(Dys)Zphilia or a custodial breaking Higgs at the LHC

Electroweak precision measurements established that custodial symmetry is preserved to a good accuracy in the gauge sector after electroweak symmetry breaking. However, recent LHC results might be interpreted as pointing towards Higgs couplings that do not respect such symmetry. Motivated by this possibility, we reconsider the presence of an explicitly custodial breaking coupling in a generic Higgs parameterization. After briefly commenting on the large UV sensitivity of the T parameter to such a coupling, we perform a fit to results of Higgs searches at LHC and Tevatron, and find that the apparent enhancement of the ZZ channel with respect to WW can be accommodated. Two degenerate best-fit points are present, which we label `Zphilic' and `dysZphilic' depending on the sign of the hZZ coupling. Finally we highlight some measurements at future linear colliders that may remove such degeneracy.