Higgs Lagrangian from gauge theories

1998

A new method of deriving the Higgs Lagrangian from vector-like gauge theories is explored. After performing a supersymmetric extension of gauge theories we identify the auxiliary field associated with the "meson" superfield, in the low energy effective theory, as the composite Higgs field. The auxiliary field, at tree level, has a "negative squared mass". By computing the one-loop effective action in the low energy effective theory, we show that a kinetic term for the auxiliary field emerges when an explicit non-perturbative mechanism for supersymmetry breaking is introduced. We find that, due to the naive choice of the Kähler potential, the Higgs potential remains unbounded from the below. A possible scenario for solving this problem is presented. It is also shown that once chiral symmetry is spontaneously broken via a non-zero vacuum expectation value of the Higgs field, the low energy composite fermion field acquires a mass and decouples, while in the supersymmetric limit it was kept massless by the 't Hooft anomaly matching conditions. 11.30.Pb, 11.30.Qc

2021

The spontaneous symmetry breaking for the massless scalar field naturally arises from the frame-work of the effective theory (the non-minimal coupling of gravity to a scalar field). A magic key ingredient is to add the large vacuum energy density, contributing to the cosmological constant, to the Lagrangian density. By applying this modified spontaneous symmetry breaking with the gauge theory (called modified Higgs mechanism), the inflation physics and the electroweak phase transition can be generated from the same framework. However, this comes with the huge price-the large cosmological constant which is known as the dark energy problem. The possible solution of this issue is also discussed.

arXiv (Cornell University), 2014

Probing the properties of the discovered Higgs boson may tell us whether or not it is the same particle as the one predicted by the Standard Model. To this aim we parametrize deviations of the Higgs couplings to matter from the Standard Model by using the Higgs Effective Field Theory framework. Starting with a general dimension-6 effective Lagrangian including both CP-even and CP-odd operators, and requiring that the operators do not introduce power divergences in the oblique parameters, we reduce the number of independent effective couplings of the theory. This framework is then used to put updated constraints on the effective couplings, using the latest Higgs rates data from the Run-I of the ATLAS and CMS experiments, and electroweak precision data from LEP, SLC and Tevatron. We show that the current data is able to significantly constrain the CP-even and some CP-odd operators of the effective Lagrangian.

2015

Depending on whether electroweak physics beyond the Standard Model is based on a linear or on a non-linear implementation of the electroweak symmetry breaking, a linear or a chiral Effective Lagrangian is more appropriate. In this talk, the main low-energy signals that allow to recognize whether the observed Higgs scalar is a dynamical (composite) particle or rather an elementary one are presented, in a model-independent way. The patterns of effective couplings produced upon the assumption of specific composite Higgs models are also discussed.

arXiv (Cornell University), 2015

The study of the properties of the scalar boson recently discovered at the LHC [1, 2] may allow us to know whether it is well described by the Standard Model. In the case where deviations from SM predictions are present, this would be an evidence for the presence of new physics. We focus on the study of the Higgs couplings to matter in a model-independent approach by introducing a dimension-6 effective Lagrangian that includes both CP-even and CP-odd effective couplings. Constraints are set on some of these coefficients using experimental data from ATLAS and CMS as well as electroweak precision measurements from LEP, SLC and Tevatron. These data meaningfully constrain CPeven and some CP-odd couplings. 1

Spontaneous Breaking of Global Gauge Symmetries in the Higgs Mechanism, 2024

The Higgs mechanism is invoked to explain how gauge bosons can be massive while Yang-Mills theory describes only massless gauge fields. Central to it is the notion of spontaneous symmetry breaking (SSB), applied to the SU(2) × U(1) gauge symmetry of the electroweak theory. However, over the past two decades, philosophers of physics have challenged the standard narrative of the Higgs mechanism as an instance of gauge symmetry breaking. They have pointed out the apparent contradiction between the status of gauge symmetries as mathematical redundancies and the account of mass generation in the Higgs mechanism by means of gauge symmetry breaking. In addition, they have pointed to Elitzur's theorem, a result from lattice gauge theory forbidding local gauge symmetry breaking. This has led philosophers to the conclusion that there cannot be any SSB in the Higgs mechanism, an idea supported by the dressing field method of gauge symmetry reduction. In this thesis we mitigate this conclusion by showing that global gauge symmetries, i.e. transformations independent of spacetime, are not mere mathematical redundancies but carry direct empirical significance. This can be seen from constrained Hamiltonian analysis by the fact that the Gauss constraint in Yang-Mills theory only generates gauge transformations which asymptotically become the identity. The classical Higgs mechanism can indeed be reformulated as a breaking of only this global gauge symmetry. We subsequently extend this result to quantum field theory by considering SSB in algebraic quantum field theory (AQFT). The Abelian U(1) Higgs mechanism can be shown to be an instance of SSB in the algebraic sense and we discuss the extent to which this can be generalised to the non-Abelian case. Finally we discuss the implications of our results for the interpretation of the electroweak phase transition and the analogy between the Higgs mechanism and superconductivity.

The European Physical Journal C, 2008

We compute the relevant parameters of the combined Higgs and φ scalar effective potential in the Littlest Higgs (LH) model. These parameters are obtained as the sum of two kind of contributions. The first one is the one-loop radiative corrections coming from fermions and gauge bosons. The second one is obtained at the tree level from the higher order effective operators needed for the ultraviolet completion of the model. Finally we analyze the restrictions that the requirement of reproducing the standard electroweak symmetry breaking of the SM set on the LH model parameters.

Advanced series on directions in high energy physics, 1997

We review the constraints on Higgs boson properties from effective potential methods. In the Standard Model, the requirement of stability (or metastability) of the standard electroweak minimum puts an upper bound on the scale of new physics as a function of the Higgs mass. This upper bound is below the Planck scale if the Higgs weights < ∼ 130 GeV. In supersymmetric extensions of the Standard Model the former methods are useful to compute the Higgs mass spectrum, and couplings, after resumming higher loop effects. In particular, if the Higgs mass weights > ∼ 130 GeV, the minimal supersymmetric extension of the Standard Model will be ruled out, while its non-minimal supersymmetric extension containing singlets is only marginally allowed.

2011

The Higgs mechanism gives mass to Yang-Mills gauge bosons. According to the conventional wisdom, this happens through the spontaneous breaking of gauge symmetry. Yet, gauge symmetries merely reflect a redundancy in the state description and therefore the spontaneous breaking can not be an essential ingredient. Indeed, as already shown by Higgs and Kibble, the mechanism can be explained in terms of gauge invariant variables, without invoking spontaneous symmetry breaking. In this paper, we present a general discussion of such gauge invariant treatments for the case of the Abelian Higgs model, in the context of classical field theory. We thereby distinguish between two different notions of gauge: one that takes all local transformations to be gauge and one that relates gauge to a failure of determinism.

Assuming dynamical spontaneous breakdown of chiral symmetry for massless gauge theory without scalar fields, we present a method how to construct an effective action of the dynamical Nambu-Goldstone bosons and elemetary fermions by using auxiliary fields. Here dynamical particles are asssumed to be composed of elementary fermions. Various quantities including decay constants are calculated from this effective action. This technique is also applied to gauge symmetry breakdown, SU (5) → SU (4), to obtain massive gauge fields.