Abstract: First observations of the rare decays B (+) -> K (+)pi (+) pi (-) μ(+) μ(-) and B (+)-> phi K+ mu(+)mu(-) are presented using data corresponding to an integrated luminosity of 3.0 fb(-1), collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The branching fractions of the decays are B(B (+) -> K (+)pi (+) pi (-) μ(+) μ(-) ) = (4.36 (-0.27) (+0.29) (stat) +/- 0.21 (syst) +/- (norm)) x 10(-7), B(B (+)-> phi K+ mu(+)mu(-)) = (0.82 (+0.19)(-0.17) (stat) (+0.10)(-0.04) (syst) +/- 0.27 (norm)) x 10(-7) where the uncertainties are statistical, systematic, and due to the uncertainty on the branching fractions of the normalisation modes. A measurement of the differential branching fraction in bins of the invariant mass squared of the dimuon system is also presented for the decay B (+) -> K (+)pi (+) pi (-) μ(+) μ(-)

Abstract: We report on measurements of the time-dependent CP violating observables in B-s(0) -> D-s(-/+) K--/+ decays using a dataset corresponding to 1.0 fb(-1) of pp collisions recorded with the LHCb detector. We find the CP violating observables C-f = 0.53 +/- 0.25 +/- 0.04, A(f)(Delta Gamma) = 0.37 +/- 0.42 +/- 0.20, A((f) over bar)(Delta Gamma) = 0.20 +/- 0.41 +/- 0.20, S-f = -1.09 +/- 0.33 +/- 0.08, S-(f) over bar = -0.36 +/- 0.34 +/- 0.08, where the uncertainties are statistical and systematic, respectively. Using these observables together with a recent measurement of the B-s(0) mixing phase -2 beta(s) leads to the first extraction of the CKM angle gamma from B-s(0) -> D-s(-/+) K--/+ decays, finding gamma = (115(-43)(+28))degrees modulo 180 degrees at 68% CL, where the error contains both statistical and systematic uncertainties.

Abstract: In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where “one-loop” diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale p is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all one-particle reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.