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Register a new userThe framework for a common origin of $delta_{rm CKM}$ and $delta_{rm PMNS}$
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We analyse a possible connection between CP violations in the quark and lepton sectors, parametrised by the CKM and PMNS phases. If one assumes that CP breaking arises from complex Yukawa couplings, both in the quark and lepton sectors, the above connection is not possible in general, since Yukawa couplings in the two sectors have independent flavour structures. We show that both the CKM and PMNS phases can instead be generated by a vacuum phase in a class of two Higgs doublet models, and in this case a connection may be established. This scenario requires the presence of scalar FCNC at tree level, both in the quark and lepton sectors. The appearance of these FCNC is an obstacle and a blessing. An obstacle since one has to analyse which models are able to conform to the strict experimental limits on FCNC, both in the quark and lepton sectors. A blessing, because this class of models is falsifiable since FCNC arise at a level which can be probed experimentally in the near future, specially in the processes $hto e^pmtau^mp$ and $tto h c$. The connection between CP violations in CKM and PMNS is explicitely illustrated in models with Minimal Flavour Violation.
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The recent established large $theta_{13}$ in neutrino mixing provides an optimistic possibility for the investigation of the CP violation, therefore it is necessary to study the CP-violating phase $delta_{rm CP}$ in detail. Based on the maximal CP violation hypothesis in the original Kobayashi-Maskawa (KM) scheme of neutrino mixing matrix, i.e., $delta_{rm KM}=90^circ$, we calculate $delta_{rm CK}$ for both quarks and leptons in the Chau-Keung (CK) scheme of the standard parametrization and find that $delta^{mathrm{quark}}_{mathrm{CK}}=(68.62^{+0.89}_{-0.81})^circ$ and $delta^{mathrm{lepton}}_{mathrm{CK}}=(85.39^{+4.76}_{-1.82})^circ$, provided with three mixing angles to be given. We also examine the sensitivity of $|V_{ij}|$ and $|U_{ij}|$ to $delta_{rm CK}$ and $delta_{rm KM}$. As a convention-independent investigation, we discuss the $Phi$ matrix, which has elements correspond to angles of the unitarity triangles. We demonstrate the $Phi$ matrices for both quark and lepton sectors and discuss the implications as well as the variations of the $Phi$ matrix elements with $delta_{rm CP}$.
A bonus of the framed standard model (FSM), constructed initially to explain the mass and mixing patterns of quarks and leptons, is asolution (without axions) of the strong CP problem by cancelling the theta-angle term $theta_I$ $Tr (H^{mu u} H^*_{mu u})$ in colour by a chiral transformation on a quark zero mode which is inherent in FSM, and produces thereby a CP-violating phase in the CKM matrix similar in size to what is observed. Extending here to flavour, one finds that there are two terms proportional to $Tr (G^{mu u}G^*_{mu u})$: (a) in the action from flavour instantons with unknown coefficient, say $theta_I$, (b) induced by the above FSM solution to the strong CP-problem with therefore known coefficient $theta_C$. Both terms can be cancelled in the FSM by a chiral transformation on the lepton zero mode to give a Jarlskog invariant $J$ in the PMNS matrix for leptons of order $10^{-2}$, as is hinted by experiment. But if the term $theta_I$ is to be cancelled by a chiral transformation in the predicted hidden sector to solve the strong CP problem therein, leaving only the term $theta_C$ to be cancelled by the chiral transformation on leptons, then the following prediction results: $Jsim-0.012$ ($delta_{CP}sim(1.11)pi$) which is (i) of the right order, (ii) of the right sign, (iii) in the range favoured by present experiment. Together with the earlier result for quarks, this offers an attractive unified treatment of all known CP physics.
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