16,921 research outputs found
Generalised CP and Trimaximal TM Lepton Mixing in Family Symmetry
We construct two flavor models based on family symmetry and generalised
CP symmetry. In both models, the family symmetry is broken down to the
subgroup in the neutrino sector, as a consequence, the trimaximal
lepton mixing is produced. Depending on the free parameters in
the flavon potential, the Dirac CP is predicted to be either conserved or
maximally broken, and the Majorana CP phases are trivial. The two models differ
in the neutrino sector. The flavon fields are involved in the Dirac mass terms
at leading order in the first model, and the neutrino mass matrix contains
three real parameters such that the absolute neutrino masses are fixed.
Nevertheless, the flavon fields enter into the Majorana mass terms at leading
order in the second model. The leading order lepton mixing is of the
tri-bimaximal form which is broken down to by the next to leading
order contributions.Comment: 28 page
Weak Continuity of the Cartan Structural System and Compensated Compactness on Semi-Riemannian Manifolds with Lower Regularity
We are concerned with the global weak continuity of the Cartan structural
system -- or equivalently, the Gauss--Codazzi--Ricci system -- on
semi-Riemannian manifolds with lower regularity. For this purpose, we first
formulate and prove a geometric compensated compactness theorem on vector
bundles over semi-Riemannian manifolds with lower regularity (Theorem 3.2),
extending the classical quadratic theorem of compensated compactness. We then
deduce the weak continuity of the Cartan structural system for : For
a family of connection -forms on a
semi-Riemannian manifold , if is uniformly
bounded in and satisfies the Cartan structural system, then any weak
limit of is also a solution of the Cartan
structural system. Moreover, it is proved that isometric immersions of
semi-Riemannian manifolds into semi-Euclidean spaces can be constructed from
the weak solutions of the Cartan structural system or the Gauss--Codazzi--Ricci
system (Theorem 5.1), which leads to the weak continuity of the
Gauss--Codazzi--Ricci system on semi-Riemannian manifolds. As further
applications, the weak continuity of Einstein's constraint equations, general
immersed hypersurfaces, and the quasilinear wave equations is also established.Comment: 64 page
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