Abstract
We formulate a generalization of Higgs effective field theory (HEFT) including arbitrary number of extra neutral and charged Higgs bosons (generalized HEFT, GHEFT) to describe non-minimal electroweak symmetry breaking models. Using the geometrical form of the GHEFT Lagrangian, which can be regarded as a nonlinear sigma model on a scalar manifold, it is shown that the scalar boson scattering amplitudes are described in terms of the Riemann curvature tensor (geometry) of the scalar manifold and the covariant derivatives of the potential. The coefficients of the one-loop divergent terms in the oblique correction parameters S and U can also be written in terms of the Killing vectors (symmetry) and the Riemann curvature tensor (geometry). It is found that perturbative unitarity of the scattering amplitudes involving the Higgs bosons and the longitudinal gauge bosons demands the flatness of the scalar manifold. The relationship between the finiteness of the electroweak oblique corrections and perturbative unitarity of the scattering amplitudes is also clarified in this language: we verify that once the tree-level unitarity is ensured, then the one-loop finiteness of the oblique correction parameters S and U is automatically guaranteed.
Highlights
What is the origin of electroweak symmetry breaking (EWSB)? In the standard model (SM) of particle physics, EWSB is caused by a vacuum expectation value of a complex scalar field, which linearly transforms under the SUð2ÞW × Uð1ÞY electroweak gauge symmetry
As we have shown in the previous section, the tree-level perturbative unitarity requires that the generalized HEFT (GHEFT) scalar manifold be flat at the vacuum
The scalar scattering amplitudes are expressed by the geometry (Riemann curvature) and the symmetry (Killing vectors) of the scalar manifold in the GHEFT
Summary
What is the origin of electroweak symmetry breaking (EWSB)? In the standard model (SM) of particle physics, EWSB is caused by a vacuum expectation value of a complex scalar field (the SM Higgs field), which linearly transforms under the SUð2ÞW × Uð1ÞY electroweak gauge symmetry. Introducing functions the F ðhÞ and VðhÞ which parametrize the phenomenological properties of the 125 GeV Higgs, the HEFT provides a systematic description of a neutral spin-0 particle in the electroweak symmetry breaking sector, including the one-loop radiative corrections [72–83]. It can parametrize the low-energy properties of the 125 GeV Higgs particle in both the strongly and weakly interacting model context. The interaction Lagrangian needs to be arranged carefully to make the theory invariant under the electroweak gauge symmetry SUð2ÞW × Uð1ÞY These extra nonsinglet Higgs particles can be regarded as matter particles in the EWChPT Lagrangian context. We use the CCWZ formulation to construct the GHEFT Lagrangian
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