Predicting CP violation in Deviation from Tri-bimaximal mixing of Neutrinos

We study the CP violation in the deviation from the tri-bimaximal mixing (TBM) of neutrinos. We examine non-trivial relations among the mixing angles and the CP violating Dirac phase in the typical four cases of the deviation from the TBM. The first two cases are derived by the additional rotation of the 2-3 or 1-3 generations of neutrinos in the TBM basis. The other two cases are given by the additional rotation of the 1-3 or 1-2 generations of charged leptons with the TBM neutrinos. These four cases predict different relations among three mixing angles and the CP violating Dirac phase. The rotation of the 2-3 generations of neutrinos in the TBM basis predicts $\sin ^2\theta _{12}<1/3$, and the CP violating Dirac phase to be $\pm (0.09\pi\sim 0.76\pi)$ for NH ($\pm (0.15\pi\sim 0.73\pi) \ \text{for IH}$) depending on $\sin ^2\theta _{23}$. The rotation of the 1-3 generations of neutrinos in the TBM basis gives $\sin ^2\theta _{12}>1/3$. The CP violating Dirac phase is not constrained by the input of the present experimental data. For the case of the 1-3 and 1-2 rotations of charged leptons in the TBM basis, the CP violating Dirac phase is predicted in $\pm(0.35\pi\sim 0.60\pi)$ depending on $\sin ^2\theta _{12}$ for both NH and IH cases. We also discuss the specific case that $\theta_{13}$ is related with the Cabibbo angle $\lambda$ such as $\sin\theta_{13}=\lambda/\sqrt{2}$, in which the maximal CP violation is preferred. The CP violating Dirac phase can distinguish the lepton flavor mixing patterns at T2K and NO$\nu$A experiments in the future.Comment: 18 pages, 22 figures, figures are changed, discussions are adde

Searching for the squark flavor mixing in CP violations of Bs -> K+ K- and K0bar K0 decays

We study CP violations in the B_s-> K+K- and Bs->K0K0 decays in order to find the contribution of the supersymmetry, which comes from the gluino-squark mediated flavor changing current. We obtain the allowed region of the squark flavor mixing parameters by putting the experimental data, the mass difference Delta M_Bs, the CP violating phase phi_s in Bs to J/psi phi decay and the b to s gamma branching ratio. In addition to these data, we take into account the constraint from the asymmetry of B0->K+pi because the Bs->K+K- decay is related with the B0->K+pi- decay by replacing the spectator s with d. Under these constraints, we predict the magnitudes of the CP violation in the Bs->K+K- and Bs->K0K0 decays. The predicted region of the CP violation C_{K+K-} is strongly cut from the direct CP violation of barB0 to K-pi+, therefore, the deviation from the SM prediction of C_{K+K-} is not found. On the other hand, the CP violation S_{K+K-} is possibly deviated from the SM prediction considerably, in the region of 0.1- 0.5. Since the standard model predictions of C_{K0bar K0} and S_{K0bar K0} are very small, the squark contribution can be detectable in C_{K0bar K0} and S_{K0bar K0}. These magnitudes are expected in the region C_{K0bar K0}=-0.06-0.06 and S_{K0bar K0}=-0.5-0.3. More precise data of these CP violations provide us a crucial test for the gluino-squark mediated flavor changing current.Comment: 20 pages, 10 figures, discussions added, references added. arXiv admin note: substantial text overlap with arXiv:1307.037

Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method

Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.Comment: 44 pages, 11 figures, 2 tables; published versio