The Limits of Custodial Symmetry

TL;DR

This paper presents a toy model that uses custodial symmetry to protect the Z b_L bbar_L coupling, exploring the effects of a new fermion doublet and symmetry breaking on electroweak interactions.

Contribution

It introduces a doublet-extended standard model with a softly broken O(4) x U(1)_X symmetry to study custodial symmetry protection mechanisms.

Findings

The model demonstrates how adjusting the Dirac mass M interpolates between symmetric and standard-model-like regimes.

It shows potential for protecting Z b_L bbar_L coupling from large corrections.

Provides a framework for exploring custodial symmetry in top-quark sector.

Abstract

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Z b_L bbar_L coupling from large corrections. This "doublet-extended standard model" adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4) x U(1)_X = SU(2)_L x SU(2)_R x P_LR x U(1)_X symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2)_L x U(1)_Y electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M to 0) and standard-model-like (M to infinity) limits.