Higgs Bosons in Extra Dimensions

In this paper, motivated by the recent discovery of a Higgs-like boson at the LHC with a mass m_H\simeq 126 GeV, we review different models where the hierarchy problem is solved by means of a warped extra dimension. In the Randall-Sundrum model electroweak observables provide very strong bounds on the mass of KK modes which motivates extensions to overcome this problem. Two extensions are briefly discussed. One particular extension is based on the deformation of the metric such that it strongly departs from the AdS_5 structure in the IR region while it goes asymptotically to AdS_5 in the UV brane. This model has the IR brane close to a naked metric singularity (which is outside the physical interval) characteristic of soft-walls constructions. The proximity of the singularity provides a strong wave-function renormalization for the Higgs field which suppresses the T and S parameters. The second class of considered extensions are based on the introduction of an extra gauge group in the bulk such that the custodial SU(2)_R symmetry is gauged and protects the T parameter. By further enlarging the bulk gauge symmetry one can find models where the Higgs is identified with the fifth component of gauge fields and for which the Higgs potential, along with the Higgs mass, can be dynamically determined by the Coleman-Weinberg mechanism.Comment: 29 pages, 13 figures. Invited review for IJMP

Novel Effects in Electroweak Breaking from a Hidden Sector

The Higgs boson offers a unique window to hidden sector fields S_i, singlets under the Standard Model gauge group, via the renormalizable interactions |H|^2 S_i^2. We prove that such interactions can provide new patterns for electroweak breaking, including radiative breaking by dimensional transmutation consistent with LEP bounds, and trigger the strong enough first order phase transition required by electroweak baryogenesis.Comment: 4 pages, 6 figure

Electroweak and supersymmetry breaking from the Higgs discovery

We will explore the consequences on the electroweak breaking condition, the mass of supersymmetric partners and the scale at which supersymmetry is broken, for arbitrary values of the supersymmetric parameters tan(beta) and the stop mixing X_t, which follow from the Higgs discovery with a mass m_H\simeq 126 GeV at the LHC. Within the present uncertainty on the top quark mass we deduce that radiative breaking requires tan(beta) \gtrsim 7 for maximal mixing X_t\simeq \sqrt{6}, and tan(beta) \gtrsim 20 for small mixing X_t\lesssim 1. The scale at which supersymmetry is broken \mathcal M can be of order the unification or Planck scale only for large values of tan(beta) and negligible mixing X_t\simeq 0. On the other hand for maximal mixing and large values of tan(beta) supersymmetry should break at scales as low as \mathcal M\simeq 10^5 GeV. The uncertainty in those predictions stemming from the uncertainty in the top quark mass, i.e. the top Yukawa coupling, is small (large) for large (small) values of tan(beta). In fact for tan(beta)=1 the uncertainty on the value of \mathcal M is of several orders of magnitude.Comment: 16 pages, 7 figures; v2: numerical typo corrected in codes, and 2 loop radiative corrections added. Some conclusions slightly change

gμ−2g_\mu-2 from Vector-Like Leptons in Warped Space

The experimental value of the anomalous magnetic moment of the muon, as well as the LHCb anomalies, point towards new physics coupled non-universally to muons and electrons. Working in extra dimensional theories, which solve the electroweak hierarchy problem with a warped metric, strongly deformed with respect to the AdS$_5$ geometry at the infra-red brane, the LHCb anomalies can be solved by imposing that the bottom and the muon have a sizable amount of compositeness, while the electron is mainly elementary. Using this set-up as starting point we have proven that extra physics has to be introduced to describe the anomalous magnetic moment of the muon. We have proven that this job is done by a set of vector-like leptons, mixed with the physical muon through Yukawa interactions, and with a high degree of compositeness. The theory is consistent with all electroweak indirect, direct and theoretical constraints, the most sensitive ones being the modification of the $Z\bar\mu\mu$ coupling, oblique observables and constraints on the stability of the electroweak minimum. They impose lower bounds on the compositeness ($c\lesssim 0.37$) and on the mass of the lightest vector-like lepton ($\gtrsim 270$ GeV). Vector-like leptons could be easily produced in Drell-Yan processes at the LHC and detected at $\sqrt{s}=13$ TeV.Comment: 42 pages, 15 figures; v2 added reference

Electroweak vacuum stability and finite quadratic radiative corrections

If the Standard Model (SM) is an effective theory, as currently believed, it is valid up to some energy scale $\Lambda$ to which the Higgs vacuum expectation value is sensitive throughout radiative quadratic terms. The latter ones destabilize the electroweak vacuum and generate the SM hierarchy problem. For a given perturbative Ultraviolet (UV) completion, the SM cutoff can be computed in terms of fundamental parameters. If the UV mass spectrum involves several scales the cutoff is not unique and each SM sector has its own UV cutoff $\Lambda_i$. We have performed this calculation assuming the Minimal Supersymmetric Standard Model (MSSM) is the SM UV completion. As a result, from the SM point of view, the quadratic corrections to the Higgs mass are equivalent to finite threshold contributions. For the measured values of the top quark and Higgs masses, and depending on the values of the different cutoffs $\Lambda_i$, these contributions can cancel even at renormalization scales as low as multi-TeV, unlike the case of a single cutoff where the cancellation only occurs at Planckian energies, a result originally obtained by Veltman. From the MSSM point of view, the requirement of stability of the electroweak minimum under radiative corrections is incorporated into the matching conditions and provides an extra constraint on the Focus Point solution to the little hierarchy problem in the MSSM. These matching conditions can be employed for precise calculations of the Higgs sector in scenarios with heavy supersymmetric fields.Comment: 36 pages, 5 figures; v2: logarithm corrections included, figures improved, references adde

General Focus Point in the MSSM

The minimal supersymmetric extension of the Standard Model (SM) is a well motivated scenario for physics beyond the SM, which allows a perturbative description of the theory up to scales of the order of the Grand Unification scale, where gauge couplings unify. The Higgs mass parameter is insensitive to the ultraviolet physics and is only sensitive to the scale of soft supersymmetry breaking parameters. Present collider bounds suggest that the characteristic values of these parameters may be significantly larger than the weak scale. Large values of the soft breaking parameters, however, induce large radiative corrections to the Higgs mass parameter and therefore the proper electroweak scale may only be obtained by a fine tuned cancellation between the square of the holomorphic \mu-parameter and the Higgs supersymmetry breaking square mass parameter. This can only be avoided if there is a correlation between the scalar and gaugino mass parameters, such that the Higgs supersymmetry breaking parameter remains of the order of the weak scale. The scale at which this happens is dubbed as focus point. In this article, we define the general conditions required for this to happen, for different values of the messenger scale at which supersymmetry breaking is transmitted to the observable sector, and for arbitrary boundary conditions of the sfermion, gaugino, and Higgs mass parameters. Specific supersymmetry breaking scenarios in which these correlations may occur are also discussed.Comment: 19 pages, 9 figures, new refs. adde