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Register a new userEffective Field Theory for Heavy Vector Resonances Coupled to the Standard Model
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We construct an effective field theory describing the decays of a heavy vector resonance $V$ into Standard Model particles. The effective theory is built using an extension of Soft-Collinear Effective Theory called SCET$_{rm BSM}$, which provides a rigorous framework for parameterizing decay matrix elements with manifest power counting in the ratio of the electroweak scale and the mass of the resonance, $lambdasim v/m_V$. Using the renormalization-group evolution of the couplings in the effective Lagrangian, large logarithms associated with this scale ratio can be resummed to all orders. We consider in detail the two-body decays of a heavy $Z$ boson and of a Kaluza-Klein gluon at leading and subleading order in $lambda$. We illustrate the matching onto SCET$_{rm BSM}$ with a concrete example of a UV-complete new-physics model.
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We present a practical three-step procedure of using the Standard Model effective field theory (SM EFT) to connect ultraviolet (UV) models of new physics with weak scale precision observables. With this procedure, one can interpret precision measurements as constraints on a given UV model. We give a detailed explanation for calculating the effective action up to one-loop order in a manifestly gauge covariant fashion. This covariant derivative expansion method dramatically simplifies the process of matching a UV model with the SM EFT, and also makes available a universal formalism that is easy to use for a variety of UV models. A few general aspects of RG running effects and choosing operator bases are discussed. Finally, we provide mapping results between the bosonic sector of the SM EFT and a complete set of precision electroweak and Higgs observables to which present and near future experiments are sensitive. Many results and tools which should prove useful to those wishing to use the SM EFT are detailed in several appendices.
We consider a non-linear realization of the electroweak symmetry-breaking pattern $SU(2)_Ltimes SU(2)_R/SU(2)_{L+R}$ to construct a low-energy effective theory, later extended by the inclusion of heavy new-physics resonances. After assuming appropriate high-energy constraints given by Weinberg sum-rules and the asymptotic behaviour of form-factors, we obtain relations between resonance masses and some low-energy effective couplings. These predictions are compared with current experimental data and some resonance mass bounds are inferred.
We develop the geometric formulation of the Standard Model Effective Field Theory (SMEFT). Using this approach we derive all-orders results in the $sqrt{2 langle H^dagger H rangle}/Lambda$ expansion relevant for studies of electroweak precision and Higgs data.
If the Standard Model is understood as the first term of an effective field theory, the anomaly-cancellation conditions have to be worked out and fulfilled order by order in the effective field-theory expansion. We bring attention to this issue and study in detail a subset of the anomalies of the effective field theories at the electroweak scale. The end result is a set of sum rules for the operator coefficients. These conditions, which are necessary for the internal consistency of the theory, lead to a number of phenomenological consequences when implemented in analyses of experimental data. In particular, they not only decrease the number of free parameters in different physical processes but have the potential to relate processes with different flavor content. Conversely, a violation of these conditions would necessarily imply the existence of undetected non-decoupling new physics associated with the electroweak energy scale.
Electroweak baryogenesis is a simple and attractive candidate mechanism for generating the observed baryon asymmetry in the Universe. Its viability is sometimes investigated in terms of an effective field theory of the Standard Model involving higher dimension operators. We investigate the validity of such an effective field theory approach to the problem of identifying electroweak phase transitions strong enough for electroweak baryogenesis to be successful. We identify and discuss some pitfalls of this approach due to the modest hierarchy between mass scales of heavy degrees or freedom and the Higgs, and the possibility of dimensionful couplings violating the decoupling between light and heavy degrees of freedom.
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