A comprehensive study of the local and nonlocal amplitudes contributing to the decay $B^0\rightarrow K^{*0}(\to K^+\pi^-) \mu^+\mu^-$ is performed by analysing the phase-space distribution of the decay products. The analysis is based on $pp$ collision data corresponding to an integrated luminosity of 8.4fb$^{-1}$ collected by the LHCb experiment. This measurement employs for the first time a model of both one-particle and two-particle nonlocal amplitudes, and utilises the complete dimuon mass spectrum without any veto regions around the narrow charmonium resonances. In this way it is possible to explicitly isolate the local and nonlocal contributions and capture the interference between them. The results show that interference with nonlocal contributions, although larger than predicted, only has a minor impact on the Wilson Coefficients determined from the fit to the data. For the local contributions, the Wilson Coefficient $C_9$, responsible for vector dimuon currents, exhibits a $2.1\sigma$ deviation from the Standard Model expectation. The Wilson Coefficients $C_{10}$, $C_{9}'$ and $C_{10}'$ are all in better agreement than $C_{9}$ with the Standard Model and the global significance is at the level of $1.5\sigma$. The model used also accounts for nonlocal contributions from $B^{0}\to K^{*0}\left[\tau^+\tau^-\to \mu^+\mu^-\right]$ rescattering, resulting in the first direct measurement of the $b s\tau\tau$ vector effective-coupling $C_{9\tau}$.

A measurement of the differential branching fraction of the decay ${B^{0}\rightarrow K^{\ast}(892)^{0}\mu^{+}\mu^{-}}$ is presented together with a determination of the S-wave fraction of the $K^+\pi^-$ system in the decay $B^{0}\rightarrow K^{+}\pi^{-}\mu^{+}\mu^{-}$. The analysis is based on $pp$-collision data corresponding to an integrated luminosity of 3\,fb$^{-1}$ collected with the LHCb experiment. The measurements are made in bins of the invariant mass squared of the dimuon system, $q^2$. Precise theoretical predictions for the differential branching fraction of $B^{0}\rightarrow K^{\ast}(892)^{0}\mu^{+}\mu^{-}$ decays are available for the $q^2$ region $1.1<q^2<6.0\,{\rm GeV}^2/c^4$. In this $q^2$ region, for the $K^+\pi^-$ invariant mass range $796 < m_{K\pi} < 996\,{\rm MeV}/c^2$, the S-wave fraction of the $K^+\pi^-$ system in $B^{0}\rightarrow K^{+}\pi^{-}\mu^{+}\mu^{-}$ decays is found to be \begin{equation*} F_{\rm S} = 0.101\pm0.017({\rm stat})\pm0.009 ({\rm syst}), \end{equation*} and the differential branching fraction of $B^{0}\rightarrow K^{\ast}(892)^{0}\mu^{+}\mu^{-}$ decays is determined to be \begin{equation*} {\rm d}\mathcal{B}/{\rm d} q^2 = (0.342_{\,-0.017}^{\,+0.017}({\rm stat})\pm{0.009}({\rm syst})\pm0.023({\rm norm}))\times 10^{-7}c^{4}/{\rm GeV}^{2}. \end{equation*} The differential branching fraction measurements presented are the most precise to date and are found to be in agreement with Standard Model predictions.

Conventional hadronic matter consists of baryons and mesons made of three quarks and quark-antiquark pairs, respectively. The observation of a new type of hadronic state, a doubly charmed tetraquark containing two charm quarks, an anti-$u$ and an anti-$d$ quark, is reported using data collected by the LHCb experiment at the Large Hadron Collider. This exotic state with a mass of about 3875 MeV$/c^2$ manifests itself as a narrow peak in the mass spectrum of $D^0D^0\pi^+$ mesons just below the $D^{*+}D^0$ mass threshold. The near threshold mass together with a strikingly narrow width reveals the resonance nature of the state.

A test of lepton universality, performed by measuring the ratio of the branching fractions of the $B^{0} \rightarrow K^{*0}\mu^{+}\mu^{-}$ and $B^{0} \rightarrow K^{*0}e^{+}e^{-}$ decays, $R_{K^{*0}}$, is presented. The $K^{*0}$ meson is reconstructed in the final state $K^{+}\pi^{-}$, which is required to have an invariant mass within 100$\mathrm{\,MeV}c^2$ of the known $K^{*}(892)^{0}$ mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of about 3$\mathrm{\,fb}^{-1}$, collected by the LHCb experiment at centre-of-mass energies of 7 and 8$\mathrm{\,TeV}$. The ratio is measured in two regions of the dilepton invariant mass squared, $q^{2}$, to be \begin{eqnarray*} R_{K^{*0}} = \begin{cases} 0.66~^{+~0.11}_{-~0.07}\mathrm{\,(stat)} \pm 0.03\mathrm{\,(syst)} & \textrm{for } 0.045 < q^{2} < 1.1~\mathrm{\,GeV^2}c^4 \, , \\ 0.69~^{+~0.11}_{-~0.07}\mathrm{\,(stat)} \pm 0.05\mathrm{\,(syst)} & \textrm{for } 1.1\phantom{00} < q^{2} < 6.0~\mathrm{\,GeV^2}c^4 \, . \end{cases} \end{eqnarray*} 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.

An exotic narrow state in the $D^0D^0\pi^+$ mass spectrum just below the $D^{*+}D^0$ mass threshold is studied using a data set corresponding to an integrated luminosity of 9 fb$^{-1}$ acquired with the LHCb detector in proton-proton collisions at centre-of-mass energies of 7, 8 and 13 TeV. The state is consistent with the ground isoscalar $T^+_{cc}$ tetraquark with a quark content of $cc\bar{u}\bar{d}$ and spin-parity quantum numbers $\mathrm{J}^{\mathrm{P}}=1^+$. Study of the $DD$ mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell $D^{*+}$ mesons is confirmed by the $D^0\pi^+$ mass distribution. The mass of the resonance and its coupling to the $D^{*}D$ system are analysed. Resonance parameters including the pole position, scattering length, effective range and compositeness are measured to reveal important information about the nature of the $T^+_{cc}$ state. In addition, an unexpected dependence of the production rate on track multiplicity is observed.

The production fractions of $\overline{B}_s^0$ and $\Lambda_b^0$ hadrons, normalized to the sum of $B^-$ and $\overline{B}^0$ fractions, are measured in 13 TeV pp collisions using data collected by the LHCb experiment, corresponding to an integrated luminosity of 1.67/fb. These ratios, averaged over the $b$-hadron transverse momenta from 4 to 25 GeV and pseudorapidity from 2 to 5, are $0.122 \pm 0.006$ for $\overline{B}_s^0$, and $0.259 \pm 0.018$ for $\Lambda_b^0$, where the uncertainties arise from both statistical and systematic sources. The $\Lambda_b^0$ ratio depends strongly on transverse momentum, while the $\overline{B}_s^0$ ratio shows a mild dependence. Neither ratio shows variations with pseudorapidity. The measurements are made using semileptonic decays to minimize theoretical uncertainties. In addition, the ratio of $D^+$ to $D^0$ mesons produced in the sum of $\overline{B}^0$ and $B^-$ semileptonic decays is determined as $0.359\pm0.006\pm 0.009$, where the uncertainties are statistical and systematic.

A study of $\chi_{b}$ meson production at LHCb is performed on proton-proton collision data, corresponding to 3.0fb$^{-1}$ of integrated luminosity collected at centre-of-mass energies $\sqrt{s}=7$ and 8TeV. The fraction of $\Upsilon(nS)$ mesons originating from $\chi_{b}$ decays is measured as a function of the $\Upsilon$ transverse momentum in the rapidity range $2.0 < y^{\Upsilon} < 4.5$. The radiative transition of the $\chi_{b}(3P)$ meson to $\Upsilon(3S)$ is observed for the first time. The $\chi_{b1}(3P)$ mass is determined to be $$m(\chi_{b1}(3P)) = 10\,511.3 \pm 1.7 \pm 2.5 MeV/c^2,$$ where the first uncertainty is statistical and the second is systematic.

The Standard Model of particle physics currently provides our best description of fundamental particles and their interactions. The theory predicts that the different charged leptons, the electron, muon and tau, have identical electroweak interaction strengths. Previous measurements have shown a wide range of particle decays are consistent with this principle of lepton universality. This article presents evidence for the breaking of lepton universality in beauty-quark decays, with a significance of 3.1 standard deviations, based on proton-proton collision data collected with the LHCb detector at CERN's Large Hadron Collider. The measurements are of processes in which a beauty meson transforms into a strange meson with the emission of either an electron and a positron, or a muon and an antimuon. If confirmed by future measurements, this violation of lepton universality would imply physics beyond the Standard Model, such as a new fundamental interaction between quarks and leptons.

Decays of $b$ hadrons into final states containing a $D^0$ meson and a muon are used to measure the $b\bar{b}$ production cross-section in proton-proton collisions at a centre-of-mass energy of 7 TeV at the LHC. In the pseudorapidity interval $2 < \eta < 6$ and integrated over all transverse momenta we find that the average cross-section to produce $b$-flavoured or $\bar{b}$-flavoured hadrons is ($75.3 \pm 5.4 \pm 13.0$) microbarns.

The production of $B^{\pm}$ mesons is studied in $pp$ collisions at centre-of-mass energies of 7 and 13 TeV, using $B^{\pm}\rightarrow J/\psi K^{\pm}$ decays and data samples corresponding to 1.0 fb$^{-1}$ and 0.3 fb$^{-1}$, respectively. The production cross-sections summed over both charges and integrated over the transverse momentum range $0<p_{\text{T}}< 40$ GeV/$c$ and the rapidity range $2.0<y<4.5$ are measured to be $\sigma(pp \rightarrow B^{\pm} X, \sqrt{s} = \text{7 TeV}) = 43.0 \pm 0.2 \pm 2.5 \pm 1.7\mu b,$ $\sigma(pp \rightarrow B^{\pm} X, \sqrt{s} = \text{13 TeV}) = 86.6 \pm 0.5 \pm 5.4 \pm 3.4\mu b,$ where the first uncertainties are statistical, the second are systematic, and the third are due to the limited knowledge of the $B^{\pm}\rightarrow J/\psi K^{\pm}$ branching fraction. The ratio of the cross-section at 13 TeV to that at 7 TeV is determined to be $2.02\pm0.02\text{(stat)}\pm0.12\text{(syst)}$. Differential cross-sections are also reported as functions of $p_{\text{T}}$ and $y$. All results are in agreement with theoretical calculations based on the state-of-art fixed next-to-leading order quantum chromodynamics.