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Register a new user$delta_{CP}$ for leptons and a new take on CP physics with the FSM
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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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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 $delta_{rm CP}$.
In a new simple application of the non-Abelian discrete symmetry $A_4$ to charged-lepton and neutrino mass matrices, we show that for the current experimental central value of $sin^2 2 theta_{13} simeq 0.1$, leptonic CP violation is necessarily large, i.e. $|tan delta_{CP}| > 1.3$.
We have analyzed how much the $CP$ angles to be measured at B factories can deviate from the geometrical ones defined in unitarity triangle under the existence of new physics. The measurements are given in rephasing invariant form. If KM matrix is not a $3times 3$ and unitary matrix, $tildephi_1$ and $tildephi_3$ is affected, and the value of $tildephi_3$ depends on the decay mode. The deviation is constrained to be less than the experimental precision attained in the next decade by the available data of the magnitude of KM matrix elements. Deviation of the sum of three angles from $pi$ cannot be detected unless new physics contributes significantly to $b$ decay or $D$ meson system.
Assuming that neutrinos acquire radiative seesaw Majorana masses through their interactions with dark matter, i.e. scotogenic from the Greek scotos meaning darkness, and using the non-Abelian discrete symmetry $A_4$, we propose a model of neutrino masses and mixing with nonzero $theta_{13}$ and necessarily large leptonic CP violation, allowing both the normal and inverted hierarchies of neutrino masses, as well as quasi-degenerate solutions.
Contributions to B - bar B mixing from physics beyond the standard model may be detected from CP-violating asymmetries in B decays. There exists the possibility of large new contributions that cannot be detected by first generation experiments because of a discrete ambiguity. Some possible strategies for resolving this are discussed.
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