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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 search is performed for lepton-number-violating $B^{-}\to D^{(*)+}{\mu }^{-}{\mu }^{-}$ decays, using data collected by the LHCb experiment in proton-proton collisions at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$ . No significant signal is observed, and upper limits are set on the branching fractions, $\mathcal{B}(B^{-}\to D^{+}{\mu }^{-}{\mu }^{-})<4.6\times {10}^{-8}$ and $\mathcal{B}(B^{-}\to D^{*+}{\mu }^{-}{\mu }^{-})<5.9\times {10}^{-8}$ , at the 95% confidence level. 

A time- and flavor-integrated amplitude analysis of $B^0$ and $B_s^0$ decays to the $\left(K^{+}{\pi }^{-}\right)\left(K^{-}{\pi }^{+}\right)$ final state in the $K^{*}\left(892{)}^0{\overline{K}}^{*}\right(892{)}^0$ region is presented, using $pp$ collision data recorded with the LHCb detector in 2011–2018, corresponding to an integrated luminosity of $9{\mathrm{fb}}^{-1}$ . The branching fractions of the $B^0$ and $B_s^0$ decays are measured relative to the $B^0\to D^{-}{\pi }^{+}$ and $B_s^0\to D_s^{-}{\pi }^{+}$ modes, respectively. The corresponding longitudinal polarization fractions are found to be $f_L^d=0.600\pm 0.022\pm 0.017$ and $f_L^s=0.159\pm 0.010\pm 0.007$ , where the uncertainties are statistical and systematic, respectively. The theory-motivated ratio of the squared $B_s^0$ to $B^0$ longitudinally polarized decay amplitudes is found to be $L_{K^{*0}{\overline{K}}^{*0}}=4.92\pm 0.55\pm 0.48\pm 0.02\pm 0.10$ , where the uncertainties are statistical, systematic, due to uncertainty of external mass and lifetime measurements, and due to knowledge of the fragmentation fraction ratio, respectively. This confirms the previously reported tension between experimental determinations and theoretical predictions of longitudinal polarization in $B\to VV$ decays at the level of 4.4 standard deviations. 

The first searches for $B^0\to K^{+}{\pi }^{-}{\tau }^{+}{\tau }^{-}$ and $B_s^0\to K^{+}{K}^{-}{\tau }^{+}{\tau }^{-}$ decays at the LHCb experiment are conducted with $pp$ collision data corresponding to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$ . The tau leptons are reconstructed using the ${\tau }^{+}\to {\mu }^{+}{\overline{\nu }}_{\tau }{\nu }_{\mu }$ decay and the results are presented in bins of $K^{+}{\pi }^{-}$ or $K^{+}{K}^{-}$ mass. No signal is observed and upper limits are set on the branching fractions. The searches result in the first upper limits for $B^0\to K^{+}{\pi }^{-}{\tau }^{+}{\tau }^{-}$ decays outside the $K^{*}(892{)}^0$ region in $K^{+}{\pi }^{-}$ mass and the first limits for $B_s^0\to K^{+}{K}^{-}{\tau }^{+}{\tau }^{-}$ decays. The searches are recast into limits on the decays $B^0\to K^{*}(892{)}^0{\tau }^{+}{\tau }^{-}$ and $B_s^0\to \varphi \left(1020\right){\tau }^{+}{\tau }^{-}$ , yielding $2.8\times {10}^{-4}$ ( $2.5\times {10}^{-4}$ ) and $4.7\times {10}^{-4}$ ( $4.1\times {10}^{-4}$ ) at the 95% (90%) confidence level, respectively. For the decay $B^0\to K^{*}(892{)}^0{\tau }^{+}{\tau }^{-}$ , this result improves on the current best upper limit by an order of magnitude. 

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 search for $K_{\mathrm{S}\left(\mathrm{L}\right)}^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ decays is performed using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$ . No $K_{\mathrm{S}\left(\mathrm{L}\right)}^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-}$ signals are found and upper limits are set for the first time on the branching fractions $\mathcal{B}(K_{\mathrm{S}}^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-})<1.4\times {10}^{-9}$ and $\mathcal{B}(K_{\mathrm{L}}^0\to {\pi }^{+}{\pi }^{-}{\mu }^{+}{\mu }^{-})<6.6\times {10}^{-7}$ , at the 90% confidence level. 

The first search for the $B_s^0\to K^{-}{\pi }^{+}\gamma$ decay in the range $796<m\left(K^{-}{\pi }^{+}\right)<1800\mathrm{MeV}/c^2$ is performed using 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 photons are reconstructed through their conversion into an electron-positron pair, which significantly improves the mass resolution of the reconstructed decays with respect to decays with an unconverted photon. A signal excess with a significance of 3.5 standard deviations is measured, constituting the first experimental evidence for this decay. In the range $796<m\left(K^{-}{\pi }^{+}\right)<996\mathrm{MeV}/c^2$ , the ratio $\mathcal{R}$ between the branching fractions of the signal decay and the favored ${\overline{B}}^0\to K^{-}{\pi }^{+}\gamma$ decay is measured to be $\mathcal{R}=(3.7\pm 1.2\pm 0.4)\times {10}^{-2}$ where the first uncertainty is statistical and the second is systematic. This measurement is consistent with the value predicted in the Standard Model. In the range $996<m\left(K^{-}{\pi }^{+}\right)<1800\mathrm{MeV}/c^2$ , the ratio $\mathcal{R}=(0.2\pm 2.7\pm 1.3)\times {10}^{-2}$ is measured. 

The first four-dimensional amplitude analysis of the $B^{+}\to \psi \left(2S\right)K_{\mathrm{S}}^0{\pi }^{+}$ decay is performed with proton-proton collision data collected by the LHCb experiment at $\sqrt{s}=13\mathrm{TeV}$ , corresponding to an integrated luminosity of $5.4\mathrm{f}{\mathrm{b}}^{-1}$ . The data cannot be fully explained by $B^{+}\to \psi \left(2S\right)K^{*+}$ contributions alone. A significantly better description of the data is obtained by adding a $T_{c\overline{c}}^{+}$ contribution decaying to $\psi \left(2S\right){\pi }^{+}$ . The properties of the $T_{c\overline{c}}^{+}$ structure are consistent with the exotic state $T_{c\overline{c}1}(4430{)}^{+}$ reported in the isospin-related ${\overline{B}}^0\to \psi \left(2S\right)K^{-}{\pi }^{+}$ decay. Effects of a possible $T_{c\overline{c}1}(4430{)}^{+}\to {\overline{D}}_1^{*}(2600{)}^0{D}^{+}$ decay mode on the $T_{c\overline{c}1}(4430{)}^{+}\to \psi (2S){\pi }^{+}$ mass distribution are investigated through a Flatté parametrization, providing constraints on the relative decay strength. A description of the $T_{c\overline{c}1}(4430{)}^{+}$ structure using the triangle singularity mechanism is studied and also found to be consistent with the data. 

The decay $B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm }$ , with a $CP$ asymmetry expected to be close to zero in the standard model, is theoretically clean and sensitive to potential new physics. An analysis of the decays $B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm }$ and $B^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }$ is performed using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$ . The $CP$ asymmetries are determined to be ${\mathcal{A}}^{CP}(B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm })=-0.028\pm 0.009\pm 0.009$ and ${\mathcal{A}}^{CP}(B^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm })=0.118\pm 0.062\pm 0.031$ , and the branching fraction ratio is measured to be $\mathcal{B}(B^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm })/\mathcal{B}(B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm })=0.055\pm 0.004\pm 0.002$ , where the first uncertainties are statistical and the second are systematic. These results are the most precise measurements of these quantities to date. A search for the rare decay $B_c^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm }$ is also performed. No significant signal is observed, and the upper limit on the product of the branching fraction ratio $\mathcal{B}(B_c^{\pm }\to K_{\mathrm{S}}^0{K}^{\pm })/\mathcal{B}(B^{\pm }\to K_{\mathrm{S}}^0{\pi }^{\pm })$ and the fragmentation-fraction ratio $f_c/f_u$ is set to be 0.015 (0.016) at the 90% (95%) confidence level. 

A<sc>bstract</sc> Charged-hadron distributions in heavy-flavor jets are measured in proton-proton collisions at a center-of-mass energy of$$ \sqrt{s}=13 $$ $\sqrt{s}=13$ TeV collected by the LHCb experiment. Distributions of the longitudinal momentum fraction, transverse momentum, and radial profile of charged hadrons are measured separately in beauty and charm jets. The distributions are compared to those previously measured by the LHCb collaboration in jets produced back-to-back with aZboson, which in the forward region are primarily light-quark-initiated, to compare the hadronization mechanisms of heavy and light quarks. The observed differences between the heavy- and light-jet distributions are consistent with the heavy-quark dynamics expected to arise from the dead-cone effect, as well as with a hard fragmentation of the heavy-flavor hadron as previously measured in single-hadron fragmentation functions. This measurement provides additional constraints for the extraction of collinear and transverse-momentum-dependent heavy-flavor fragmentation functions and offers another approach to probing the mechanisms that govern heavy-flavor hadronization.