Oscar Cata

Complete electroweak chiral Lagrangian with a light Higgs at NLO

We consider the Standard Model, including a light scalar boson h, as an effective theory at the weak scale v = 246 GeV of some unknown dynamics of electroweak symmetry breaking. This dynamics may be strong, with h emerging as a pseudo-Goldstone boson. The symmetry breaking scale Λ is taken to be at 4 π v or above. We review the leading-order Lagrangian within this framework, which is nonrenormalizable in general. A chiral Lagrangian can then be constructed based on a loop expansion. A systematic power counting is derived and used to identify the classes of counterterms that appear at one loop order. With this result the complete Lagrangian is constructed at next-to-leading order, O ( v 2 / Λ 2 ) . This Lagrangian is the most general effective description of the Standard Model containing a light scalar boson, in general with strong dynamics of electroweak symmetry breaking. Scenarios such as the {SILH} ansatz or the dimension-6 Lagrangian of a linearly realized Higgs sector can be recovered as special cases.

Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO

A bstractWe consider the Standard Model as an effective theory at the weak scale v of a generic new strong interaction that dynamically breaks electroweak symmetry at the energy scale Λ ~ (few) TeV. Assuming only the minimal field content with the Standard Model fermions and gauge bosons, but without a light Higgs particle, we construct the complete Lagrangian through next-to-leading order, that is, including terms of order v2/Λ2. The systematics behind this expansion is clarified. Although similar to chiral perturbation theory, it is not governed by the dimension of operators alone, but depends in an essential way on the loop expansion. Power-counting formulas are derived that indicate the classes of operators required at the next-to-leading order. The complete set of operators at leading and next-to-leading order is then listed, based on the restrictions implied by the Standard Model gauge symmetries. We recover the well-known operators discussed in the literature in connection with the electroweak chiral Lagrangian and in similar contexts, but we collect a complete and systematic list of all terms through order v2/Λ2. This includes some operators not discussed in explicit terms before. We also show that a few of the previously considered operators can be eliminated via the equations of motion. As another important result we confirm the known list of dimension-6 operators in the Standard Model with an elementary Higgs doublet, essentially as a special case of our scenario.

On the power counting in effective field theories

Abstract We discuss the systematics of power counting in general effective field theories, focusing on those that are nonrenormalizable at leading order. As an illuminating example we consider chiral perturbation theory gauged under the electromagnetic U ( 1 ) symmetry. This theory describes the low-energy interactions of the octet of pseudo-Goldstone bosons in QCD with photons and has been discussed extensively in the literature. Peculiarities of the standard approach are pointed out and it is shown how these are resolved within our scheme. The presentation follows closely our recent discussion of power counting for the electroweak chiral Lagrangian. The systematics of the latter is reviewed and shown to be consistent with the concept of chiral dimensions. The results imply that naive dimensional analysis (NDA) is incomplete in general effective field theories, while still reproducing the correct counting in special cases.

A systematic approach to the SILH Lagrangian

Abstract We consider the electroweak chiral Lagrangian, including a light scalar boson, in the limit of small ξ = v 2 / f 2 . Here v is the electroweak scale and f is the corresponding scale of the new strong dynamics. We show how the conventional SILH Lagrangian, defined as the effective theory of a strongly-interacting light Higgs (SILH) to first order in ξ , can be obtained as a limiting case of the complete electroweak chiral Lagrangian. The approach presented here ensures the completeness of the operator basis at the considered order, it clarifies the systematics of the effective Lagrangian, guarantees a consistent and unambiguous power counting, and it shows how the generalization of the effective field theory to higher orders in ξ has to be performed. We point out that terms of order ξ 2 , which are usually not included in the SILH Lagrangian, are parametrically larger than terms of order ξ / 16 π 2 that are retained, as long as ξ ≳ 1 / 16 π 2 . Conceptual issues such as custodial symmetry and its breaking are also discussed. For illustration, the minimal composite Higgs model based on the coset SO ( 5 ) / SO ( 4 ) is considered at next-to-leading order in the chiral expansion. It is shown how the effective Lagrangian for this model is contained as a special case in the electroweak chiral Lagrangian based on SU ( 2 ) L ⊗ SU ( 2 ) R / SU ( 2 ) V .

Nonstandard Higgs couplings from angular distributions in h\rightarrow Z\ell ^+\ell ^-

We compute the fully differential rate for the Higgs-boson decay

Note on anomalous Higgs-boson couplings in effective field theory

hrightarrow Zell ^+ell ^-

Dark Matter Decays from Nonminimal Coupling to Gravity

h→Zℓ+ℓ-, with