Abstract
We discuss the Z_2 symmetric two-Higgs-doublet model with a real soft-breaking term (real 2HDM). We explain in detail why it is not tenable to assume CP conservation in the scalar sector to keep the dimension two term real, while CP is violated by the dimension four Yukawa couplings. We propose the calculation of the infinite tadpole of the (would-be) pseudoscalar neutral scalar. We construct a simple toy model with the same flaws, where the unrenormalizable infinity is easier to calculate. We then consider the same tadpole in the real 2HDM. We spearhead this effort focusing on diagrams involving solely bare quantities. This involves hundreds of Feynman three-loop diagrams that could feed the CP violation from the quark into the scalar sector, and is only possible with state of the art automatic computation tools. Remarkably, some intermediate results agree when using three independent derivations, including the peculiar cancellation of the leading pole divergence due to a subtle interplay between masses and the Jarlskog invariant, which we calculate analytically. The calculation is not complete however, since the full two-loop renormalization of the real 2HDM is not yet available in the literature. Still, we argue convincingly that there is an irremovable infinity.
Highlights
The exact implementation of the symmetry breaking sector of the gauge theory describing fundamental particles is one of the most interesting open problems
We argued that the real 2HDM can suffer from theoretical inconsistencies, as the simultaneous enforcement of CP conservation in the potential and allowance of CP violation in another sector may lead to divergences that cannot be removed by the counterterms
In order to highlight its potential theoretical unsoundness we introduced a simple toy model, characterized by the same inconsistency as the real 2HDM
Summary
The exact implementation of the symmetry breaking sector of the gauge theory describing fundamental particles is one of the most interesting open problems. The most studied model includes two Higgs doublets (2HDM) with a Z2 symmetry, softly broken by a real parameter, with the additional requirement that the vacuum expectation values (vev) are taken as real. The crucial point is that the experimentally observed CP violation [6] is accounted for by complex Yukawa couplings This is sometimes referred to as the “real 2HDM”, because the soft Z2 breaking parameter is taken as real. This most prevalent model can suffer from theoretical inconsistencies regarding renormalization, a fact that is mostly ignored.. 2, we discuss the inconsistency of requiring CP conservation in the potential of the real 2HDM, while allowing for CP violation elsewhere.
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