A simultaneous analysis of the $B^{+}\to K^{+}{\ell }^{+}{\ell }^{-}$ and $B^0\to K^{*0}{\ell }^{+}{\ell }^{-}$ decays is performed to test muon-electron universality in two ranges of the square of the dilepton invariant mass, $q^2$. The measurement uses a sample of beauty meson decays produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. A sequence of multivariate selections and strict particle identification requirements produce a higher signal purity and a better statistical sensitivity per unit luminosity than previous LHCb lepton universality tests using the same decay modes. Residual backgrounds due to misidentified hadronic decays are studied using data and included in the fit model. Each of the four lepton universality measurements reported is either the first in the given $q^2$ interval or supersedes previous LHCb measurements. The results are compatible with the predictions of the Standard Model.

The branching fraction $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })$ is measured relative to that of the normalization mode $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ using hadronic ${\tau }^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}({\pi }^0){\overline{\nu }}_{\tau }$ decays in proton-proton collision data at a center-of-mass energy of 13 TeV collected by the LHCb experiment, corresponding to an integrated luminosity of $2{\mathrm{fb}}^{-1}$. The measured ratio is $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})=1.70\pm 0.10_{-0.10}^{+0.11}$, where the first uncertainty is statistical and the second is related to systematic effects. Using established branching fractions for the $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ and $B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu }$ modes, the lepton universality test $\mathcal{R}(D^{*-})\equiv \mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu })$ is calculated, $\mathcal{R}(D^{*-})=0.247\pm 0.015\pm 0.015\pm 0.012$, where the third uncertainty is due to the uncertainties on the external branching fractions. This result is consistent with the Standard Model prediction and with previous measurements.

The LHCb upgrade represents a major change of the experiment. The detectors have been almost completely renewed to allow running at an instantaneous luminosity five times larger than that of the previous running periods. Readout of all detectors into an all-software trigger is central to the new design, facilitating the reconstruction of events at the maximum LHC interaction rate, and their selection in real time. The experiment's tracking system has been completely upgraded with a new pixel vertex detector, a silicon tracker upstream of the dipole magnet and three scintillating fibre tracking stations downstream of the magnet. The whole photon detection system of the RICH detectors has been renewed and the readout electronics of the calorimeter and muon systems have been fully overhauled. The first stage of the all-software trigger is implemented on a GPU farm. The output of the trigger provides a combination of totally reconstructed physics objects, such as tracks and vertices, ready for final analysis, and of entire events which need further offline reprocessing. This scheme required a complete revision of the computing model and rewriting of the experiment's software.

Resonant contributions in $B^0\to \overline{D}{{}^{0}D}_s^{+}{\pi }^{-}$ and $B^{+}\to D^{-}{D}_s^{+}{\pi }^{+}$ decays are determined with an amplitude analysis, which is performed both separately and simultaneously, where in the latter case isospin symmetry between the decays is assumed. The analysis is based on data collected by the LHCb detector in proton-proton collisions at center-of-mass energies of 7, 8, and 13 TeV. The full data sample corresponds to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. A doubly charged spin-0 open-charm tetraquark candidate together with a neutral partner, both with masses near 2.9 GeV, are observed in the $D_s\pi$ decay channel.

We have explored, computationally and experimentally, the magnetic properties of (${\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x$)${}_2\mathrm{B}$ alloys. Calculations provide a good agreement with experiment in terms of the saturation magnetization and the magnetocrystalline anisotropy energy with some difficulty in describing ${\mathrm{Co}}_2\mathrm{B}$, for which it is found that both full potential effects and electron correlations treated within dynamical mean field theory are of importance for a correct description. The material exhibits a uniaxial magnetic anisotropy for a range of cobalt concentrations between $x=0.1$ and $x=0.5$. A simple model for the temperature dependence of magnetic anisotropy suggests that the complicated nonmonotonic behavior is mainly due to variations in the band structure as the exchange splitting is reduced by temperature. Using density functional theory based calculations we have explored the effect of substitutionally doping the transition metal sublattice by the whole range of $5d$ transition metals and found that doping by Re or W elements should significantly enhance the magnetocrystalline anisotropy energy. Experimentally, W doping did not succeed in enhancing the magnetic anisotropy due to formation of other phases. On the other hand, doping by Ir and Re was successful and resulted in magnetic anisotropies that are in agreement with theoretical predictions. In particular, doping by 2.5 at. % of Re on the Fe/Co site shows a magnetocrystalline anisotropy energy which is increased by 50% compared to its parent (${\mathrm{Fe}}_{0.7}{\mathrm{Co}}_{0.3}$)${}_2\mathrm{B}$ compound, making this system interesting, for example, in the context of permanent magnet replacement materials or in other areas where a large magnetic anisotropy is of importance.