We present the final report from a series of precision measurements of the muon anomalous magnetic moment, a µ = (g − 2)/2. The details of the experimental method, apparatus, data taking, and analysis are summarized. Data obtained at Brookhaven National Laboratory, using nearly equal samples of positive and negative muons, were used to deduce a µ (Expt) = 11 659 208.0(5.4)(3.3) × 10 −10 , where the statistical and systematic uncertainties are given, respectively. The combined uncertainty of 0.54 ppm represents a 14-fold improvement compared to previous measurements at CERN. The standard model value for a µ includes contributions from virtual QED, weak, and hadronic processes. While the QED processes account for most of the anomaly, the largest theoretical uncertainty, ≈ 0.55 ppm, is associated with first-order hadronic vacuum polarization. Present standard model evaluations, based on e + e − hadronic cross sections, lie 2.2 -2.7 standard deviations below the experimental result.

A measurement of the ratio of the branching fractions of the B(+) → K(+)μ(+)μ(-) and B(+) → K(+)e(+)e(-) decays is presented using proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb(-1), recorded with the LHCb experiment at center-of-mass energies of 7 and 8 TeV. The value of the ratio of branching fractions for the dilepton invariant mass squared range 1 < q(2) < 6 GeV(2)/c(4) is measured to be 0.745(-0.074)(+0.090)(stat) ± 0.036(syst). This value is the most precise measurement of the ratio of branching fractions to date and is compatible with the standard model prediction within 2.6 standard deviations.

A test of lepton universality, performed by measuring the ratio of the branching fractions of the B 0 → K * 0 µ + µ − and B 0 → K * 0 e + e − decays, R K * 0 , is presented. The K * 0 meson is reconstructed in the final state K + π − , which is required to have an invariant mass within 100 MeV/c 2 of the known K * (892) 0 mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of about 3 fb −1 , collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The ratio is measured in two regions of the dilepton invariant mass squared, q 2 , to be− 0.07 (stat) ± 0.03 (syst) for 0.045 < q 2 < 1.1 GeV 2 /c 4 , 0.69 + 0.11 − 0.07 (stat) ± 0.05 (syst) for 1.1 < q 2 < 6.0 GeV 2 /c 4 .The corresponding 95.4% confidence level intervals are [0.52, 0.89] and [0.53, 0.94]. The results, which represent the most precise measurements of R K * 0 to date, are compatible with the Standard Model expectations at the level of 2.1-2.3 and 2.4-2.5 standard deviations in the two q 2 regions, respectively.

A narrow pentaquark state, P c ð4312Þ þ , decaying to J=ψp, is discovered with a statistical significance of 7.3σ in a data sample of Λ 0 b → J=ψpK − decays, which is an order of magnitude larger than that previously analyzed by the LHCb Collaboration. The P c ð4450Þ þ pentaquark structure formerly reported by LHCb is confirmed and observed to consist of two narrow overlapping peaks, P c ð4440Þ þ and P c ð4457Þ þ , where the statistical significance of this two-peak interpretation is 5.4σ. The proximity of the Σ þ cD 0 and Σ þ cD Ã0 thresholds to the observed narrow peaks suggests that they play an important role in the dynamics of these states.

Observations of exotic structures in the J=ψp channel, which we refer to as charmonium-pentaquark states, in Λ 0 b → J=ψK − p decays are presented. The data sample corresponds to an integrated luminosity of 3 fb −1 acquired with the LHCb detector from 7 and 8 TeV pp collisions. An amplitude analysis of the three-body final state reproduces the two-body mass and angular distributions. To obtain a satisfactory fit of the structures seen in the J=ψp mass spectrum, it is necessary to include two Breit-Wigner amplitudes that each describe a resonant state. The significance of each of these resonances is more than 9 standard deviations. One has a mass of 4380 AE 8 AE 29 MeV and a width of 205 AE 18 AE 86 MeV, while the second is narrower, with a mass of 4449.8 AE 1.7 AE 2.5 MeV and a width of 39 AE 5 AE 19 MeV. The preferred J P assignments are of opposite parity, with one state having spin 3=2 and the other 5=2.

The branching fraction ratio R(D^{*})≡B(B[over ¯]^{0}→D^{*+}τ^{-}ν[over ¯]_{τ})/B(B[over ¯]^{0}→D^{*+}μ^{-}ν[over ¯]_{μ}) is measured using a sample of proton-proton collision data corresponding to 3.0 fb^{-1} of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode τ^{-}→μ^{-}ν[over ¯]_{μ}ν_{τ}. The semitauonic decay is sensitive to contributions from non-standard-model particles that preferentially couple to the third generation of fermions, in particular, Higgs-like charged scalars. A multidimensional fit to kinematic distributions of the candidate B[over ¯]^{0} decays gives R(D^{*})=0.336±0.027(stat)±0.030(syst). This result, which is the first measurement of this quantity at a hadron collider, is 2.1 standard deviations larger than the value expected from lepton universality in the standard model.

A measurement of the ratio of branching fractions of the decays B þ → K þ μ þ μ − and B þ → K þ e þ e − is presented. The proton-proton collision data used correspond to an integrated luminosity of 5.0 fb −1 recorded with the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV. For the dilepton mass-squared range 1.1 < q 2 < 6.0 GeV 2 =c 4 the ratio of branching fractions is measured to be R K ¼ 0.846 þ0.060 −0.054 þ0.016 −0.014 , where the first uncertainty is statistical and the second systematic. This is the most precise measurement of R K to date and is compatible with the standard model at the level of 2.5 standard deviations.

An angular analysis of the B 0 → K *0(→ K + π −)μ + μ − decay is presented. The dataset corresponds to an integrated luminosity of 3.0 fb−1 of pp collision data collected at the LHCb experiment. The complete angular information from the decay is used to determine CP-averaged observables and CP asymmetries, taking account of possible contamination from decays with the K + π − system in an S-wave configuration. The angular observables and their correlations are reported in bins of q 2, the invariant mass squared of the dimuon system. The observables are determined both from an unbinned maximum likelihood fit and by using the principal moments of the angular distribution. In addition, by fitting for q 2-dependent decay amplitudes in the region 1.1 < q 2 < 6.0 GeV2/c 4, the zero-crossing points of several angular observables are computed. A global fit is performed to the complete set of CP-averaged observables obtained from the maximum likelihood fit. This fit indicates differences with predictions based on the Standard Model at the level of 3.4 standard deviations. These differences could be explained by contributions from physics beyond the Standard Model, or by an unexpectedly large hadronic effect that is not accounted for in the Standard Model predictions

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