Abstract: In this paper we discuss SU(5)3 with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate SU(5) for each fermion family, with the light Higgs doublet(s) arising from the third family SU(5), providing a basis for charged fermion mass hierarchies. SU(5)3 tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{U}}{\left(1\right)}_{Y}<^>{3}$$\end{document} based on an SU(5)3 framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic SU(5)3 gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant e+pi 0 channel.

Abstract: An angular analysis of the decay B-s(0) -> K*(0)(K) over bar*(0) is performed using pp collisions corresponding to an integrated luminosity of 1.0 fb(-1) collected by the LHCb experiment at a centre-of-mass energy root s = 7TeV. A combined angular and mass analysis separates six helicity amplitudes and allows the measurement of the longitudinal polarisation fraction f(L) = 0.201 +/- 0.057 (stat.) +/- 0.040 (syst.) for the B-s(0) -> K*(892)(0)(K) over bar*(892)(0) decay. A large scalar contribution from the K*(0) (1430) and K*(0) (800) resonances is found, allowing the determination of additional CP asymmetries. Triple product and direct CP asymmetries are determined to be compatible with the Standard Model expectations. The branching fraction B(B-s(0) -> K*(892)(0)(K) over bar*(892)(0)) is measured to be (10.8 +/- 2.1 (stat.) +/- 1.4 (syst.) +/- 0.6 (f(d)/f(s))) x 10(-6).

Abstract: An angular analysis of the B-0 -> K*(0)e(+)e(-) decay is performed using a data sample corresponding to an integrated luminosity of 9 fb(-1) of pp collisions collected with the LHCb experiment. The analysis is conducted in the very low dielectron mass squared (q(2)) interval between 0.0008 and 0.257 GeV2, where the rate is dominated by the B-0 -> K*(0)gamma transition with a virtual photon. The fraction of longitudinal polarisation of the K*(0) meson, F-L, is measured to be F-L = (4.4 +/- 2.6 +/- 1.4)%, where the first uncertainty is statistical and the second systematic. The A(T)(Re) observable, which is related to the lepton forward-backward asymmetry, is measured to be A(T)(Re) = -0.06 +/- 0.08 +/- 0.02. The A(T)((2)) and A(T)(Im) transverse asymmetries, which are sensitive to the virtual photon polarisation, are found to be A(T)((2)) = 0.11 +/- 0.10 +/- 0.02 and A(T)(Im) = 0.02 +/- 0.10 +/- 0.01. The results are consistent with Standard Model predictions and provide the world's best constraint on the b -> s gamma photon polarisation.