability problem, but also satisfy the recent ATLAS and CMS bounds from search for \(Z^\prime \) boson resonance at the LHC Run-2. Considering self-energy corrections to the SM Higgs doublet through the right-handed neutrinos and the \(Z^\prime \) boson, we derive the naturalness bound on the model parameters to realize the electroweak scale without fine-tunings.     

Higgs as a pseudo-Goldstone boson, the mu problem and gauge-mediated supersymmetry breaking

We study the interplay between the spontaneous breaking of a global symmetry of the Higgs sector and gauge-mediated supersymmetry breaking, in the framework of a supersymmetric model with global SU(3) symmetry. In addition to solving the supersymmetric flavor problem and alleviating the little hierarchy problem, this scenario automatically triggers the breaking of the global symmetry and provides an elegant solution to the μ/Bμ problem of gauge mediation. We study in detail the processes of global symmetry and electroweak symmetry breaking, including the contributions of the top/stop and gauge-Higgs sectors to the one-loop effective potential of the pseudo-Goldstone Higgs boson. While the joint effect of supersymmetry and of the global symmetry allows in principle the electroweak symmetry to be broken with little fine-tuning, the simplest version of the model fails to bring the Higgs mass above the LEP bound due to a suppressed tree-level quartic coupling. To cure this problem, we consider the possibility of additional SU(3)-breaking contributions to the Higgs potential, which results in a moderate fine-tuning. The model predicts a rather low messenger scale, a small tanβ value, a light Higgs boson with Standard Model-like properties, and heavy higgsinos.     

Remarks on Higgs inflation

We discuss models where the Higgs boson of the electroweak standard model plays the role of the inflaton. We focus on the question of the violation of perturbative unitarity due to the coupling of the Higgs boson either to the Ricci scalar or to the Einstein tensor and discuss the background dependence of the unitarity bounds. Our conclusion is that the simplest model which restricts itself to the standard model Higgs boson without introducing further degrees of freedom has a serious problem. However, in the asymptotically safe gravity scenario, the Higgs boson of the standard model could be the inflaton and no physics beyond the standard model is required to explain both inflation and the spontaneous breaking of the electroweak symmetry of the standard model.     

Origin and phenomenology of weak-doublet spin-1 bosons

We study phenomenological consequences of the Standard Model extension by the new spin-1 fields with the internal quantum numbers of the electroweak Higgs doublets. We show, that there are at least three different classes of theories, all motivated by the hierarchy problem, which predict appearance of such vector weak-doublets not far from the weak scale. The common feature for all the models is the existence of an SUW(3) gauge extension of the weak SUW(2) group, which is broken down to the latter at some energy scale around TeV. The Higgs doublet then emerges as either a pseudo-Nambu-Goldstone boson of a global remnant of SUW(3), or as a symmetry partner of the true eaten-up Goldstone boson. In the third class, the Higgs is a scalar component of a high-dimensional SUW(3) gauge field. The common phenomenological feature of these theories is the existence of the electroweak doublet vectors (Z^?,W^?), which in contrast to well-known Z^′ and W^′ bosons posses only anomalous (magnetic moment type) couplings with ordinary light fermions. This fact leads to some unique signatures for their detection at the hadron colliders.     

Six-quark decays of the Higgs boson in supersymmetry with R-parity violation

Both electroweak precision measurements and simple supersymmetric extensions of the standard model prefer a mass of the Higgs boson less than the experimental lower limit (on a standard-model-like Higgs boson) of 114 GeV. We show that supersymmetric models with R parity violation and baryon-number violation have a significant range of parameter space in which the Higgs boson dominantly decays to six jets. These decays are much more weakly constrained by current CERN LEP analyses and would allow for a Higgs boson mass near that of the Z. In general, lighter scalar quark and other superpartner masses are allowed. The Higgs boson would potentially be discovered at hadron colliders via the appearance of new displaced vertices.     

Numerical tests of the electroweak phase transition and thermodynamics of the electroweak plasma

The finite temperature phase transition in the SU(2) Higgs model at a Higgs boson mass M_H ≅ 34 GeV is studied in numerical simulations on four-dimensional lattices with time-like extensions up to L_t = 5. The effects of the finite volume and finite lattice spacing on masses and couplings are studied in detail. The errors due to uncertainties in the critical hopping parameter are estimated. The thermodynamics of the electroweak plasma near the phase transition is investigated by determining the relation between energy density and pressure.     

Higgsless approach to electroweak symmetry breaking

Higgsless models are an attempt to achieve a breaking of the electroweak symmetry via boundary conditions at the end-points of a fifth dimension compactified on an interval, as an alternative to the usual Higgs mechanism. There is no physical Higgs scalar in the spectrum and the perturbative unitarity violation scale is delayed via the exchange of massive spin-1 KK resonances. The correct mass spectrum is reproduced in a model in warped space, which inherits a custodial symmetry from a left–right gauge symmetry in the bulk. Phenomenological challenges as well as collider signatures are presented. From the AdS/CFT perspective, this model appears as a weakly coupled dual to walking technicolour models. To cite this article: C. Grojean, C. R. Physique 8 (2007).     

Critical bubbles and fluctuations at the electroweak phase transition

We discuss the critical bubbles of the electroweak phase transition using an effective high-temperature 3-dimensional action for the Higgs field ϕ. The separate integration of gauge and Goldstone boson degrees of freedom is conveniently described in the 't Hooft-Feynman covariant background gauge. The effective dimensionless gauge coupling g3 (T) z in the broken phase is well behaved throughout the phase transition. However, the behavior of the one-loop Z(ϕ) factors of the Higgs and gauge kinetic terms signalizes the breakdown of the derivative expansion and of the perturbative expansion for a range of small ϕ values increasing with the Higgs mass m_H Taking a functional S_z [ϕ] with constant Z(ϕ) = z instead of the full non-local effective action in some neighborhood of the saddle point we are calculating the critical bubbles for several temperatures. The fluctuation determinant is calculated to high accuracy using a variant of the heat kernel method. It gives a strong suppression of the transition rate compared to previous estimates.     

Unconventional low-energy SUSY from warped geometry

Supersymmetric models with a warped fifth spatial dimension can solve the hierarchy problem, avoiding some shortcomings of non-supersymmetric constructions, and predict a plethora of new phenomena at typical scales Λ not far from the electroweak scale (Λ∼ a few TeV). In this paper we derive the low-energy effective theories of these models, valid at energies below Λ. We find that, in general, such effective theories can deviate significantly from the Minimal Supersymmetric Standard Model (MSSM) or other popular extensions of it, like the NMSSM: they have non-minimal Kähler potentials (even in the M_p→∞ limit), and the radion is coupled to the visible fields, both in the superpotential and the Kähler potential, in a non-trivial (and quite model-independent) fashion. The corresponding phenomenology is pretty unconventional, in particular the electroweak breaking occurs in a non-radiative way, with tanβ≃1 as a quite robust prediction, while the mass of the lightest Higgs boson can be as high as ∼ 700 GeV.     

Upper bounds on higgs boson masses

The low energy perturbative consistency of various models of electroweak interactions is discussed in the limit of large Higgs boson massesM _H . In each case an upper bound onM _H is found.     

Higgs searches at the LHC

We review the prospects for searches of the Standard Model Higgs boson at the LHC, based on detailed studies performed by the ATLAS and CMS Collaborations. The search channels and strategies are described, resulting in the assessment of the discovery potential for the two experiments. We discuss the prospects for measurements in the Higgs sector. To cite this article: A. De Roeck, G. Polesello, C. R. Physique 8 (2007).     

Higgs physics at LHC

The large hadron collider (LHC) and its detectors, ATLAS and CMS, are being built to study TeV scale physics, and to fully understand the electroweak symmetry breaking mechanism. The Monte-Carlo simulation results for the standard model and minimal super symmetric standard model Higgs boson searches and parameter measurements are discussed. Emphasis is placed on recent investigations of Higgs produced in association with top quarks and in vector boson fusion channels. These results indicate that Higgs sector can be explored in many channels within a couple of years of LHC operation, i.e.,L = 30 fb⁻¹. Complete coverage including measurements of Higgs parameters can be carried out with full LHC program.     

The Higgs boson of the Standard Model

An introduction is made to the key concepts of gauge invariance and spontaneous symmetry breaking which are the foundations of the Standard Model of particle physics. A new scalar field corresponding to a spin-0 particle, the Higgs boson, is a necessary consequence of this model. Properties of the Higgs boson are constrained; however, its mass is not. Searches using LEP have been both unique, intense, and also efficient: the Standard Model Higgs boson must be heavier than 114 GeV$/{\mathrm{c}}^2$. A hint of a signal was obtained at 115 GeV$/{\mathrm{c}}^2$, but will have to be confirmed (or falsified) by forthcoming experiments at the Tevatron and LHC. To cite this article: M. Davier, C. R. Physique 8 (2007).