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

Abstract

Models with two scalar doublets are among the simplest extensions of the Standard Model which fulfill the relation ρ = 1 at lowest order for the ρ parameter as favored by experimental data for electroweak observables allowing only small deviations from unity. Such small deviations Δρ originate exclusively from quantum effects with special sensitivity to mass splittings between different isospin components of fermions and scalars. In this paper the dominant twoloop electroweak corrections to Δρ are calculated in the C Pconserving 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 C P-even neutral scalars represents the scalar boson observed by the LHC experiments, with standard properties, the two-loop non-standard contributions in Δρ 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 β and λ 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.

Constraining the gauge and scalar sectors of the doublet left-right symmetric model

“…There are also computations of the related quantity ∆ρ which is defined as the difference of the Z and W self-energies at zero momentum transfer, each being weighted by the inverse of the square of the mass of the respective gauge boson, for example in the framework of the two Higgs doublet model [60,61]. In the SM the loop corrections to ∆ρ are finite, but this feature is not necessarily true in models beyond the SM.…”

Muon g−2 in the 2HDM: Maximum results and detailed phenomenology

“…Similar to the quantity Δρ, this contribution is enhanced by large mass splittings jM H − M H AE j between the heavy Higgs bosons. Conversely, constraints on Δρ restrict this mass splitting [22,51] and thus a non-Yuk μ . We find that a non-Yuk μ is similarly negligible as Eq.…”

“…(iv) The mass splitting between M H and M H AE is unimportant. It is strongly restricted by limits from electroweak precision observables [22,51] and we have checked that its remaining influence on the limits on ζ l , ζ u and on the bosonic contributions a B μ is negligible. Hence we set M H ¼ M H AE in all our numerical examples.…”

New scenario for aligned Higgs couplings originated from the twisted custodial symmetry at high energies

“…This indicates that Z 7 can take a non-zero value while keeping the smallness of the T parameter at the one-loop level. However, we have finite scalar-loop contributions to ∆T at two-loop level in such a scenario [64]. In this paper, we do not consider such a scenario and, we concentrate on explaining the values of low energy observables in terms of the global symmetry of the Higgs potential.…”