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

A New Type of Massive Spin-One Boson: and its Relation with Maxwell Equations

First, we show that in the $(1,0)\oplus(0,1)$ representation space there exist not one but two theories for charged particles. In the Weinberg construct, the boson and its antiboson carry {\it same} relative intrinsic parity, whereas in our construct the relative intrinsic parities of the boson and its antiboson are {\it opposite}. These results originate from the commutativity of the operations of Charge conjugation and Parity in Weinberg's theory, and from the anti-commutativity of the operations of Charge conjugation and Parity in our theory. We thus claim that we have constructed a first non-trivial quantum theory of fields for the Wigner-type particles. Second, the massless limit of both theories seems formally identical and suggests a fundamental modification of Maxwell equations. At its simplest level, the modification to Maxwell equations enters via additional boundary condition(s).Comment: Invited talk presented at ``The Present Status of Quantum Theory of Light: A Symposium to Honour Jean-Pierre Vigier,'' held at York University, Toronto, August 27-30, 1995. 15 pages, latex (crckapb.sty needed

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

A CP-Violating Kinematic Structure

A CP violating kinematic structure is presented. The essential physical input is to question the textbook wisdom, ``Now when a particle is at rest, one cannot define its spin as either left- or right-handed, so phi_R(0) = phi_L(0),'' as found, e.g., in Lewis Ryder's Quantum Field Theory, and in many other books on the representations of the Lorentz group. It is suggested that this equality is true only up to a phase. The demand of C, P, and T covariances, separately, fixes this phase to be pm 1. If these conditions are relaxed, a natural CP-violating kinematic structure emerges. Having established a CP-violating kinematic structure, we then discuss how Planck scale physics necessarily invokes non-commutative space-time and that such changes in the structure of space-time will force upon us additional violations/deformations of the CPT structure of space-time, and a violation of the principle of equivalence via a violation of the Lorentz symmetries. The latter may carry significant consequences for understanding the data on ultra high energy cosmic rays.Comment: Invited talk (International Workshop on Observing Ultra-High Energy Cosmic Rays, August 2000, Metepec, Mexico). Latex with aipproc.sty, 10 pages. To appear in the proceeding