The Limits of Custodial Symmetry

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the 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) × U(1)_X ~ SU(2)_L × SU(2)_R × P_LR × U(1)_X symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2)_L × 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 → 0) and standard-model-like (M → ∞) limits.