Twisted Custodial Symmetry in Two-Higgs-Doublet Models

In the standard model for electroweak interactions, the Higgs sector is known to display a custodial symmetry protecting the mass relation $m_{W^{\pm }}^2=m_{W_3}^2$ from large corrections. When considering extensions of the scalar sector, this symmetry has to be introduced by hand in order to pass current electroweak precision tests in a natural way. In this Letter, we implement a generalized custodial symmetry in the two-Higgs-doublet model. Assuming the invariance of the potential under $CP$ transformations, we prove the existence of a new custodial scenario characterized by $m_{H^{\pm }}^2=m_{H^0}^2$ instead of $m_{H^{\pm }}^2=m_{A^0}^2$. Consequently, the pseudoscalar $A^0$ may be much lighter than the charged $H^{\pm }$, giving rise to interesting phenomenology.