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Cosmic-ray physics in the GeV-to-TeV energy range has entered a precision era thanks to recent data from space-based experiments. However, the poor knowledge of nuclear reactions, in particular for the production of antimatter and secondary nuclei, limits the information that can be extracted from these data, such as source properties, transport in the Galaxy and indirect searches for particle dark matter. The Cross-Section for Cosmic Rays at CERN workshop series has addressed the challenges encountered in the interpretation of high-precision cosmic-ray data, with the goal of strengthening emergent synergies and taking advantage of the complementarity and know-how in different communities, from theoretical and experimental astroparticle physics to high-energy and nuclear physics. In this paper, we present the outcomes of the third edition of the workshop that took place in 2024. We present the current state of cosmic-ray experiments and their perspectives, and provide a detailed road map to close the most urgent gaps in cross-section data, in order to efficiently progress on many open physics cases, which are motivated in the paper. Finally, with the aim of being as exhaustive as possible, this report touches several other fields -- such as cosmogenic studies, space radiation protection and hadrontherapy -- where overlapping and specific new cross-section measurements, as well as nuclear code improvement and benchmarking efforts, are also needed. We also briefly highlight further synergies between astroparticle and high-energy physics on the question of cross-sections. 

The goal of the LHCspin project is to develop innovative solutions for measuring the 3D structure of nucleons in high-energy polarized fixed-target collisions at LHC, exploring new processes and exploiting new probes in a unique, previously unexplored, kinematic regime. A precise multi-dimensional description of the hadron structure has, in fact, the potential to deepen our understanding of the strong interactions and to provide a much more precise framework for measuring both Standard Model and Beyond Standard Model observables. This ambitious task poses its basis on the recent experience with the successful installation and operation of the SMOG2 unpolarized gas target in front of the LHCb spectrometer. Besides allowing for interest- ing physics studies ranging from astrophysics to heavy-ion physics, SMOG2 provides an ideal benchmark for studying beam-target dynamics at the LHC and demonstrates the feasibility of simultaneous operation with beam-beam collisions. With the installation of the proposed polarized target system, LHCb will become the first experiment to simultaneously collect data from unpolarized beam-beam collisions at √s=14 TeV and polarized and unpolar- ized beam-target collisions at √sNN ∼100 GeV. LHCspin has the potential to open new frontiers in physics by exploiting the capabilities of the world’s most powerful collider and one of the most advanced spectrometers. This document also highlights the need to perform an R&D campaign and the commissioning of the apparatus at the LHC Interaction Region 4 during the Run 4, before its final installation in LHCb. This opportunity could also allow to undertake preliminary physics measurements with unprecedented conditions. 

A<sc>bstract</sc> An angular analysis ofB⁰→ K^*0e⁺e⁻decays is presented using proton-proton collision data collected by the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV, corresponding to an integrated luminosity of 9 fb⁻¹. The analysis is performed in the region of the dilepton invariant mass squared of 1.1–6.0 GeV²/c⁴. In addition, a test of lepton flavour universality is performed by comparing the obtained angular observables with those measured inB⁰→ K^*0μ⁺μ⁻decays. In general, the angular observables are found to be consistent with the Standard Model expectations as well as with global analyses of otherb → sℓ⁺ℓ⁻processes, whereℓis either a muon or an electron. No sign of lepton-flavour-violating effects is observed. 

A<sc>bstract</sc> A search for the decay$$ {B}_c^{+} $$ $B_c^{+}$→ χ_c1(3872)π⁺is reported using proton-proton collision data collected with the LHCb detector between 2011 and 2018 at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of 9 fb⁻¹. No significant signal is observed. Using the decay$$ {B}_c^{+} $$ $B_c^{+}$→ψ(2S)π⁺as a normalisation channel, an upper limit for the ratio of branching fractions$$ {\mathcal{R}}_{\psi (2S)}^{\chi_{c1}(3872)}=\frac{{\mathcal{B}}_{B_c^{+}\to {\chi}_{c1}(3872){\pi}^{+}}}{{\mathcal{B}}_{B_c^{+}\to \psi (2S){\pi}^{+}}}\times \frac{{\mathcal{B}}_{\chi_{c1}(3872)\to J/\psi {\pi}^{+}{\pi}^{-}}}{{\mathcal{B}}_{\psi (2S)\to J/\psi {\pi}^{+}{\pi}^{-}}}<0.05(0.06), $$ $R_{\psi \left(2S\right)}^{{\chi }_{c1}\left(3872\right)}=\frac{B_{B_c^{+}\to {\chi }_{c1}\left(3872\right){\pi }^{+}}}{B_{B_c^{+}\to \psi \left(2S\right){\pi }^{+}}}\times \frac{B_{{\chi }_{c1}\left(3872\right)\to J/\psi {\pi }^{+}{\pi }^{-}}}{B_{\psi \left(2S\right)\to J/\psi {\pi }^{+}{\pi }^{-}}}<0.05\left(0.06\right),$ is set at the 90 (95)% confidence level. 

The branching fraction of the decay $B^{+}\to \psi \left(2S\right)\varphi \left(1020\right)K^{+}$, relative to the topologically similar decay $B^{+}\to J/\psi \varphi \left(1020\right)K^{+}$, is measured using proton-proton collision data collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. The ratio is found to be $0.061\pm 0.004\pm 0.009$, where the first uncertainty is statistical and the second systematic. Using the world-average branching fraction for $B^{+}\to J/\psi \varphi \left(1020\right)K^{+}$, the branching fraction for the decay $B^{+}\to \psi \left(2S\right)\varphi \left(1020\right)K^{+}$is found to be $(3.0\pm 0.2\pm 0.5\pm 0.2)\times {10}^{-6}$, where the first uncertainty is statistical, the second systematic, and the third is due to the branching fraction of the normalization channel. © 2025 CERN, for the LHCb Collaboration2025CERN 

The first measurement of the $CP$asymmetry of the decay rate ( $A_{CP}$) and the $CP$average ( $\mathrm{\Sigma }{A}_{\mathrm{FB}}$) and $CP$asymmetry ( $\mathrm{\Delta }{A}_{\mathrm{FB}}$) of the forward-backward asymmetry in the muon system of ${\mathrm{\Lambda }}_c^{+}\to p{\mu }^{+}{\mu }^{-}$decays is reported. The measurement is performed using a data sample of proton-proton collisions, recorded by the LHCb experiment from 2016 to 2018 at a center-of-mass energy of 13 TeV, which corresponds to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$. The asymmetries are measured in two regions of dimuon mass near the  $\varphi$-meson mass peak. The dimuon-mass integrated results are $A_{CP}=(-1.1\pm 4.0\pm 0.5)\%$, $\mathrm{\Sigma }{A}_{\mathrm{FB}}=(3.9\pm 4.0\pm 0.6)\%$, $\mathrm{\Delta }{A}_{\mathrm{FB}}=(3.1\pm 4.0\pm 0.4)\%$, where the first uncertainty is statistical and the second systematic. The results are consistent with the conservation of $CP$symmetry and the Standard Model expectations. © 2025 CERN, for the LHCb Collaboration2025CERN 

A search for $CP$violation in ${\mathrm{\Lambda }}_b^0\to p{K}^{-}$and ${\mathrm{\Lambda }}_b^0\to p{\pi }^{-}$decays is presented using the full Run 1 and Run 2 data samples of $pp$collisions collected with the LHCb detector, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$at center-of-mass energies of 7, 8, and 13 TeV. For the Run 2 data sample, the $CP$-violating asymmetries are measured to be $A_{CP}^{p{K}^{-}}=(-1.4\pm 0.7\pm 0.4)\%$and $A_{CP}^{p{\pi }^{-}}=(0.4\pm 0.9\pm 0.4)\%$, where the first uncertainty is statistical and the second is systematic. Following significant improvements in the evaluation of systematic uncertainties compared to the previous LHCb measurement, the Run 1 dataset is reanalyzed to update the corresponding results. When combining the Run 2 and updated Run 1 measurements, the final results are found to be $A_{CP}^{p{K}^{-}}=(-1.1\pm 0.7\pm 0.4)\%$and $A_{CP}^{p{\pi }^{-}}=(0.2\pm 0.8\pm 0.4)\%$, constituting the most precise measurements of these asymmetries to date. © 2025 CERN, for the LHCb Collaboration2025CERN 

A<sc>bstract</sc> TheΥ(2S) andΥ(3S) production cross-sections are measured relative to that of theΥ(1S) meson, as a function of charged-particle multiplicity in proton-proton collisions at a centre-of-mass energy of 13 TeV. The measurement uses data collected by the LHCb experiment in 2018 corresponding to an integrated luminosity of 2 fb⁻¹. Both theΥ(2S)-to-Υ(1S) andΥ(3S)-to-Υ(1S) cross-section ratios are found to decrease significantly as a function of event multiplicity, with theΥ(3S)-to-Υ(1S) ratio showing a steeper decline towards high multiplicity. This hierarchy is qualitatively consistent with the comover model predictions, indicating that final-state interactions play an important role in bottomonia production in high-multiplicity events. 

The first test of lepton flavor universality between muons and electrons using $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$( $\ell =e$, $\mu$) decays is presented. The measurement is performed with data from proton-proton collisions collected by the LHCb experiment at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$. The ratio of branching fractions between $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$and $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$decays is measured in the dilepton invariant-mass-squared range $1.1<q^2<7.0{\mathrm{GeV}}^2/c^4$and is found to be $R_{K\pi \pi }^{-1}=1.31_{-0.17}^{+0.18}\left(\mathrm{stat}){}_{-0.09}^{+0.12}\right(\mathrm{syst})$, in agreement with the standard model prediction. The first observation of the $B^{+}\to K^{+}{\pi }^{+}{\pi }^{-}{e}^{+}{e}^{-}$decay is also reported. © 2025 CERN, for the LHCb Collaboration2025CERN