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Abstract Kaon physics is at a turning point – while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop, held in September 2023 at CERN. 

A<sc>bstract</sc> Thepp→W^±(→μ^±ν_μ)Xcross-sections are measured at a proton-proton centre-of-mass energy$$ \sqrt{s}=5.02 $$ $\sqrt{s}=5.02$TeV using a dataset corresponding to an integrated luminosity of 100 pb⁻¹recorded by the LHCb experiment. Considering muons in the pseudorapidity range 2.2< η <4.4, the cross-sections are measured differentially in twelve intervals of muon transverse momentum between 28< p_T<52 GeV. Integrated overp_T, the measured cross-sections are$$ {\displaystyle \begin{array}{c}{\sigma}_{W^{+}\to {\mu}^{+}{\nu}_{\mu }}=300.9\pm 2.4\pm 3.8\pm 6.0\ \textrm{pb},\\ {}{\sigma}_{W^{-}\to {\mu}^{-}{\overline{\nu}}_{\mu }}=236.9\pm 2.1\pm 2.7\pm 4.7\ \textrm{pb},\end{array}} $$ $\begin{array}{c}{\sigma }_{W^{+}\to {\mu }^{+}{\nu }_{\mu }}=300.9\pm 2.4\pm 3.8\pm 6.0\mathrm{pb},\\ {\sigma }_{W^{-}\to {\mu }^{-}{\overline{\nu }}_{\mu }}=236.9\pm 2.1\pm 2.7\pm 4.7\mathrm{pb},\end{array}$ where the first uncertainties are statistical, the second are systematic, and the third are associated with the luminosity calibration. These integrated results are consistent with theoretical predictions. This analysis introduces a new method to determine theW-boson mass using the measured differential cross-sections corrected for detector effects. The measurement is performed on this statistically limited dataset as a proof of principle and yields$$ {m}_W=80369\pm 130\pm 33\ \textrm{MeV}, $$ $m_W=80369\pm 130\pm 33\mathrm{MeV},$ where the first uncertainty is experimental and the second is theoretical. 

The first dedicated $Z$-boson mass measurement at the LHC with $Z\to {\mu }^{+}{\mu }^{-}$decays is reported. The dataset uses proton-proton collisions at a center-of-mass energy of 13 TeV, recorded in 2016 by the LHCb experiment, and corresponds to an integrated luminosity of $1.7{\mathrm{fb}}^{-1}$. A template fit to the ${\mu }^{+}{\mu }^{-}$mass distribution yields the following result for the $Z$-boson mass: $m_Z=91,185.7\pm 8.3\pm 3.9\mathrm{MeV}$, where the first uncertainty is statistical and the second systematic. This result is consistent with previous measurements and predictions from global electroweak fits. 

The substructure of jets in quantum chromodynamics (QCD) has garnered significant attention with the advent of infrared- and collinear-safe clustering algorithms and observables. A key question emerging from these studies is how in-jet emissions at soft and hard energy scales, across collinear and wide angles relative to the emitter, differ with the mass of the emitting parton. The Lund jet plane (LJP) is a perturbatively well-defined substructure observable that maps the radiation pattern of jets onto a plane, visually distinguishing emissions with different kinematic properties. Comparing LJP for jets containing hadrons of low versus high mass enables the testing of QCD splitting functions from first-principles calculations across both soft and hard regimes and at different radiation angles. This article presents the first measurement of the LJP for light-quark-enriched and beauty-initiated jets at a center-of-mass energy of 13 TeV at LHCb. This marks the first direct observation of the dead-cone effect in beauty-quark jets, measured in the collinear region of the LJP. 

A bstract The NA62 experiment at CERN targets the measurement of the ultra-rare $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ K + → π + ν ν ¯ decay, and carries out a broad physics programme that includes probes for symmetry violations and searches for exotic particles. Data were collected in 2016–2018 using a multi-level trigger system, which is described highlighting performance studies based on 2018 data. 

A bstract A sample of 2 . 8 × 10 4 K + → π + μ + μ − candidates with negligible background was collected by the NA62 experiment at the CERN SPS in 2017–2018. The model-independent branching fraction is measured to be (9 . 15 ± 0 . 08) × 10 − 8 , a factor three more precise than previous measurements. The decay form factor is presented as a function of the squared dimuon mass. A measurement of the form factor parameters and their uncertainties is performed using a description based on Chiral Perturbation Theory at $$ \mathcal{O} $$ O ( p 6 ).