Abstract: A search for rare B. D mu+ mu- decays is performed using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb-1. No significant signals are observed in the non-resonant mu+ mu- modes, and upper limits of B -> B0. D0 mu+ mu- < 5.1 x 10-8, B B+. D+ s mu+ mu- -> < 3.2 x 10-8, B -> B0 s. D0 mu+ mu--> < 1.6 x 10-7 and fc/fu center dot B B+ c. D+ s mu+ mu--> < 9.6 x 10-8 are set at the 95% confidence level, where fc and fu are the fragmentation fractions of a B meson with a c and u quark respectively in proton-proton collisions. Each result is either the first such measurement or an improvement by three orders of magnitude on an existing limit. Separate upper limits are calculated when the muon pair originates from a J/.. mu+ mu- decay. The branching fraction of B+ c. D+ s J/. multiplied by the fragmentation-fraction ratio is measured to be fc fu center dot B -> B+ c. D+ s J/.-> = (1.63 +/- 0.15 +/- 0.13) x 10-5, where the first uncertainty is statistical and the second systematic.

Abstract: The associated production of prompt J/psi and Υ mesons in pp collisions at a centre-of-mass energy of root s = 13T eV is studied using LHCb data, corresponding to an integrated luminosity of 4 fb(-1). The measurement is performed for J/psi (Υ) mesons with a transverse momentum pT < 10 (30) GeV/ c in the rapidity range 2.0 < y < 4.5. In this kinematic range, the cross-section of the associated production of prompt J/psi and Υ(1S) mesons is measured to be 133 +/- 22 +/- 7 +/- 3 pb, with a significance of 7.9 s, and that of prompt J/psi and Υ(2S) mesons to be 76 +/- 21 +/- 4 +/- 7 pb, with a significance of 4.9 sigma. The first uncertainty is statistical, the second systematic, and the third due to uncertainties on the used branching fractions. This is the first observation of the associated production of J/psi and Υ(1S) in proton-proton collisions. Differential cross-sections are measured as functions of variables that are sensitive to kinematic correlations between the J/psi and Υ(1S) mesons. The effective cross-sections of the associated production of prompt J/psi and Υ mesons are obtained and found to be compatible with measurements using other particle productions.

Abstract: The multihadron decays Lambda(0)(b) -> D(+)p pi(-)pi(-) and Lambda(0 )(b)-> D-*+p pi(-)pi(-) are observed in data corresponding to an integrated luminosity of 3fb(-1), collected in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV by the LHCb detector. Using the decay Lambda(0)(b) -> Lambda(+)(c)pi(+)pi(-)pi(-) as a normalisation channel, the ratio of branching fractions is measured to be B(Lambda(0)(b) -> D(+)p pi(-)pi(-))/B(Lambda(0)(b) -> Lambda(+)(c)pi(+)pi(-)pi(-)) x B(D+ -> K-pi(+)pi(+))/B(Lambda(+)(c)-> pK(-)pi(+)) = (5.35 +/- 0.21 +/- 0.16) %, where the first uncertainty is statistical and the second systematic. The ratio of branching fractions for the Lambda(0)(b)-> D-*+p pi(-)pi(-) and Lambda(0)(b) -> D(+)p pi(-)pi(-) decays is found to be B(Lambda(0)(b)-> D-*+p pi(-)pi(-))/B(Lambda(0)(b) -> D(+)p pi(-)pi(-)) x (B(D-*+-> D+pi(0)) + B(D (*)+-> D- (+)gamma)) = (61.3 +/- 4.3 +/- 4.0) %.

Abstract: Searches for rare B-s(0) and B-0 decays into four muons are performed using proton-proton collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of 9 fb(-1). Direct decays and decays via light scalar and J/psi resonances are considered. No evidence for the six decays searched for is found and upper limits at the 95% confidence level on their branching fractions ranging between 1.8 x 10(-10) and 2.6 x 10(-9) are set.

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.