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A<sc>bstract</sc> This paper presents a study of the charmless three-body decays$$ {B}_{(s)}^0\to {K}_{\mathrm{S}}^0{h}^{+}h{\prime}^{-} $$ $B_{\left(s\right)}^0\to K_S^0{h}^{+}h{\prime }^{-}$ (whereh⁽′⁾=π, K), using a sample ofppcollision data collected by the LHCb experiment during Runs 1 and 2 of the LHC, corresponding to an integrated luminosity of 9 fb⁻¹. The decay$$ {B}_s^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-} $$ $B_s^0\to K_S^0{K}^{+}{K}^{-}$ is observed for the first time, and the following ratios of branching fractions are measured:$$ {\displaystyle \begin{array}{l}\frac{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.578\pm 0.007\pm 0.017,\\ {}\frac{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{K}^{\mp}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.1363\pm 0.0035\pm 0.051,\\ {}\begin{array}{l}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.269\pm 0.011\pm 0.015\pm 0.008,\\ {}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{K}^{+}{K}^{-}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=0.0303\pm 0.0041\pm 0.0025\pm 0.0009,\\ {}\frac{\mathcal{B}\left({B}_s^0\to {K}_{\mathrm{S}}^0{K}^{\pm }{\pi}^{\mp}\right)}{\mathcal{B}\left({B}^0\to {K}_{\mathrm{S}}^0{\pi}^{+}{\pi}^{-}\right)}=1.818\pm 0.021\pm 0.031\pm 0.056,\end{array}\end{array}} $$ $\begin{array}{c}\frac{B\left(B^0\to K_S^0{K}^{+}{K}^{-}\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=0.578\pm 0.007\pm 0.017,\\ \frac{B\left(B^0\to K_S^0{K}^{\pm }{K}^{\mp }\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=0.1363\pm 0.0035\pm 0.051,\\ \begin{array}{c}\frac{B\left(B_s^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=0.269\pm 0.011\pm 0.015\pm 0.008,\\ \frac{B\left(B_s^0\to K_S^0{K}^{+}{K}^{-}\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=0.0303\pm 0.0041\pm 0.0025\pm 0.0009,\\ \frac{B\left(B_s^0\to K_S^0{K}^{\pm }{\pi }^{\mp }\right)}{B\left(B^0\to K_S^0{\pi }^{+}{\pi }^{-}\right)}=1.818\pm 0.021\pm 0.031\pm 0.056,\end{array}\end{array}$ where the uncertainties are statistical, systematic, and due to knowledge of the ratio of hadronisation fractions of the$$ {B}_s^0 $$ $B_s^0$ andB⁰mesons, respectively. 

A<sc>bstract</sc> A model-independent determination of the CKM angleγis presented, using theB^±→ [K⁺K⁻π⁺π⁻]_Dh^±andB^±→ [π⁺π⁻π⁺π⁻]_Dh^±decays, withh=K, π. This measurement is the first phase-space binned study of these decay modes, and uses a sample of proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of 9 fb⁻¹. The phase-space bins are optimised for sensitivity toγ, and in each bin external inputs from the BESIII experiment are used to constrain the charm strong-phase parameters. The result of this binned analysis is$$ \gamma ={\left(53.{9}_{-8.9}^{+9.5}\right)}^{{}^{\circ}} $$ $\gamma ={\left(53.9_{-8.9}^{+9.5}\right)}^{°}$ , where the uncertainty includes both statistical and systematic contributions. Furthermore, when combining with existing phase-space integrated measurements of the same decay modes, a value of$$ \gamma ={\left(52.{6}_{-6.4}^{+8.5}\right)}^{{}^{\circ}} $$ $\gamma ={\left(52.6_{-6.4}^{+8.5}\right)}^{°}$ is obtained, which is one of the most precise determinations ofγto date. 

The observation of a wide peaking structure in the $B_c^{+}\gamma$ mass spectrum is reported using proton-proton collision data collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of $9{\mathrm{fb}}^{-1}$ . The statistical significance over the background-only hypothesis exceeds seven standard deviations. The width of the observed structure is larger than the expectation from a single-peak hypothesis, and is well described by an effective minimal model consisting of two narrow peaks located at $6704.8\pm 5.5\pm 2.8\pm 0.3\mathrm{MeV}/c^2$ and $6752.4\pm 9.5\pm 3.1\pm 0.3\mathrm{MeV}/c^2$ . The uncertainty terms are statistical, systematic, and associated to the knowledge of the $B_c^{+}$ mass, respectively. The measured peak locations are in line with theoretical predictions for lowest excited $P$ -wave $B_c^{+}$ states, marking the first observation of orbitally excited beauty-charm mesons and providing important insights into the internal dynamics of hadrons containing two heavy quarks. 

A<sc>bstract</sc> A search for the decayB⁰→ ϕϕis made usingppcollision data collected with the LHCb detector 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, and an upper limit on the branching fraction of 1.3 (1.4) × 10⁻⁸at 90 (95)% confidence level is set. This result supersedes the previous LHCb study and improves the upper limit by a factor of two. 

A<sc>bstract</sc> The ratio between the branching fractions of theB⁰→ρ(770)⁰γandB⁰→K^*(892)⁰γdecays is measured with 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 measured value is$$ \frac{\mathcal{B}\left({B}^0\to \rho {(770)}^0\gamma \right)}{\mathcal{B}\left({B}^0\to {K}^{\ast }{(892)}^0\gamma \right)}=0.0189\pm 0.0007\pm 0.0005, $$ $\frac{B\left(B^0\to \rho {\left(770\right)}^0\gamma \right)}{B\left(B^0\to K^{\ast }{\left(892\right)}^0\gamma \right)}=0.0189\pm 0.0007\pm 0.0005,$ where the first uncertainty is statistical and the second systematic. The branching fraction forB⁰→ ρ(770)⁰γdecays is hence obtained as$$ \mathcal{B}\left({B}^0\to \rho {(770)}^0\gamma \right)=\left(7.9\pm 0.3\pm 0.2\pm 0.2\right)\times {10}^{-7}, $$ $B\left(B^0\to \rho {\left(770\right)}^0\gamma \right)=\left(7.9\pm 0.3\pm 0.2\pm 0.2\right)\times {10}^{-7},$ where the last uncertainty is due to the branching fraction of the normalisation mode. This result assumes that both theρ(770)⁰andK^*(892)⁰decays saturate the dihadron mass spectra considered in the analysis. It is consistent with the current world-average value and by far the most precise measurement to date. 

The transverse polarization of $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ hyperons is measured in $p\mathrm{Pb}$ collisions collected by the LHCb experiment at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The polarization is averaged over hyperon transverse momentum in the range $0.15<p_{\mathrm{T}}<6.00\mathrm{GeV}/c$ , and Feynman- $x$ in the ranges $0.005<x_{\mathrm{F}}<0.040$ (forward region) and $-0.10<x_{\mathrm{F}}<-0.01$ (backward region) defined relative to the proton beam direction. The transverse polarization is found to be compatible with zero for both $\mathrm{\Lambda }$ and $\overline{\mathrm{\Lambda }}$ hyperons. The results are also measured as a function of $p_{\mathrm{T}}$ and $x_{\mathrm{F}}$ with no significant dependence on these variables observed. The results are compared with previous experimental measurements at different center-of-mass energies and collision environments. 

The study of a wide peaking structure in the $B_c^{+}\gamma$ mass spectrum is reported using a data sample of proton-proton collisions collected by the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$ . The observed structure is consistent with the lowest excited $P$ -wave $B_c^{+}$ states and exhibits a statistical significance exceeding 7 standard deviations relative to the background-only hypothesis. A two-peak model serves as an effective description of the data, with various theory-constrained models further explored to provide physical interpretation. Based on the predictions for the $B_c(1P{)}^{+}$ spectrum, the relative production cross section of the overall $B_c(1P{)}^{+}$ states with respect to the $B_c^{+}$ ground state with the transverse momentum $p_{\mathrm{T}}$ and rapidity $y$ of $B_c^{+}$ mesons in the regions $p_{\mathrm{T}}<20\mathrm{GeV}/c$ and $2.0<y<4.5$ at $\sqrt{s}=13\mathrm{TeV}$ is measured to be $0.20\pm 0.03\pm 0.02\pm 0.03$ , where the uncertainty terms represent statistical, systematic, and uncertainties related to the choice of theoretical models, respectively. The results provide a test of theoretical models and deepen our understanding of quantum chromodynamics. 

A<sc>bstract</sc> A first search at LHCb for the lepton-flavour-violating decaysB⁰→K^*0τ^±e^∓is presented. The analysis is performed using a sample of proton-proton collision data, collected with the LHCb detector at a centre-of-mass energy of 13 TeV between 2016 and 2018, corresponding to an integrated luminosity of 5.4 fb⁻¹. No significant signal is observed, and upper limits on the branching fractions are determined to be$$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{-}{e}^{+}\right)<5.9(7.1)\times {10}^{-6} $$ $B\left(B^0\to K^{\ast 0}{\tau }^{-}{e}^{+}\right)<5.9\left(7.1\right)\times {10}^{-6}$ and$$ \mathcal{B}\left({B}^0\to {K}^{\ast 0}{\tau}^{+}{e}^{-}\right)<4.9(5.9)\times {10}^{-6} $$ $B\left(B^0\to K^{\ast 0}{\tau }^{+}{e}^{-}\right)<4.9\left(5.9\right)\times {10}^{-6}$ at the 90% (95%) confidence level. These results correspond to the current most stringent upper limits forb→sτltransitions. 

An amplitude analysis of the ${\mathrm{\Xi }}_c^{+}\to p{K}^{-}{\pi }^{+}$ decay together with a measurement of the ${\mathrm{\Xi }}_c^{+}$ polarization vector in semileptonic beauty-hadron decays is presented. The analysis is performed using proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$ . An amplitude model is developed and the resonance fractions as well as two- and three-body decay parameters are reported. A sizeable ${\mathrm{\Xi }}_c^{+}$ polarization is found. A large sensitivity of the ${\mathrm{\Xi }}_c^{+}\to p{K}^{-}{\pi }^{+}$ decay to the polarization is seen, making the amplitude model suitable for ${\mathrm{\Xi }}_c^{+}$ polarization measurements in other systems. 

A<sc>bstract</sc> The production ratio ofψ(2S) toJ/ψcharmonium states is presented as a function of multiplicity in proton-lead collisions at a centre-of-mass energy of$$ \sqrt{s_{\textrm{NN}}}=8.16 $$ $\sqrt{s_{\mathrm{NN}}}=8.16$ TeV, for both prompt and nonprompt sources. The total luminosity recorded by the LHCb experiment corresponds to 13.6 nb⁻¹forpPb collisions and 20.8 nb⁻¹for Pbpcollisions, where the first particle corresponds to the particle traveling towards the detector. Measurements are performed in the dimuon final state at forward (backward) centre-of-mass rapidity, with respect to the proton direction, 1.5< y^*<4.0 (−5.0< y^*<−2.5) forpPb (Pbp) collisions. A multiplicity dependence of the prompt production ratio is observed inpPb collisions, whereas no dependence is found in nonprompt production, nor in either prompt or nonprompt production in Pbpcollisions. These results suggest that in the Pb-going direction additional suppression mechanisms beyond comover effects may be present, possibly related to the formation of quark-gluon plasma. This highlights a transition from small to large collision systems and provides important insight into the suppression of charmonia in proton-nucleus collisions.