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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. 

Abstract An amplitude analysis of the$${{{B} ^0} \!\rightarrow {\eta _{c}} (1S) {{K} ^+} {{\pi } ^-}} $$ $B^0\to {\eta }_c\left(1S\right)K^{+}{\pi }^{-}$ decays with$${\eta _{c}} (1S) \rightarrow {p} {\overline{{p}}} $$ ${\eta }_c\left(1S\right)\to p\overline{p}$ is performed using a sample corresponding to an integrated luminosity of 9$$\,\text {fb} ^{-1}$$ ${\text{fb}}^{-1}$ of$$p $$ $p$ $$p $$ $p$ collision data collected by the LHCb detector at centre-of-mass energies of$$\sqrt{s}$$ $\sqrt{s}$ = 7, 8 and 13$$\,\text {Te\hspace{-1.00006pt}V}$$ $\text{Te}\text{V}$ . The data are described with a model including only intermediate contributions from known$${K} ^{*0}$$ $K_{}^{\ast 0}$ resonances. Evidence for an exotic resonance in the$${\eta _{c}} (1S) {{\pi } ^-} $$ ${\eta }_c\left(1S\right){\pi }^{-}$ system, reported in a previous analysis of this decay channel, is not confirmed. The inclusive branching fraction of the$${{B} ^0} \rightarrow {\eta _{c}} (1S) {{K} ^+} {{\pi } ^-} $$ $B^0\to {\eta }_c\left(1S\right)K^{+}{\pi }^{-}$ decays is measured to be$$\begin{aligned}&\mathcal {B}({{B} ^0} \rightarrow {\eta _{c}} (1S) {{K} ^+} {{\pi } ^-}) \\&\quad = (5.82 \pm 0.20 \pm 0.23 \pm 0.55) \times 10^{-4}, \end{aligned}$$ $\begin{array}{cc}& B(B^0\to {\eta }_c\left(1S\right)K^{+}{\pi }^{-})\\ & =(5.82\pm 0.20\pm 0.23\pm 0.55)\times {10}^{-4},\end{array}$ where the first uncertainty is statistical, the second systematic, and the third arises from the limited knowledge of external branching fractions. 

A<sc>bstract</sc> A measurement of the branching fraction for the decay$$ \Lambda \to p{\mu}^{-}{\overline{\nu}}_{\mu } $$ $\Lambda \to p{\mu }^{-}{\overline{\nu }}_{\mu }$ is presented usingppcollision data collected by the LHCb experiment at a centre-of-mass energy of 13 TeV. The analysis is based on data recorded between 2016 and 2018, corresponding to an integrated luminosity of 5.4 fb⁻¹. The result is obtained using Λ→ pμ⁻decays as a normalisation channel. The measured branching fraction is$$ \mathcal{B}\left(\Lambda \to p{\mu}^{-}{\overline{\nu}}_{\mu}\right)=\left(1.462\pm 0.016\pm 0.100\pm 0.011\right)\times {10}^{-4} $$ $B\left(\Lambda \to p{\mu }^{-}{\overline{\nu }}_{\mu }\right)=\left(1.462\pm 0.016\pm 0.100\pm 0.011\right)\times {10}^{-4}$ , where the uncertainties are statistical, systematic, and due to the limited knowledge of the normalisation mode branching fraction, respectively. This result improves the precision of the branching fraction measurement by a factor of two compared to the previous best measurement and sets a more stringent bound on lepton flavour universality ins → uquark transitions. It is consistent with previous measurements, and the extracted lepton flavour universality test observable,$$ {R}^{\mu e}=\frac{\Gamma \left(\Lambda \to p{\mu}^{-}{\overline{\nu}}_{\mu}\right)}{\Gamma \left(\Lambda \to p{e}^{-}{\overline{\nu}}_e\right)}=0.175\pm 0.012 $$ $R^{\mathrm{\mu e}}=\frac{\Gamma \left(\Lambda \to p{\mu }^{-}{\overline{\nu }}_{\mu }\right)}{\Gamma \left(\Lambda \to p{e}^{-}{\overline{\nu }}_e\right)}=0.175\pm 0.012$ , agrees with the Standard Model prediction. 

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. 

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. 

Searches are presented for $B_c^{+}\to D{h}^{+}{h}^{-}$ decays, where $D$ is a charmed meson and $h^{\pm }$ is a charged pion or kaon, using $pp$ collision data collected by the LHCb experiment corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$ . The decays $B_c^{+}\to D^{+}{K}^{+}{\pi }^{-}$ , $B_c^{+}\to D^{*+}{K}^{+}{\pi }^{-}$ , and $B_c^{+}\to D_s^{+}{K}^{+}{K}^{-}$ are observed for the first time. Their branching fractions, expressed as ratios relative to that of the $B_c^{+}\to B_s^0{\pi }^{+}$ decay, are determined to be $\mathcal{R}(B_c^{+}\to D^{+}{K}^{+}{\pi }^{-})=(1.96\pm 0.23\pm 0.08\pm 0.10)\times {10}^{-3}$ , $\mathcal{R}(B_c^{+}\to D^{*+}{K}^{+}{\pi }^{-})=(3.67\pm 0.55\pm 0.24\pm 0.20)\times {10}^{-3}$ , $\mathcal{R}(B_c^{+}\to D_s^{+}{K}^{+}{K}^{-})=(1.61\pm 0.35\pm 0.13\pm 0.07)\times {10}^{-3}$ , where the first uncertainty is statistical, the second is systematic, and the third is due to the limited precision on the $D$ -meson branching fractions. The decay channels proceed primarily through excited $K^0$ or $D^0$ resonances or $\varphi$ mesons, and open a new avenue for studies of charge-parity violation in beauty mesons. 

An amplitude analysis of the $B^{+}\to \left({\pi }^{+}{\pi }^{-}\right)\left(K_{\mathrm{S}}^0{\pi }^{+}\right)$ decay is performed in the mass regions $0.30<m_{{\pi }^{+}{\pi }^{-}}<1.10\mathrm{GeV}/c^2$ and $0.75<m_{K_{\mathrm{S}}^0{\pi }^{+}}<1.20\mathrm{GeV}/c^2$ , using $pp$ collision data recorded with the LHCb detector corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$ . The polarization fractions and $CP$ asymmetries for $B^{+}\to \rho \left(770{)}^0{K}^{*}\right(892{)}^{+}$ decays are measured. Violation of the $CP$ symmetry in the decay $B^{+}\to \rho \left(770{)}^0{K}^{*}\right(892{)}^{+}$ is observed for the first time, with a significance exceeding 9 standard deviations. The $CP$ asymmetry is measured to be ${\mathcal{A}}_{CP}=0.507\pm 0.062\left(\mathrm{stat}\right)\pm 0.024\left(\mathrm{syst}\right)$ and the $CP$ -averaged longitudinal polarization fraction of $f_L=0.720\pm 0.028\left(\mathrm{stat}\right)\pm 0.009\left(\mathrm{syst}\right)$ . The measurements help to shed light on the polarization puzzle of $B$ mesons decaying to two vector mesons.