A search is performed for rare and forbidden charm decays of the form $D_{(s)}^+ \to h^\pm \ell^+ \ell^{(\prime)\mp}$, where $h^\pm$ is a pion or kaon and $\ell^{(')\pm}$ is an electron or muon. The measurements are performed using proton-proton collision data, corresponding to an integrated luminosity of $1.6\text{fb}^{-1}$, collected by the LHCb experiment in 2016. No evidence is observed for the 25 decay modes that are investigated and $90\%$ confidence level limits on the branching fractions are set between $1.4\times10^{-8}$ and $6.4\times10^{-6}$. In most cases, these results represent an improvement on existing limits by one to two orders of magnitude.

The first untagged decay-time-integrated amplitude analysis of $B^{0}_{s} rightarrow K^{0}_{textrm{S}} K^{pm}pi^{mp}$ decays is performed using a sample corresponding to $3.0,$fb$^{-1}$ of $pp$ collision data recorded with the LHCb detector during 2011 and 2012. The data are described with an amplitude model that contains contributions from the intermediate resonances $K^{*}(892)^{0,+}$, $K^*_2(1430)^{0,+}$ and $K^*_0(1430)^{0,+}$, and their charge conjugates. Measurements of the branching fractions of the decay modes $B^{0}_{s} rightarrow K^{*}(892)^{pm}K^{mp}$ and $B^{0}_{s} rightarrow K^{*}(892)^{0}kern 0.2emoverline{kern -0.2em K}{}^{0}, kern 0.2emoverline{kern -0.2em K}{}^{*}(892)^{0}K^{0}$ are in agreement with, and more precise than, previous results. The decays $B^{0}_{s} rightarrow K^*_0(1430)^{pm} K^{mp}$ and $B^{0}_{s} rightarrow K^{*}_{0}(1430)^{0}kern 0.2emoverline{kern -0.2em K}{}^{0}, kern 0.2emoverline{kern -0.2em K}{}^{*}_{0}(1430)^{0}K^{0}$ are observed for the first time, each with significance over 10 standard deviations.

A search for charge-parity (CP) violation in Cabibbo-suppressed Ds+→KS0π+, D+→KS0K+, and D+→ϕπ+ decays is reported using proton-proton collision data, corresponding to an integrated luminosity of 3.8  fb-1, collected at a center-of-mass energy of 13 TeV with the LHCb detector. High-yield samples of kinematically and topologically similar Cabibbo-favored D(s)+ decays are analyzed to subtract nuisance asymmetries due to production and detection effects, including those induced by CP violation in the neutral kaon system. The results areACP(Ds+→KS0π+)=(1.3±1.9±0.5)×10-3,ACP(D+→KS0K+)=(-0.09±0.65±0.48)×10-3,ACP(D+→ϕπ+)=(0.05±0.42±0.29)×10-3,where the first uncertainties are statistical and the second systematic. They are the most precise measurements of these quantities to date, and are consistent with CP symmetry. A combination with previous LHCb measurements, based on data collected at 7 and 8 TeV, is also reported.

The production fraction of the Bc-meson with respect to the sum of B- A nd B0 mesons is measured in both 7 and 13 TeV center-of-mass (c.m.) energy pp collisions produced by the Large Hadron Collider (LHC), using the LHCb detector. The rate, approximately 3.7 per mille, does not change with energy, but shows a transverse momentum dependence. The Bc-Bc+ production asymmetry is also measured and is consistent with zero within the determined statistical and systematic uncertainties of a few percent.

The doubly Cabibbo-suppressed decay Ξ$_{c}^{+}$  → pϕ with ϕ → K$^{+}$K$^{−}$ is observed for the first time, with a statistical significance of more than fifteen standard deviations. The data sample used in this analysis corresponds to an integrated luminosity of 2 fb$^{−1}$ recorded with the LHCb detector in pp collisions at a centre-of-mass energy of 8 TeV. The ratio of branching fractions between the decay Ξ$_{c}^{+}$  → pϕ and the singly Cabibbo-suppressed decay Ξ$_{c}^{+}$  → pK$^{−}$π$^{+}$ is measured to be $ frac{mathrm{mathcal{B}}left({varXi}_c^{+}to pphi right)}{mathrm{mathcal{B}}left({varXi}_c^{+}to p{K}^{-}{pi}^{+}right)}=left(19.8pm 0.7pm 0.9pm 0.2right)times {10}^{-3}, $

Decays of $B_{s}^{0}$ and $overline{B}{}_{s}^{0}$ mesons into $J/psipi^+pi^-$ final states are studied in a data sample corresponding to 1.9 fb$^{-1}$ of integrated luminosity collected with the LHCb detector in 13 TeV $pp$ collisions. A time-dependent amplitude analysis is used to determine the final-state resonance contributions, the $CP$-violating phase $phi_s=-0.057pm 0.060pm 0.011$ rad, the decay-width difference between the heavier mass $B_{s}^{0}$ eigenstate and the $B^{0}$ meson of $-0.050pm 0.004pm 0.004$ ps$^{-1}$, and the $CP$-violating parameter $|lambda|=1.01_{-0.06}^{+0.08}pm0.03$, where the first uncertainty is statistical and the second systematic. These results are combined with previous LHCb measurements in the same decay channel using 7 TeV and 8 TeV $pp$ collisions obtaining $phi_s =0.002pm0.044pm0.012$ rad, and $|lambda| =0.949pm0.036pm0.019$.

A search for the rare leptonic decay $B^{+} rightarrow {mu}^{+}{mu}^{-}{mu}^{+}{nu}_{{mu}}$ is performed using proton-proton collision data corresponding to an integrated luminosity of $4.7$ fb$^{-1}$ collected by the LHCb experiment. The search is carried out in the region where the lowest of the two ${mu}^{+}{mu}^{-}$ mass combinations is below $980$MeV/c$^{2}$. The data are consistent with the background-only hypothesis and an upper limit of $1.6 times 10^{-8}$ at 95% confidence level is set on the branching fraction in the stated kinematic region.

The first observation of the Bs0→D¯*0ϕ decay is reported, with a significance of more than seven standard deviations, from an analysis of pp collision data corresponding to an integrated luminosity of 3  fb-1, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The branching fraction is measured relative to that of the topologically similar decay B0→D¯0π+π- and is found to be B(Bs0→D¯*0ϕ)=(3.7±0.5±0.3±0.2)×10-5, where the first uncertainty is statistical, the second systematic, and the third from the branching fraction of the B0→D¯0π+π- decay. The fraction of longitudinal polarization in this decay is measured to be fL=(73±15±4)%. The most precise determination of the branching fraction for the Bs0→D¯0ϕ decay is also obtained, B(Bs0→D¯0ϕ)=(3.0±0.3±0.2±0.2)×10-5. An upper limit, B(B0→D¯0ϕ)u003c2.0 (2.3)×10-6 at 90% (95%) confidence level is set. A constraint on the ω-ϕ mixing angle δ is set at |δ|u003c5.2° (5.5°) at 90% (95%) confidence level.

The doubly charmed baryon decay Ξcc++→Ξc+π+ is observed for the first time, with a statistical significance of 5.9σ, confirming a recent observation of the baryon in the Λc+K-π+π+ final state. The data sample used corresponds to an integrated luminosity of 1.7  fb-1, collected by the LHCb experiment in pp collisions at a center-of-mass energy of 13 TeV. The Ξcc++ mass is measured to be 3620.6±1.5(stat)±0.4(syst)±0.3(Ξc+)  MeV/c2 and is consistent with the previous result. The ratio of branching fractions between the decay modes is measured to be [B(Ξcc++→Ξc+π+)×B(Ξc+→pK-π+)]/[B(Ξcc++→Λc+K-π+π+)×B(Λc+→pK-π+)]=0.035±0.009(stat)±0.003(syst).

The branching fraction and direct $C!P$ asymmetry of the decay $B^{+}rightarrow J/psi rho^{+}$ are measured using proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7 and 8 TeV, corresponding to a total integrated luminosity of 3$mbox{fb}^{-1}$. The following results are obtained: begin{align} mathcal{B}(B^{+}rightarrow J/psi rho^{+}) u0026= (3.81 ^{+0.25}_{-0.24} pm 0.35) times 10^{-5}, nonumber mathcal{A}^{C!P} (B^{+}rightarrow J/psi rho^{+}) u0026= -0.045^{+0.056}_{-0.057} pm 0.008, nonumber end{align} where the first uncertainties are statistical and the second systematic. Both measurements are the most precise to date.

A measurement of the time-integrated $CP$ asymmetry in $D^0rightarrow K^0_S K^0_S$ decays is reported. The data correspond to an integrated luminosity of about $2$ fb$^{-1}$ collected in 2015-2016 by the LHCb collaboration in $pp$ collisions at a centre-of-mass energy of $13$ TeV. The $D^0$ candidate is required to originate from a $D^{ast +} rightarrow D^0 pi^+$ decay, allowing the determination of the flavour of the $D^0$ meson using the pion charge. The $D^0 rightarrow K^{+}K^{-}$ decay, which has a well measured $CP$ asymmetry, is used as a calibration channel. The $CP$ asymmetry for $D^0rightarrow K^0_S K^0_S$ is measured to be begin{equation*} mathcal{A}^{CP}(D^0rightarrow K^0_S K^0_S) = (4.3pm 3.4pm 1.0)%, end{equation*} where the first uncertainty is statistical and the second is systematic. This result is combined with the previous LHCb measurement at lower centre-of-mass energies to obtain begin{equation*} mathcal{A}^{CP}(D^0rightarrow K^0_S K^0_S) = (2.3pm 2.8pm 0.9)%. end{equation*}

A search for CP violation in Λb0→pK− and Λb0→pπ− decays is presented using a sample of pp collisions collected with the LHCb detector and corresponding to an integrated luminosity of 3.0 fb−1 . The CP -violating asymmetries are measured to be ACPpK−=−0.020±0.013±0.019 and ACPpπ−=−0.035±0.017±0.020 , and their difference ACPpK−−ACPpπ−=0.014±0.022±0.010 , where the first uncertainties are statistical and the second systematic. These are the most precise measurements of such asymmetries to date.

The first observation of the $B_s^0 overline{D}^0 K^+ K^-$ decay is reported, together with the most precise branching fraction measurement of the mode $B^0 overline{D}^0 K^+ K^-$. The results are obtained from an analysis of $pp$ collision data corresponding to an integrated luminosity of $3.0~textrm{fb}^{-1}$. The data were collected with the LHCb detector at centre-of-mass energies of $7$ and $8$ TeV. The branching fraction of the $B^0 overline{D}^0 K^+ K^-$ decay is measured relative to that of the decay $B^0 overline{D}^0 pi^+ pi^-$ to be $$frac{mathcal{B}(B^0 overline{D}^0 K^+ K^-)}{mathcal{B}(B^0 overline{D}^0 pi^+ pi^-)} = (6.9 pm 0.4 pm 0.3)%,$$ where the first uncertainty is statistical and the second is systematic. The measured branching fraction of the $B_s^0 overline{D}^0 K^+ K^-$ decay mode relative to that of the corresponding $B^0$ decay is $$frac{mathcal{B}(B_s^0 overline{D}^0 K^+ K^-)}{mathcal{B}(B^0 overline{D}^0 K^+ K^-)} = (93.0 pm 8.9 pm 6.9)%.$$ Using the known branching fraction of ${B^0 overline{D}^0 pi^+ pi^-}$, the values of ${{mathcal B}(B^0 overline{D}^0 K^+ K^- )=(6.1 pm 0.4 pm 0.3 pm 0.3) times 10^{-5}}$, and ${{cal B}(B_s^0 overline{D}^0 K^+ K^-)=}$ $(5.7 pm 0.5 pm 0.4 pm 0.5) times 10^{-5}$ are obtained, where the third uncertainties arise from the branching fraction of the decay modes ${B^0 overline{D}^0 pi^+ pi^-}$ and $B^0 overline{D}^0 K^+ K^-$, respectively.

Amplitude models are constructed describe the resonance structure of ${D^{0}to K^{-}pi^{+}pi^{+}pi^{-}}$ and ${D^{0} to K^{+}pi^{-}pi^{-}pi^{+}}$ decays using $pp$ collision data collected at centre-of-mass energies of 7 and 8 TeV with the LHCb experiment, corresponding an integrated luminosity of $3.0mathrm{fb}^{-1}$. The largest contributions both decay amplitudes are found come from axial resonances, with decay modes $D^{0} to a_1(1260)^{+} K^{-}$ and $D^{0} to K_1(1270/1400)^{+} pi^{-}$ being prominent in ${D^{0}to K^{-}pi^{+}pi^{+}pi^{-}}$ and $D^{0}to K^{+}pi^{-}pi^{-}pi^{+}$, respectively. Precise measurements of the lineshape parameters and couplings of the $a_1(1260)^{+}$, $K_1(1270)^{-}$ and $K(1460)^{-}$ resonances are made, and a quasi model-independent study of the $K(1460)^{-}$ resonance is performed. The coherence factor of the decays is calculated from the amplitude models be $R_{K3pi} = 0.459pm 0.010,(mathrm{stat}) pm 0.012,(mathrm{syst}) pm 0.020,(mathrm{model})$, which is consistent with direct measurements. These models will be useful in future measurements of the unitary-triangle angle $gamma$ and studies of charm mixing and $C!P$ violation.

A search for CP violation in the Cabibbo-suppressed D0 → K+K−π+π− decay mode is performed using an amplitude analysis. The measurement uses a sample of pp collisions recorded by the LHCb experiment during 2011 and 2012, corresponding to an integrated luminosity of 3.0 fb−1. The D0 mesons are reconstructed from semileptonic b-hadron decays into D0μ−X final states. The selected sample contains more than 160 000 signal decays, allowing the most precise amplitude modelling of this D0 decay to date. The obtained amplitude model is used to perform the search for CP violation. The result is compatible with CP symmetry, with a sensitivity ranging from 1% to 15% depending on the amplitude considered.

The first observation of two structures consistent with resonances in the final states Λ_{b}^{0}π^{-} and Λ_{b}^{0}π^{+} is reported using samples of pp collision data collected by the LHCb experiment at sqrt[s]=7 and 8 TeV, corresponding to an integrated luminosity of 3  fb^{-1}. The ground states Σ_{b}^{±} and Σ_{b}^{*±} are also confirmed and their masses and widths are precisely measured.