Colorful Imprints of Heavy States in the Electroweak Effective Theory

TL;DR

This paper develops a model-independent framework to analyze the effects of heavy states from ultraviolet completions of the Standard Model on low-energy electroweak couplings, including colored resonances and various spin states.

Contribution

It generalizes previous formalisms to include colored heavy states and provides a comprehensive method to derive low-energy couplings from heavy particle integrations.

Findings

Derived the complete pattern of low-energy couplings from heavy states.

Extended formalism to include colored bosonic and fermionic resonances.

Connected theoretical framework with current experimental searches.

Abstract

We analyze heavy states from generic ultraviolet completions of the Standard Model in a model-independent way and investigate their implications on the low-energy couplings of the electroweak effective theory. We build a general effective Lagrangian, implementing the electroweak symmetry breaking $SU(2)_L\otimes SU(2)_R\to SU(2)_{L+R}$ with a non-linear Nambu-Goldstone realization, which couples the known particles to the heavy states. We generalize the formalism developed in previous works~[1,2] to include colored resonances, both of bosonic and fermionic type. We study bosonic heavy states with $J^P=0^\pm$ and $J^P=1^\pm$, in singlet or triplet $SU(2)_{L+R}$ representations and in singlet or octet representations of $SU(3)_C$, and fermionic resonances with $J=\frac{1}{2}$ that are electroweak doublets and QCD triplets or singlets. Integrating out the heavy scales, we determine the complete pattern of low-energy couplings at the lowest non-trivial order. Some specific types of (strongly- and weakly-coupled) ultraviolet completions are discussed to illustrate the generality of our approach and to make contact with current experimental searches.