CP4 miracle: shaping Yukawa sector with CP symmetry of order four

Abstract

We explore the phenomenology of a unique three-Higgs-doublet model based on the single CP symmetry of order 4 (CP4) without any accidental symmetries. The CP4 symmetry is imposed on the scalar potential and Yukawa interactions, strongly shaping both sectors of the model and leading to a very characteristic phenomenology. The scalar sector is analyzed in detail, and in the Yukawa sector we list all possible CP4-symmetric structures which do not run into immediate conflict with experiment, namely, do not lead to massless or mass-degenerate quarks nor to insufficient mixing or CP -violation in the CKM matrix. We show that the parameter space of the model, although very constrained by CP4, is large enough to comply with the electroweak precision data and the LHC results for the 125 GeV Higgs boson phenomenology, as well as to perfectly reproduce all fermion masses, mixing, and CP violation. Despite the presence of flavor changing neutral currents mediated by heavy Higgs scalars, we find through a parameter space scan many points which accurately reproduce the kaon CP -violating parameter K as well as oscillation parameters in K and B (s) mesons. Thus, CP4 offers a novel minimalistic framework for building models with very few assumptions, sufficient predictive power, and rich phenomenology yet to be explored.

Radiative neutrino masses from order-4 CP symmetry

“…If CP4 remains unbroken, it produces pairwise mass-degenerate scalar sector and DM candidates with peculiar properties. The same CP4 can also be extended to the quark sector [21,22], also strongly shaping the Yukawa matrices. However, CP4 must be broken in this case to avoid massdegenerate fermions.…”

“…We also see that λ 6 in this model plays the role of λ 5 of the inert doublet model: it governs the mass splitting of the two pairs of inert neutral scalars. CP4 symmetry can also be extended to the fermion sector [21,22]. Requirement that the Yukawa interactions are CP4 invariant forces this transformation to mix fermion generations as well, in the way similar to (2.9).…”

“…The matrices U accompanying a generalized CP transformation can be different for left doublets and right charged lepton and neutrino singlets, see [22] for the similar construction in the quark sector. To avoid massless or mass-degenerate charged leptons, we must assume that CP4 acts trivially on L α and Rα .…”

“…In terminology of [22], this amounts to selecting case A for charged leptons among four possibilities.…”

“…If CP4 remains unbroken, it leads to mass-degenerate quarks or leptons, which must be avoided. One can either assume that CP4 is spontaneously broken -this route was taken in [22]-or decouple fermions from the inert doublets altogether. In the latter path, we can nevertheless allow RH neutrinos to transform non-trivially under CP4, which will lead us to the desired scotogenic model.…”