Theoretical constraints on the Higgs effective couplings

We derive constraints on the sign of couplings in an effective Higgs Lagrangian using prime principles such as the naturalness principle, global symmetries, and unitarity. Specifically, we study four dimension-six operators, O-H, O-y, O-g, and O-gamma, which contribute to the production and decay of the Higgs boson at the Large Hadron Collider (LHC), among other things. Assuming the Higgs is a fundamental scalar, we find: 1) the coefficient of O-H is positive except when there are triplet scalars, resulting in a reduction in the Higgs on-shell coupling from their standard model (SM) expectations if no other operators contribute, 2) the linear combination of O-H and O-y controlling the overall Higgs coupling to fermion is always reduced, 3) the sign of O-g induced by a new colored fermion is such that it interferes destructively with the SM top contribution in the gluon fusion production of the Higgs, if the new fermion cancels the top quadratic divergence in the Higgs mass, and 4) the correlation between naturalness and the sign of O-gamma is similar to that of O-g, when there is a new set of heavy electroweak gauge bosons. Next considering a composite scalar for the Higgs, we find the reduction in the on-shell Higgs couplings persists. If further assuming a collective breaking mechanism as in little Higgs theories, the coefficient of O-H remains positive even in the presence of triplet scalars. In the end, we conclude that the gluon fusion production of the Higgs boson is reduced from the SM rate in all composite Higgs models. Our study suggests a wealth of information could be revealed by precise measurements of the Higgs couplings, providing strong motivations for both improving on measurements at the LHC and building a precision machine such as the linear collider.

Effective Lagrangian Perspectives on Electroweak Symmetry Breaking

Andrea Thamm

We use an effective Lagrangian approach to address the question of the dynamics of electroweak symmetry breaking in the Standard Model (SM) and its relation to the hierarchy problem. Composite Higgs models provide a solution by describing the recently discovered Higgs-like scalar particle as a composite pseudo Nambu-Goldstone boson that dissolves into its constituents above a certain high energy scale. We discuss many features of the low energy description of composite Higgs models and present an explicit realisation in a flat extra dimension showing explicitly that top partners with masses below 1TeV are expected in a natural theory. Naturalness requires New Physics not much above the weak scale and hence motivates the search for direct and indirect evidence of physics beyond the SM at the LHC and future colliders. As an indirect probe at the LHC, we propose a dedicated analysis of single top production in association with a Higgs boson to lift the degeneracy in the sign of the top Yukawa coupling. We move on to an extensive study of WW scattering, double and triple Higgs production at future linear colliders to estimate their impact on the parameter space of a strongly interacting Higgs boson. Direct probes of New Physics at the LHC include the search for heavy vectors and fermions. We introduce a model-independent strategy to study narrow resonances which we apply to a heavy vector triplet of the SM for illustration. We conclude by summarising current constraints and the expected reach of future colliders on the parameter space of a minimal composite Higgs model. This thesis is based on the papers in Refs. [1–4].

EPFL2014

Composite Higgs as a Viable Scenario for Electro-Weak Symmetry Breaking

Jan Mrazek

This thesis presents a general discussion of the Composite Higgs scenario of Electro-Weak Symmetry Breaking (EWSB). We start by reviewing the Standard Model of Electro-Weak interaction, discussing its experimental tests and conceptual pitfalls. Emphasis is given to the effective field theory point of view. In particular, the inherent tension related to the stability of the Electro-Weak scale motivates us to explore the possibility of having the Higgs field emerging as a Nambu-Goldstone boson from a new strongly coupled sector. Our construction is to a large extent inspired by the picture of the long range dynamics of QCD. The main ingredients are the symmetry of the UV theory, the pattern of its spontaneous breakdown and the sources of explicit breaking. In QCD, the latter are provided by the light quark masses and by the electromagnetic interaction. In Composite Higgs models, the most relevant symmetry breaking couplings are those related to the generation of the third family quark Yukawas through partial compositeness. They generate a potential for the Higgs and thus trigger EWSB. The constraints on the scenario are exposed, with a particular emphasis on the composite Two Higgs Doublet Model (THDM). While a residual SO(4) symmetry is sufficient to ensure a realistic phenomenology in presence of a single composite Higgs doublet, an extended Higgs sector needs more symmetries. For two doublets we show how either CP or a ℤ2 symmetry can play this role and construct a model for each realisation relying on the SO(6)/SO(4) × SO(2) coset. Finally, we discuss the phenomenology of this scenario. In particular, we present de differences between an elementary and a composite THDM. We also conclude that composite fermions associated to the third family quarks seem to be the most promising experimental handles for these models. We discuss their discovery range at the LHC, and the possibility of measuring the structure of their couplings. This knowledge would allow important insight into the strong dynamics.

EPFL2011

Naturalness and Neutral Naturalness in the LHC Era

Davide Greco

We present two different approaches to solve the hierarchy problem of the Standard Model and to provide a consistent dynamical mechanism for electroweak symmetry breaking. As a first scenario, we follow the naturalness paradigm as realized in Composite Higgs theories, which conceive the Higgs particle as a bound state of a new strongly interacting sector confining at the TeV scale. We present a minimal implementation of the model and study in detail the phenomenology of vector resonances, which are predicted as states excited from the vacuum by the conserved currents of the new strong dynamics. This analysis allows us to derive constraints on the parameter space of Composite Higgs models from the presently available LHC data and to confront naturalness with experimental results. Motivated by the rising tension between theoretical expectations and the absence of new physics signals at the LHC, we consider as a second possibility the neutral naturalness paradigm and address the hierarchy problem by posing the existence of a mirror copy of the Standard Model, as realized in Twin Higgs theories. This new color-blind sector is the main actor in protecting the Higgs mass from large radiative corrections and is un-discoverable at the LHC, allowing us to push far in the ultraviolet the scale where the Standard Model effective theory breaks down and colored resonances appear. We present an implementation of the Twin Higgs program into a composite model and discuss the requirements for uplifting the symmetry protection mechanism also to the ultraviolet theory. After introducing a consistent Composite Twin Higgs model, we consider the constraints imposed on the scale where colored resonances are expected by the determination of the Higgs mass at three loops order, electroweak precision tests and perturbativity of the ultraviolet-complete model. We show that, although allowing in principle the new physics scale to lie far out of the LHC reach, these constructions need the existence of light colored top partners, with a mass of around 2-4 TeV, to comply with indirect observations. Neutral naturalness models may then evade detection at the LHC, but they can be probed and falsified at future colliders.