Abstract: The cross-section for inelastic proton-proton collisions at a centre-of-mass energy of 13 TeV is measured with the LHCb detector. The fiducial cross-section for inelastic interactions producing at least one prompt long-lived charged particle with momentum p > 2 GeV/c in the pseudorapidity range 2 < eta < 5 is determined to be sigma(acc) = 62.2 +/- 0.2 +/- 2.5 mb. The first uncertainty is the intrinsic systematic uncertainty of the measurement, the second is due to the uncertainty on the integrated luminosity. The statistical uncertainty is negligible. Extrapolation to full phase space yields the total inelastic proton-proton cross-section sigma(inel) = 75.4 +/- 3.0 +/- 4.5 mb, where the first uncertainty is experimental and the second due to the extrapolation. An updated value of the inelastic cross-section at a centre-of-mass energy of 7 TeV is also reported.

Abstract: The first untagged decay-time-integrated amplitude analysis of B 0 s ! K 0 S K decays is performed using a sample corresponding to 3: 0 fb of pp collision data recorded with the LHCb detector during 2011 and 2012. The data are described with an amplitude model that contains contributions from the intermediate resonances K 9892) 0;+, K 2 91430) 0;+ and K 0 91430) 0;+, and their charge conjugates. Measurements of the branching fractions of the decay modes B 0 s ! K 9892) K and B 0 s ! K 9892) 0 K 0 are in agreement with, and more precise than, previous results. The decays B 0 s ! K 0 91430) K and B 0 s ! K 0 91430) 0 K 0 are observed for the fi rst time, each with signi fi cance over 10 standard deviations.

Abstract: This paper presents an analysis of the Lambda(0)(b) -> J/psi Lambda angular distribution and the transverse production polarisation of Lambda(0)(b) baryons in proton-proton collisions at centre-of-mass energies of 7, 8 and 13TeV. The measurements are performed using data corresponding to an integrated luminosity of 4.9 fb(-1), collected with the LHCb experiment. The polarisation is determined in a fiducial region of Lambda(0)(b) transverse momentum and pseudorapidity of 1 < p(T) < 20 GeV/c and 2 < eta < 5, respectively. The data are consistent with Lambda(0)(b) baryons being produced unpolarised in this region. The parity-violating asymmetry parameter of the Lambda -> p pi(-) decay is also determined from the data and its value is found to be consistent with a recent measurement by the BES III collaboration.

Abstract: A search is presented for the lepton flavour violating decay B+ -> K+mu (-)tau (+) using a sample of proton-proton collisions at centre-of-mass energies of 7, 8, and 13 TeV, collected with the LHCb detector and corresponding to a total integrated luminosity of 9 fb(-1). The tau leptons are selected inclusively, primarily via decays with a single charged particle. The four-momentum of the tau lepton is determined by using B+ mesons from Bs20 -> B+K- decays. No significant excess is observed, and an upper limit is set on the branching fractionB(B+-> K+mu (-)tau (+))<3.9x10(-5)at90%confidence level.The obtained limit is comparable to the world-best limit.

Abstract: An amplitude analysis of the decay Lambda(0)(b) -> D(0)p pi(-) is performed in the part of the phase space containing resonances in the D(0)p channel. The study is based on a data sample corresponding to an integrated luminosity of 3.0 fb(-1) of pp collisions recorded by the LHCb experiment. The spectrum of excited Lambda(+)(c) states that decay into D(0)p is studied. The masses, widths and quantum numbers of the Lambda(c)(2880)(+) and Lambda(c) (2940)(+) resonances are measured. The constraints on the spin and parity for the Lambda(c)(2940)(+) state are obtained for the first time. A near-threshold enhancement in the D(0)p amplitude is investigated and found to be consistent with a new resonance, denoted the Lambda(c) (2860)(+), of spin 3/2 and positive parity.