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The first search for nonresonant [Formula omitted] decays is reported. The analysis uses proton-proton collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 [Formula omitted]. No evidence for an excess of signal events over background is observed and an upper limit is set on the branching fraction ratio [Formula omitted] at [Formula omitted] confidence level. Additionally, an updated measurement of the ratio of the [Formula omitted] and [Formula omitted] branching fractions is reported. The ratio [Formula omitted] is measured to be [Formula omitted], where the first uncertainty is statistical, the second systematic, and the third is due to the uncertainties on the branching fractions of the leptonic [Formula omitted] and [Formula omitted] decays. This measurement is the most precise to date and is consistent with previous LHCb results.

A search for the very rare [Formula omitted] and [Formula omitted] decays is conducted by analysing the [Formula omitted] process. The analysis uses proton-proton collision data collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 [Formula omitted]. The signal signatures correspond to simultaneous peaks in the [Formula omitted] and [Formula omitted] invariant masses. No evidence for an excess of events over background is observed for either signal decay mode. Upper limits at the [Formula omitted] confidence level are set on the branching fractions relative to that for [Formula omitted] decays, RB*0(+-)[pi]+/J/[psi][pi]+3.8x10-5andRBs*0(+-)[pi]+/J/[psi][pi]+5.0x10-5.

Charmonium production cross-section in proton-proton collisions is measured at the centre-of-mass energy [Formula omitted] using decays to [Formula omitted] final state. The study is performed using a data sample corresponding to an integrated luminosity of [Formula omitted] collected in 2018 with the [Formula omitted] detector. The production cross-section of the [Formula omitted] meson is measured in a rapidity range of [Formula omitted] and in a transverse momentum range of [Formula omitted], which is extended compared with previous [Formula omitted] analyses. The differential cross-section is measured in bins of [Formula omitted] and, for the first time, of y. Upper limits, at 90% and 95% confidence levels, on the [Formula omitted] and [Formula omitted] prompt production cross-sections are determined for the first time.

A measurement of the phase difference between the short- and long-distance contributions to the [Formula: see text] decay is performed by analysing the dimuon mass distribution. The analysis is based on collision data corresponding to an integrated luminosity of 3[Formula: see text] collected by the LHCb experiment in 2011 and 2012. The long-distance contribution to the [Formula: see text] decay is modelled as a sum of relativistic Breit-Wigner amplitudes representing different vector meson resonances decaying to muon pairs, each with their own magnitude and phase. The measured phases of the [Formula: see text] and [Formula: see text] resonances are such that the interference with the short-distance component in dimuon mass regions far from their pole masses is small. In addition, constraints are placed on the Wilson coefficients, [Formula: see text] and [Formula: see text], and the branching fraction of the short-distance component is measured.

The decays [Formula omitted] and [Formula omitted] are observed for the first time, in proton-proton collision data at [Formula omitted], corresponding to an integrated luminosity of 5.4 [Formula omitted] collected with the LHCb detector. Their ratios of branching fractions with respect to the [Formula omitted] mode are measured to be B[LAMBDA]b0[right arrow][LAMBDA]c+D¯0K-B[LAMBDA]b0[right arrow][LAMBDA]c+Ds-=0.1908-0.0034+0.0036-0.0018+0.0016±0.0038,B[LAMBDA]b0[right arrow][LAMBDA]c+D¯*0K-B[LAMBDA]b0[right arrow][LAMBDA]c+Ds-=0.589-0.017+0.018-0.018+0.017±0.012,B[LAMBDA]b0[right arrow][LAMBDA]c+Ds*-B[LAMBDA]b0[right arrow][LAMBDA]c+Ds-=1.668±0.022-0.055+0.061,where the first uncertainties are statistical, the second systematic, and the third, for the [Formula omitted] decays, are due to the uncertainties on the branching fractions of the [Formula omitted] and [Formula omitted] decay modes. The measured branching fractions probe factorization assumptions in effective theories and provide the normalization for future pentaquark searches in [Formula omitted] decay channels.

The [Formula omitted] and [Formula omitted] decays are observed for the first time using proton-proton collision data collected by the LHCb experiment at a centre-of-mass energy of [Formula omitted], corresponding to an integrated luminosity of [Formula omitted]. The branching fractions times the production cross-sections of [Formula omitted] baryons relative to that of [Formula omitted] baryon are measured to be R[Xi]b0[LAMBDA]b0[identical to][sigma][Xi]b0[sigma][LAMBDA]b0xB[Xi]b0[right arrow][Xi]c+Ds-B[LAMBDA]b0[right arrow][LAMBDA]c0Ds-=(15.8±1.1±0.6±7.7)%,R[Xi]b-[LAMBDA]b0[identical to][sigma][Xi]b-[sigma][LAMBDA]b0xB[Xi]b-[right arrow][Xi]c0Ds-B[LAMBDA]b0[right arrow][LAMBDA]c0Ds-=(16.9±1.3±0.9±4.3)%,where the first uncertainties are statistical, the second systematic, and the third due to the uncertainties on the decay branching fractions of relevant charmed baryons. The masses of [Formula omitted] and [Formula omitted] baryons are measured to be [Formula omitted] and [Formula omitted], where the uncertainties are statistical, systematic, and those due to charmed-hadron masses, respectively.

A model-independent study of [Formula omitted] violation in [Formula omitted] decays is presented using data corresponding to an integrated luminosity of 9 [Formula omitted] collected by the LHCb experiment at centre-of-mass energies of [Formula omitted] and 13 [Formula omitted]. The CKM angle [Formula omitted] is determined by examining the distributions of signal decays in phase-space bins of the self-conjugate [Formula omitted] decays, where [Formula omitted]. Observables related to [Formula omitted] violation are measured and the angle [Formula omitted] is determined to be [Formula omitted]. Measurements of the amplitude ratio and strong-phase difference between the favoured and suppressed [Formula omitted] decays are also presented.

The very rare [Formula omitted] decay is searched for by analysing [Formula omitted] decays. The analysis uses a sample of beauty mesons produced in proton-proton collisions collected with the LHCb detector between 2011 and 2018, corresponding to an integrated luminosity of 9 [Formula omitted]. The signal signature corresponds to simultaneous peaks in the [Formula omitted] and [Formula omitted] invariant masses. No evidence for an excess of events over background is observed and an upper limit is set on the branching fraction of the decay at [Formula omitted] at [Formula omitted] confidence level. This is the first limit on the branching fraction of [Formula omitted] decays and the most stringent limit on [Formula omitted] decays to leptonic final states. The analysis is the first search for a rare charm-meson decay exploiting production via beauty decays.