CP violating Tri-bimaximal-Cabibbo mixing

In view of the new data from the Daya Bay and RENO collaborations, King has presented a very natural deformation of tri-bimaximal mixing. Here we show that L/E flatness of the e-like event ratio in the atmospheric neutrino data, when coupled with King's observation that the smallest neutrino mixing angle, \theta_{13}, seems to be related to the largest quark mixing angle (the Cabibbo angle \theta_C), leads to a CP violating tri-bimaximal-Cabibbo mixing. King's tri-bimaximal-Cabibbo mixing follows as a leading order approximation from our result.Comment: 6 page

Book Review: The Quantum Theory of Fields, Vol. I and II by S. Weinberg

Review of the two volume set "The Quantum Theory of Fields" by S. Weinberg is presented

Theory of Neutral Particles: Mclennan-Case Construct for Neutrino, Its Generalization, and a New Wave Equation

Continuing our recent argument where we constructed a FNBWW-type spin-$1$ boson having opposite relative intrinsic parity to that of the associated antiparticle, we now study eigenstates of the Charge Conjugation operator. Based on the observation that if $\phi_{_{L}}(p^\mu)$ transforms as a $(0,\,j)$ spinor under Lorentz boosts, then $\Theta_{[j]}\,\phi_{_{L}}^\ast(p^\mu)$ transforms as a $(j,\,0)$ spinor (with a similar relationship existing between $\phi_{_{R}}(p^\mu)$ and $\Theta_{[j]}\,\phi_{_{R}}^\ast(p^\mu)$; where $\Theta_{[j]}\,{\bf J}\,\Theta_{[j]}^{-1}\,=\,-\,{\bf J}^\ast$ with $\Theta_{[j]}$ the well known Wigner matrix involved in the operation of time reversal) we introduce McLennan-Case type $(j,\,0)\oplus(0,\,j)$ spinors. Relative phases between $\phi_{_{R}}(p^\mu)$ and $\Theta_{[j]}\,\phi_{_{R}}^\ast(p^\mu)$, and $\Theta_{[j]}\,\phi_{_{L}}^\ast(p^\mu)$ and $\phi_{_{L}}(p^\mu)$, turn out to have physical significance and are fixed by appropriate requirements. Explicit construction, and a series of physically relevant properties, for these spinors are obtained for spin-$1/2$ and spin-$1$ culminating in the construction of a new wave equation and introduction of Dirac-like and Majorana-like quantum fields.Comment: Revised and re-written version to appear in Int. J. Mod. Phys. A. At present violations of various symmetries, such as C, P, and T, are assumed to arise from interactions. It is argued that the violation is more fundamental than that and is to be found at basic level of the representations of the Lorentz group. Revtex 3.0 (20 pages