A Twisted custodial symmetry in the two-Higgs-doublet model

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. Comment: 4 pages, RevTeX