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Register a new userA prediction of neutrino mixing matrix with CP violating phase
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The latest experimental progress have established three kinds of neutrino oscillations with three mixing angles measured to rather high precision. There is still one parameter, i.e., the CP violating phase, missing in the neutrino mixing matrix. It is shown that a replay between different parametrizations of the mixing matrix can determine the full neutrino mixing matrix together with the CP violating phase. From the maximal CP violation observed in the original Kobayashi-Maskawa (KM) scheme of quark mixing matrix, we make an Ansatz of maximal CP violation in the neutrino mixing matrix. This leads to the prediction of all nine elements of the neutrino mixing matrix and also a remarkable prediction of the CP violating phase $delta_{rm CK}=(85.48^{+4.67(+12.87)}_{-1.80(-4.90)})^circ$ within $1sigma (3sigma)$ range from available experimental information. We also predict the three angles of the unitarity triangle corresponding to the quark sector for confronting with the CP-violation related measurements.
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We propose that the CP violating phase in the CKM mixing matrix is identical to the CP phases responsible for the spontaneous CP violation in the Higgs potential. A specific multi-Higgs model with Peccei-Quinn (PQ) symmetry is constructed to realize this idea. The CP violating phase does not vanish when all Higgs masses become large. There are flavor changing neutral current (FCNC) interactions mediated by neutral Higgs bosons at the tree level. However, unlike general multi-Higgs models, the FCNC Yukawa couplings are fixed in terms of the quark masses and CKM mixing angles. Implications for meson-anti-meson mixing, including recent data on $D-bar D$ mixing, and neutron electric dipole moment (EDM) are studied. We find that the neutral Higgs boson masses can be at the order of one hundred GeV. The neutron EDM can be close to the present experimental upper bound.
A model independent analysis of the leptonic Dirac CP-violating phase ({delta}) is presented. The analysis uses the experimentally determined values of the mixing angles in the lepton mixing matrix in order to explore the allowed values for {delta} and possible general forms for the charged lepton mixing matrix. This is done under two general assumptions: 1) that the mixing matrix in the neutrino sector is the so-called tribimaximal matrix and hence the non zero value for {theta}13 arises due to the mixing matrix in the charged lepton sector and 2) the charged lepton mixing matrix is parametrized in terms of three angles and one phase. It is found that any value of {delta} is still consistent with the data and that, considering the assumptions above, regardless of the value for {delta}, the 1-3 mixing angle in the charged lepton sector is small but non zero and the 2-3 mixing angle can take values in only two possible small ranges around 0 and {pi}/2 respectively.
In the next generation of long-baseline neutrino oscillation experiments, aiming to determine the charge-parity violating phase $delta_{CP}$ in the appearance channel, fine-grained time-projection chambers are expected to play an important role. In this Letter, we analyze an influence of realistic detector capabilities on the $delta_{CP}$ sensitivity for a setup similar to that of the Deep Underground Neutrino Experiment. We find that the effect of the missing energy, carried out by undetected particles, is sizable. Although the reconstructed neutrino energy can be corrected for the missing energy, the accuracy of such procedure has to exceed 20%, to avoid a sizable bias in the extracted $delta_{CP}$ value.
The model of neutrino mass matrix with minimal texture is now tightly constrained by experiment so that it can yield a prediction for the phase of CP violation. This phase is predicted to lie in the range $delta_{CP}=0.77pi - 1.24pi$. If neutrino oscillation experiment would find the CP violation phase outside this range, this means that the minimal-texture neutrino mass matrix, the element of which is all real, fails and the neutrino mass matrix must be complex, i.e., the phase must be present that is responsible for leptogenesis.
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 $delta_{rm CP}$.
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