The Limits of Custodial Symmetry

TL;DR

This paper presents a toy model that uses custodial symmetry to protect the Zbb coupling, exploring how varying a Dirac mass parameter influences the model's symmetry properties and deviations from the Standard Model.

Contribution

It introduces a doublet-extended standard model with a softly broken custodial symmetry to study Zbb coupling corrections and symmetry breaking effects.

Findings

The model maintains custodial symmetry for certain parameter ranges.

Adjusting the Dirac mass M interpolates between symmetric and Standard Model-like regimes.

The framework provides insights into protecting Zbb coupling from large corrections.

Abstract

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Zbb 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 that protects the Zbb coupling. 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.