Correlating the Higgs and Kaon Sector CP Violations

Taking the most general two-doublet models with explicit CP violation in the Higgs sector but no phase in the CKM matrix, we determine the correlation between the Higgs and Kaon sectors using the experimental values of ∆MK and ǫK . It is found that: there is a direct correlation between strength of FCNC couplings and the Higgs masses, and the lightest Higgs is nearly pure CP–even, but this small CP–odd composition gives large enough contribution to ǫK . In the standard electroweak theory (SM), the single phase in the CKM matrix [1] is the unique source of CP violation which can appear only in the charged current interactions. The physics beyond the SM, however, introduces novel sources of CP violation which can arise in charged as well as neutral current vertices. Indeed, CP violation observables offer quite useful tools [2] in search for new physics in near future B factories such as LHC-B [3]. However, for a given model comprising the SM one has to saturate all observables either conserving or violating the CP symmetry. In this letter, we assume that there is no CP violation in the SM, i.e., CKM matrix is real. Furthermore, we take the most general two–doublet model with explicit CP violation. Then we attempt to answer the following question: ”Under such circumtances, what is the correlation between Higgs sector and (B, K)CP observables ?” In fact, possibility of a real CKM matrix was discussed in [4] by taking into account all constraints from K and B systems: The present experimental constraints allow for a real CKM matrix provided that the physics beyond the SM contributes to both K and B d systems. In particular, at least 20% of ∆MBd should follow from new physics contribution modulo other conditions coming from K system. Unlike [4] which assumes spontaneous CP violation, we will restrict ourselves to explicit CP violation in the Higgs sector. In case of spontaneous CP violation which guarantees CP invariance of the Lagrangian before the electroweak Preprint submitted to Physics Letters B breaking, it is possible to keep CKM matrix real by introducing appropriate discrete symmetries [4]. However, with explicit CP violation in the Higgs sector one can not generate a real CKM matrix naturally. In such a case one can take reality of CKM matrix granted and analyze (K, B)CP observables with pure new physics CP violation coming from the Higgs sector only. In passing, one notes that in case of spontaneous CP violation electroweak baryogenesis constraints imply a light pseudoscalar Higgs [5]. In summary, in what follows we will assume that CKM matrix is pure real and all CP violation effects in the (K, B) system spring from the explicit CP violation in the Higgs potential. We adopt a general two–doublet model [6] with most general CP–violating soft and hard operators: V (Φ1,Φ2) = μ 2 1 Φ†1Φ1 + μ 2 2 Φ†2Φ2 + [ μ 12 Φ†1Φ2 + h.c. ] +λ1(Φ † 1Φ1) 2 + λ2(Φ † 2Φ2) 2 + λ3(Φ † 1Φ1Φ † 2Φ2) + λ4(Φ † 1Φ2Φ † 2Φ1) + 1 2 [ λ5(Φ † 1Φ2) 2 + h.c. ]