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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. 

A<sc>bstract</sc> An angular analysis of the$$ {B}_s^0 $$ $B_s^0$→ ϕe⁺e⁻decay is performed using the proton-proton collision dataset collected between 2011 and 2018 by the LHCb experiment, corresponding to an integrated luminosity of 9 fb⁻¹at centre-of-mass energies of 7, 8 and 13 TeV. The analysis is performed in the very low dielectron invariant mass-squared region between 0.0009 and 0.2615 GeV²/c⁴. The longitudinal polarisation fraction of theϕmeson is measured to be less than 11.5% at 90% confidence level. The$$ {A}_{\textrm{T}}^{\mathcal{R} eCP} $$ $A_T^{R\mathrm{eCP}}$observable, which is related to the lepton forward-backward asymmetry, is measured to be 0.116±0.155±0.006, where the first uncertainty is statistical and the second systematic. The transverse asymmetries,$$ {A}_{\textrm{T}}^{(2)} $$ $A_T^{\left(2\right)}$and$$ {A}_{\textrm{T}}^{\mathcal{I} mCP} $$ $A_T^{I\mathrm{mCP}}$, which are sensitive to the virtual photon polarisation, are found to be−0.045±0.235±0.014 and 0.002±0.247±0.016, respectively. The results are consistent with Standard Model predictions. 

A<sc>bstract</sc> An analysis of the flavour oscillations of the charmed neutral meson is presented. The ratio ofD⁰→K⁺π⁻andD⁰→K⁻π⁺decay rates is measured as a function of the decay time of theD⁰meson and compared with the charge-conjugated system to search for charge-parity violation. The meson flavour at production is double-tagged by the charges of the muon and pion in the preceding$$ \overline{B}\to {D}^{\ast }{(2010)}^{+}{\mu}^{-}X $$ $\overline{B}\to D^{\ast }{\left(2010\right)}^{+}{\mu }^{-}X$andD^∗(2010)⁺ → D⁰π⁺decays, respectively. These decays are selected from proton-proton collision data collected by the LHCb experiment at a centre-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 5.4 fb⁻¹. The flavour oscillation parameters, relating to the differences in mass and width of the mass eigenstates, are found to bey′ = (5.8 ± 1.6) × 10⁻³and (x′)²= (0.0 ± 1.2) × 10⁻⁴. No evidence for charge-parity violation is seen either in the flavour oscillations or in the decay, where the direct charge-parity asymmetry is measured to beA_D= (2.3 ± 1.7) %. 

A<sc>bstract</sc> A search for the fully reconstructed$$ {B}_s^0 $$ $B_s^0$→ μ⁺μ⁻γdecay is performed at the LHCb experiment using proton-proton collisions at$$ \sqrt{s} $$ $\sqrt{s}$= 13 TeV corresponding to an integrated luminosity of 5.4 fb⁻¹. No significant signal is found and upper limits on the branching fraction in intervals of the dimuon mass are set$$ {\displaystyle \begin{array}{cc}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[2{m}_{\mu },1.70\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<7.7\times {10}^{-8},&\ m\left({\mu}^{+}{\mu}^{-}\right)\in \left[\textrm{1.70,2.88}\right]\textrm{GeV}/{c}^2,\\ {}\mathcal{B}\left({B}_s^0\to {\mu}^{+}{\mu}^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu}^{+}{\mu}^{-}\right)\in \left[3.92,{m}_{B_s^0}\right]\textrm{GeV}/{c}^2,\end{array}} $$ $\begin{array}{cc}B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(2m_{\mu },1.70\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<7.7\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(\mathrm{1.70,\; 2.88}\right)\mathrm{GeV}/c^2,\\ B\left(B_s^0\to {\mu }^{+}{\mu }^{-}\gamma \right)<4.2\times {10}^{-8},& m\left({\mu }^{+}{\mu }^{-}\right)\in \left(3.92,m_{B_s^0}\right)\mathrm{GeV}/c^2,\end{array}$ at 95% confidence level. Additionally, upper limits are set on the branching fraction in the [2m_μ,1.70] GeV/c²dimuon mass region excluding the contribution from the intermediateϕ(1020) meson, and in the region combining all dimuon-mass intervals. 

A search for hidden-charm pentaquark states decaying to a range of ${\mathrm{\Sigma }}_c\overline{D}$and ${\mathrm{\Lambda }}_c^{+}\overline{D}$final states, as well as doubly charmed pentaquark states to ${\mathrm{\Sigma }}_{c}D$and ${\mathrm{\Lambda }}_c^{+}D$, is made using samples of proton-proton collision data corresponding to an integrated luminosity of $5.7{\mathrm{fb}}^{-1}$recorded by the LHCb detector at $\sqrt{s}=13\mathrm{TeV}$. Since no significant signals are found, upper limits are set on the pentaquark yields relative to that of the ${\mathrm{\Lambda }}_c^{+}$baryon in the ${\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+}$decay mode. The known pentaquark states are also investigated, and their signal yields are found to be consistent with zero in all cases. © 2024 CERN, for the LHCb Collaboration2024CERN 

A bstract A first search for the lepton-flavour violating decays B 0 → K *0 τ ± μ ∓ is presented. The analysis is performed using a sample of proton-proton collision data, collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV between 2011 and 2018, corresponding to an integrated luminosity of 9 fb − 1 . No significant signal is observed, and upper limits on the branching fractions are determined to be $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{+}{\mu}^{-}\right)<1.0(1.2)\times {10}^{-5} $$ B B 0 → K ∗ 0 τ + μ − < 1.0 1.2 × 10 − 5 and $$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{-}{\mu}^{+}\right)<8.2(9.8)\times {10}^{-6} $$ B B 0 → K ∗ 0 τ − μ + < 8.2 9.8 × 10 − 6 at the 90% (95%) confidence level. 

A bstract An amplitude analysis of the D + → π − π + π + decay is performed with a sample corresponding to 1.5 fb − 1 of integrated luminosity of pp collisions at a centre-of-mass energy $$ \sqrt{s} $$ s = 8 TeV collected by the LHCb detector in 2012. The sample contains approximately six hundred thousand candidates with a signal purity of 95%. The resonant structure is studied through a fit to the Dalitz plot where the π − π + S-wave amplitude is extracted as a function of π − π + mass, and spin-1 and spin-2 resonances are included coherently through an isobar model. The S-wave component is found to be dominant, followed by the ρ (770) 0 π + and f 2 (1270) π + components. A small contribution from the ω (782) → π − π + decay is seen for the first time in the D + → π − π + π + decay. 

A bstract We report on a measurement of the $$ {\Lambda}_c^{+} $$ Λ c + to D 0 production ratio in peripheral PbPb collisions at $$ \sqrt{s_{\textrm{NN}}} $$ s NN = 5 . 02 TeV with the LHCb detector in the forward rapidity region 2 < y < 4 . 5. The $$ {\Lambda}_c^{+} $$ Λ c + ( D 0 ) hadrons are reconstructed via the decay channel $$ {\Lambda}_c^{+} $$ Λ c + → pK − π + ( D 0 → K − π + ) for 2 < p T < 8 GeV/ c and in the centrality range of about 65–90%. The results show no significant dependence on p T , y or the mean number of participating nucleons. They are also consistent with similar measurements obtained by the LHCb collaboration in pPb and Pbp collisions at $$ \sqrt{s_{\textrm{NN}}} $$ s NN = 5 . 02 TeV. The data agree well with predictions from PYTHIA in pp collisions at $$ \sqrt{s} $$ s = 5 TeV but are in tension with predictions of the Statistical Hadronization model. 

A bstract A search for the lepton-flavour violating decays B 0 → K *0 μ ± e ∓ and $$ {B}_s^0 $$ B s 0 → ϕμ ± e ∓ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of 9 fb − 1 . No significant signals are observed and upper limits of $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{+}{e}^{-}\right)<5.7\times {10}^{-9}\left(6.9\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{-}{e}^{+}\right)<6.8\times {10}^{-9}\left(7.9\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{\pm }{e}^{\mp}\right)<10.1\times {10}^{-9}\left(11.7\times {10}^{-9}\right),\\ {}\mathcal{B}\left({B}_s^0\to \phi {\mu}^{\pm }{e}^{\mp}\right)<16.0\times {10}^{-9}\left(19.8\times {10}^{-9}\right)\end{array}} $$ B B 0 → K ∗ 0 μ + e − < 5.7 × 10 − 9 6.9 × 10 − 9 , B B 0 → K ∗ 0 μ − e + < 6.8 × 10 − 9 7.9 × 10 − 9 , B B 0 → K ∗ 0 μ ± e ∓ < 10.1 × 10 − 9 11.7 × 10 − 9 , B B s 0 → ϕ μ ± e ∓ < 16.0 × 10 − 9 19.8 × 10 − 9 are set at 90% (95%) confidence level. These results constitute the world’s most stringent limits to date, with the limit on the decay $$ {B}_s^0 $$ B s 0 → ϕμ ± e ∓ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios. 

This is the full high-level report of Snowmass 2021, the most recent of the U.S. High Energy Physics (HEP) Community Planning Exercises, sponsored by the Division of Particles and Fields (DPF) of the American Physical Society (APS), with strong consultation from the aligned APS Divisions of Nuclear Physics, Astrophysics, Gravitational Physics, and Physics of Beams. The goal of these community studies, the first of which was in 1982, has been to identify the most important scientific questions in HEP for the following decade, with an eye to the decade after that, and the facilities, infrastructure, and \R&D needed to pursue them. This report consists of an overall summary, chapters on each of the ten main working groups of the study, called "Frontiers", a chapter on the work of the Snowmass Early Career Organization, a chapter on the ongoing search for dark matter as an example of cross-Frontier and cross-disciplinary physics, and a short Conclusion. Many reports and white papers provided input to this document and they are also available on an associated website.