Fingerprints of heavy scales in electroweak effective Lagrangians

TL;DR

This paper develops a comprehensive electroweak effective Lagrangian incorporating heavy states, analyzing how integrating out these states influences low-energy couplings, with implications for understanding physics beyond the Standard Model.

Contribution

It constructs a general electroweak effective Lagrangian with heavy bosonic states, exploring their impact on low-energy couplings without assuming a specific Higgs doublet structure.

Findings

Heavy heavy states induce specific patterns in low-energy couplings.

Different descriptions of massive spin-1 fields are shown to be equivalent.

The formalism accommodates a singlet Higgs without assuming doublet structure.

Abstract

The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective Lagrangian, implementing the electroweak chiral symmetry breaking $SU(2)_L\otimes SU(2)_R\to SU(2)_{L+R}$, which couples the known particle fields to heavier states with bosonic quantum numbers $J^P=0^\pm$ and $1^\pm$. We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.