This article reviews our present understanding of QCD spin physics: the proton spin puzzle and new developments aimed at understanding the transverse structure of the nucleon. Present experimental investigations of the nucleon's internal spin structure, the theoretical interpretation of the different measurements, and the open questions and challenges for future investigation are discussed.

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.

In the QCD evolution of transverse momentum dependent parton distribution and fragmentation functions, the Collins-Soper evolution kernel includes both a perturbative short-distance contribution and a large-distance nonperturbative, but strongly universal, contribution. In the past, global fits, based mainly on larger $Q$ Drell-Yan–like processes, have found substantial contributions from nonperturbative regions in the Collins-Soper evolution kernel. In this article, we investigate semi-inclusive deep inelastic scattering measurements in the region of relatively small $Q$, of the order of a few GeV, where sensitivity to nonperturbative transverse momentum dependence may become more important or even dominate the evolution. Using recently available deep inelastic scattering data from the COMPASS experiment, we provide estimates of the regions of coordinate space that dominate in transverse momentum dependent (TMD) processes when the hard scale is of the order of only a few GeV. We find that distance scales that are much larger than those commonly probed in large $Q$ measurements become important, suggesting that the details of nonperturbative effects in TMD evolution are especially significant in the region of intermediate $Q$. We highlight the strongly universal nature of the nonperturbative component of evolution and its potential to be tightly constrained by fits from a wide variety of observables that include both large and moderate $Q$. On this basis, we recommend detailed treatments of the nonperturbative component of the Collins-Soper evolution kernel for future TMD studies.