Two-loop corrections to the $\rho$ parameter in Two-Higgs-Doublet Models

Models with two scalar doublets are among the simplest extensions of the Standard Model which fulfill the relation \(\rho = 1\) at lowest order for the \(\rho \) parameter as favored by experimental data for electroweak observables allowing only small deviations from unity. Such small deviations \(\varDelta \rho \) originate exclusively from quantum effects with special sensitivity to mass splittings between different isospin components of fermions and scalars. In this paper the dominant two-loop electroweak corrections to \(\varDelta \rho \) are calculated in the CP-conserving THDM, resulting from the top-Yukawa coupling and the self-couplings of the Higgs bosons in the gauge-less limit. The on-shell renormalization scheme is applied. With the assumption that one of the CP-even neutral scalars represents the scalar boson observed by the LHC experiments, with standard properties, the two-loop non-standard contributions in \(\varDelta \rho \) can be separated from the standard ones. These contributions are of particular interest since they increase with mass splittings between non-standard Higgs bosons and can be additionally enhanced by \(\tan \beta \) and \(\lambda _5\), an additional free coefficient of the Higgs potential, and can thus modify the one-loop result substantially. Numerical results are given for the dependence on the various non-standard parameters, and the influence on the calculation of electroweak precision observables is discussed.