Leaks of CP violation in the real two-Higgs-doublet model

Abstract

We discuss the $$Z_2$$ 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.

The one-loop impact of a dependent mass: the role of $m_3$ in the C2HDM

“…Details on the Type II C2HDM and its renormalization can be found in refs. [24,25]. Here, we summarize the most relevant aspects for the analysis of the mass and decays of h 3 .…”

“…2 As a consequence, m 2 3R cannot be set equal to the squared pole mass of h 3 , which we identify with m 2 3P . Up to one-loop level, the two masses are related by [24]:…”

“…[3][4][5]. One of the most common models-the so-called real 2-Higgs-Doublet model (2HDM), where CP is assumed to be conserved in the potential-was recently suspected of theoretical unsoundness [6]. The model that heals it in the simplest fashion-while accounting for the already observed CP violation-is the complex 2HDM (C2HDM) [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26],…”

“…These require the inclusion of oneloop electroweak corrections, which in turn require the one-loop electroweak renormalization of the model at stake. We have recently presented the one-loop renormalization of the C2HDM [24], and showed that it configures a rather unique program of renormalization. Indeed, there are more independent counterterms than independent renormalized parameters, which means that several combinations of the former can be chosen for the same set of the latter.…”

CP Phases in 2HDM and Effective Potential: A Geometrical View

“…Ref. [29] studied the possibility of the Jarlskog invariant entering the effective potential at three loop level, but their calculation of three-loop tadpole diagrams of the CP-odd scalar field shows no impact from the Jarlskog invariant. We notice that the CP violation effect appears in the effective potential only in the form of SO(3) K tensors.…”