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.

The description of strong interaction physics of low-lying resonances is out of the valid range of perturbative QCD. Chiral effective field theories (EFTs) have been developed to tackle the issue. Partial wave dynamics is the systematic tool to decode the underlying physics and reveal the properties of those resonances. It is extremely powerful and helpful for our understanding of the non-perturbative regime, especially when dispersion techniques are utilized simultaneously. Recently, plenty of exotic/ordinary hadrons have been reported by experiment collaborations, e.g. LHCb, Belle, and BESIII, etc. In this review, we summarize the recent progress on the applications of partial wave dynamics combined with chiral EFTs and dispersion relations, on related topics, with emphasis on ππ , πK , πN and K ̄ N scatterings.

In this paper we perform an amplitude analysis of essentially all published pion and kaon pair production data from two-photon collisions below 1.5 GeV. This includes all the high statistics results from Belle, as well as older data from Mark II at SLAC, CELLO at DESY, and Crystal Ball at SLAC. The purpose of this analysis is to provide as close to a model-independent determination of the $\gamma \gamma$ to meson pair amplitudes as possible. Having data with limited angular coverage, typically $|\cos \theta |<0.6–0.8$, and no polarization information for reactions in which spin is an essential complication, the determination of the underlying amplitudes might appear an intractable problem. However, imposing the basic constraints required by analyticity, unitarity, and crossing symmetry makes up for the experimentally missing information. Above 1.5 GeV multimeson production channels become important, and we have too little information to resolve the amplitudes. Nevertheless, below 1.5 GeV the two-photon production of hadron pairs serves as a paradigm for the application of $S$-matrix techniques. Final state interactions among the meson pairs are critical to this analysis. To fix these, we include the latest $\pi \pi \to \pi \pi$, $\overline{K}K$ scattering amplitudes given by dispersive analyses, supplemented in the $\overline{K}K$ threshold region by the recent precision Dalitz plot analysis from BABAR. With these hadronic amplitudes built into unitarity, we can constrain the overall description of $\gamma \gamma \to \pi \pi$ and $\overline{K}K$ data sets, both integrated and differential cross sections, including the high statistics charged and neutral pion, as well as $K_s{K}_s$, data from Belle. Since this analysis invokes coupled hadronic channels, having data on both $\pi \pi$ and $\overline{K}K$ reduces the solution space to essentially a single form in the region where these channels saturate unitarity. For the $\pi \pi$ channel, the separation of isospin-0 and -2 and helicity-0 and -2 components is complete. We present the partial wave amplitudes, show how well they fit all the available data, and give the two-photon couplings of scalar and tensor resonances that appear. These partial waves are important inputs into forthcoming dispersive calculations of hadronic light-by-light scattering.