5,565 research outputs found

    Comment on Reparametrization Invariance of Quark-Lepton Complementarity

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    We study the complementarity between quark and lepton mixing angles (QLC), the sum of an angle in quark mixing and the corresponding angle in lepton mixing is π/4\pi/4. Experimentally in the standard PDG parametrization, two such relations exist approximately. These QLC relations are accidental which only manifest themselves in the PDG parametrization. We propose reparametrization invariant expressions for the complementarity relations in terms of the magnitude of the elements in the quark and lepton mixing matrices. In the exact QLC limit, it is found that Vus/Vud+Ve2/Ve1+Vus/VudVe2/Ve1=1|V_{us}/V_{ud}| + |V_{e2}/V_{e1}| + |V_{us}/V_{ud}| |V_{e2}/V_{e1}| =1 and Vcb/Vtb+Vμ3/Vτ3+Vcb/VtbVμ3/Vτ3=1|V_{cb}/V_{tb}| + |V_{\mu 3}/V_{\tau 3}| +|V_{cb}/V_{tb}|| {V_{\mu 3}}/V_{\tau 3}| =1. Expressions with deviations from exact complementarity are obtained. Implications of these relations are also discussed.Comment: 5 pages and 1 figure. Implications for recent Daya-Bay neutrino data on theta_{13} discusse

    Systematic search for successful lepton mixing patterns with nonzero theta_13

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    We perform a systematic search for simple but viable lepton mixing patterns. Our main criterion is that the mixing matrix can be parameterized by three rotation angles, which are simple fractions of pi. These simple rotation angles possess exact expressions for their sines and cosines, and often arise in the flavor symmetry models. All possible parameterizations of the mixing matrix are taken into account. In total, twenty successful mixing patterns are found to be consistent with the latest neutrino oscillation data (including the recent T2K results) in the CP conserving case, whereas fifteen mixing patterns are allowed in the maximal CP violating case. Potential radiative corrections to the constant mixing patterns are also calculated by solving the renormalization group equations.Comment: 10 pages, 4 figures, 2 tables; version to be published in Nuclear Physics

    Single-Particle Spin-Orbit Strengths of the Nucleon and Hyperons by SU6 Quark-Model

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    The quark-model hyperon-nucleon interaction suggests an important antisymmetric spin-orbit component. It is generated from a color analogue of the Fermi-Breit interaction dominating in the one-gluon exchange process between quarks. We discuss the strength S_B of the single-particle spin-orbit potential, following the Scheerbaum's prescription. Using the SU6 quark-model baryon-baryon interaction which was recently developed by the Kyoto-Niigata group, we calculate NN, Lambda N and Sigma N G-matrices in symmetric nuclear matter and apply them to estimate the strength S_B. The ratio of S_B to the nucleon strength S_N =~ -40 MeV*fm^5 is (S_Lambda)/(S_N) =~ 1/5 and (S_Sigma)/(S_N) =~ 1/2 in the Born approximation. The G-matrix calculation of the model FSS modifies S_Lambda to (S_Lambda)/(S_N) =~ 1/12. For S_N and S_Sigma, the effect of the short-range correlation is comparatively weak against meson-exchange potentials with a short-range repulsive core. The significant reduction of the Lambda single-particle potential arises from the combined effect of the antisymmetric LS force, the flavor-symmetry breaking originating from the strange to up-down quark-mass difference, as well as the effect of the short-range correlation. The density dependence of S_B is also examined.Comment: 26 page

    Relatively large theta13 and nearly maximal theta23 from the approximate S3 symmetry of lepton mass matrices

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    We apply the permutation symmetry S_3 to both charged-lepton and neutrino mass matrices, and suggest a useful symmetry-breaking scheme, in which the flavor symmetry is explicitly broken down via S_3 -> Z_3 -> nothing in the charged-lepton sector and via S_3 -> Z_2 -> nothing in the neutrino sector. Such a two-stage breaking scenario is reasonable in the sense that both Z_3 and Z_2 are the subgroups of S_3, while Z_3 and Z_2 only have a trivial subgroup. In this scenario, we can obtain a relatively large value of the smallest neutrino mixing angle, e.g., theta_{13} ~ 9^\circ, which is compatible with the recent result from T2K experiment and will be precisely measured in the ongoing Double Chooz and Daya Bay reactor neutrino experiments. Moreover, the maximal atmospheric mixing angle theta_{23} ~ 45^\circ can also be obtained while the best-fit value of solar mixing angle theta_{12} ~ 34^\circ is assumed, which cannot be achieved in previous S_3 symmetry models.Comment: 15 pages, no figures, minor changes, matches the published versio

    Principal series of finite subgroups of SU(3)

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    We attempt to give a complete description of the "exceptional" finite subgroups Sigma(36x3), Sigma(72x3) and Sigma(216x3) of SU(3), with the aim to make them amenable to model building for fermion masses and mixing. The information on these groups which we derive contains conjugacy classes, proper normal subgroups, irreducible representations, character tables and tensor products of their three-dimensional irreducible representations. We show that, for these three exceptional groups, usage of their principal series, i.e. ascending chains of normal subgroups, greatly facilitates the computations and illuminates the relationship between the groups. As a preparation and testing ground for the usage of principal series, we study first the dihedral-like groups Delta(27) and Delta(54) because both are members of the principal series of the three groups discussed in the paper.Comment: 43 pages, no figures; typos corrected, clarifications and references added, version matches publication in J. Phys.

    TFH Mixing Patterns, Large θ13\theta_{13} and Δ(96)\Delta(96) Flavor Symmetry

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    We perform a comprehensive analysis of the Toorop-Feruglio-Hagedorn (TFH) mixing patterns within the family symmetry Δ(96)\Delta(96). The general neutrino mass matrix for the TFH mixing and its symmetry properties are investigated. The possible realizations of the TFH mixing in Δ(96)\Delta(96) are analyzed in the minimalist approach. We propose two dynamical models which produce the TFH mixing patterns at leading order. The full flavor symmetries are Δ(96)×Z3×Z3\Delta(96)\times Z_3\times Z_3 and Δ(96)×Z5×Z2\Delta(96)\times Z_5 \times Z_2 respectively. The next to leading order terms introduce corrections of order λc2\lambda^2_c to the three mixing angles in both models. The allowed mixing patterns are studied under the condition that the Klein four subgroups and the cyclic ZNZ_N subgroups with N3N\geq3 are preserved in the neutrino and the charged lepton sector respectively. We suggest that the deformed tri-bimaximal mixing is a good leading order approximation to understanding a largish reactor angle.Comment: 43 pages, 2 figure

    Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models

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    Recent T2K results indicate a sizeable reactor angle theta_13 which would rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector (1,1,1)^T/sqrt{3}, with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable S4 model in which the 1' and 1" flavons of A4 are unified into a doublet of S4 which is spontaneously broken to A4 by a flavon which enters the neutrino sector at higher order. We study the vacuum alignment in the S4 model and show that it predicts accurate trimaximal mixing with approximate tri-bimaximal mixing, leading to a new mixing sum rule testable in future neutrino experiments. Both A4 and S4 models preserve form dominance and hence predict zero leptogenesis, up to renormalisation group corrections.Comment: 24 pages, 2 figures, version to be published in JHE
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