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We discuss the determination of the CKM angle α using the non-leptonic two-body decays B → π π , B → ρ ρ and B → ρ π using the latest data available. We illustrate the methods used in each case and extract the corresponding value of α . Combining all these elements, we obtain the determination α dir = ( 86.2 - 4.0 + 4.4 ∪ 178.4 - 5.1 + 3.9 ) ∘ . We assess the uncertainties associated to the breakdown of the isospin hypothesis and the choice of the statistical framework in detail. We also determine the hadronic amplitudes (tree and penguin) describing the QCD dynamics involved in these decays, briefly comparing our results with theoretical expectations. For each observable of interest in the B → π π , B → ρ ρ and B → ρ π systems, we perform an indirect determination based on the constraints from all the other observables available and we discuss the compatibility between indirect and direct determinations. Finally, we review the impact of future improved measurements on the determination of α .

The standard model of particle physics currently provides our best description of fundamental particles and their interactions. The theory predicts that the different charged leptons, the electron, muon and tau, have identical electroweak interaction strengths. Previous measurements have shown that a wide range of particle decays are consistent with this principle of lepton universality. This article presents evidence for the breaking of lepton universality in beauty-quark decays, with a significance of 3.1 standard deviations, based on proton–proton collision data collected with the LHCb detector at CERN’s Large Hadron Collider. The measurements are of processes in which a beauty meson transforms into a strange meson with the emission of either an electron and a positron, or a muon and an antimuon. If confirmed by future measurements, this violation of lepton universality would imply physics beyond the standard model, such as a new fundamental interaction between quarks and leptons. The Large Hadron Collider beauty collaboration reports a test of lepton flavour universality in decays of bottom mesons into strange mesons and a charged lepton pair, finding evidence of a violation of this principle postulated in the standard model.

In the Standard Model of particle physics, the strength of the couplings of the b quark to the u and c quarks, | V ub | and | V cb |, are governed by the coupling of the quarks to the Higgs boson. Using data from the LHCb experiment at the Large Hadron Collider, the probability for the Λ b 0 baryon to decay into the p final state relative to the final state is measured. Combined with theoretical calculations of the strong interaction and a previously measured value of | V cb |, the first | V ub | measurement to use a baryonic decay is performed. This measurement is consistent with previous determinations of | V ub | using B meson decays to specific final states and confirms the existing incompatibility with those using an inclusive sample of final states. The accurate determination of quark mixing parameters is essential for the understanding of the Standard Model. The LHCb collaboration now reports the coupling strength of the b quark to the u quark through the measurement of a baryonic decay mode.

Abstract The decays B+ → J/ψπ+π − K+ are studied using a data set corresponding to an integrated luminosity of 9 fb −1 collected with the LHCb detector in proton-proton collisions between 2011 and 2018. Precise measurements of the ratios of branching fractions with the intermediate ψ2(3823), χc1(3872) and ψ(2S) states are reported. The values are B B + → ψ 2 3823 K + × B ψ 2 3823 → J / ψπ + π − B B + → χ c 1 3872 K + × B χ c 1 3872 → J / ψπ + π − = 3.56 ± 0.67 ± 0.11 × 10 − 2 , B B + → ψ 2 3823 K + × B ψ 2 3823 → J / ψπ + π − B B + → ψ 2 S K + × B ψ 2 S → J / ψπ + π − = 1.31 ± 0.25 ± 0.04 × 10 − 3 , B B + → χ c 1 3872 K + × B χ c 1 3872 → J / ψπ + π − B B + → ψ 2 S K + × B ψ 2 S → J / ψπ + π − = 3.69 ± 0.07 ± 0.06 × 10 − 2 ,$$ {\\displaystyle \\begin{array}{c}\\frac{{\\mathcal{B}}_{{\\mathrm{B}}^{+}\\to {\\uppsi}_2(3823){\\mathrm{K}}^{+}}\\times {\\mathcal{B}}_{\\uppsi_2(3823)\\to \\mathrm{J}/{\\uppsi \\uppi}^{+}{\\uppi}^{-}}}{{\\mathcal{B}}_{{\\mathrm{B}}^{+}\\to {\\upchi}_{\\mathrm{c}1}(3872){\\mathrm{K}}^{+}}\\times {\\mathcal{B}}_{\\upchi_{\\mathrm{c}1}(3872)\\to \\mathrm{J}/{\\uppsi \\uppi}^{+}{\\uppi}^{-}}}=\\left(3.56\\pm 0.67\\pm 0.11\\right)\\times {10}^{-2},\\\ {}\\frac{{\\mathcal{B}}_{{\\mathrm{B}}^{+}\\to {\\uppsi}_2(3823){\\mathrm{K}}^{+}}\\times {\\mathcal{B}}_{\\uppsi_2(3823)\\to \\mathrm{J}/{\\uppsi \\uppi}^{+}{\\uppi}^{-}}}{{\\mathcal{B}}_{{\\mathrm{B}}^{+}\\to \\uppsi \\left(2\\mathrm{S}\\right){\\mathrm{K}}^{+}}\\times {\\mathcal{B}}_{\\uppsi \\left(2\\mathrm{S}\\right)\\to \\mathrm{J}/{\\uppsi \\uppi}^{+}{\\uppi}^{-}}}=\\left(1.31\\pm 0.25\\pm 0.04\\right)\\times {10}^{-3},\\\ {}\\frac{{\\mathcal{B}}_{\\mathrm{B}+\\to {\\upchi}_{\\mathrm{c}1}(3872){\\mathrm{K}}^{+}}\\times {\\mathcal{B}}_{\\upchi_{\\mathrm{c}1}(3872)\\to \\mathrm{J}/{\\uppsi \\uppi}^{+}{\\uppi}^{-}}}{{\\mathcal{B}}_{{\\mathrm{B}}^{+}\\to \\uppsi \\left(2\\mathrm{S}\\right){\\mathrm{K}}^{+}}\\times {\\mathcal{B}}_{\\uppsi \\left(2\\mathrm{S}\\right)\\to \\mathrm{J}/{\\uppsi \\uppi}^{+}{\\uppi}^{-}}}=\\left(3.69\\pm 0.07\\pm 0.06\\right)\\times {10}^{-2},\\end{array}} $$where the first uncertainty is statistical and the second is systematic. The decay of B+ → ψ2(3823)K+ with ψ2(3823) → J/ψπ+π − is observed for the first time with a significance of 5.1 standard deviations. The mass differences between the ψ2(3823), χc1(3872) and ψ(2S) states are measured to be m χ c 1 3872 − m ψ 2 3823 = 47.50 ± 0.53 ± 0.13 MeV / c 2 , m ψ 2 3823 − m ψ 2 2 S = 137.98 ± 0.53 ± 0.14 MeV / c 2 , m χ c 1 3872 − m ψ 2 2 S = 185.49 ± 0.06 ± 0.03 MeV / c 2 ,$$ {\\displaystyle \\begin{array}{c}{m}_{\\upchi_{\\mathrm{c}1}(3872)}-{m}_{\\uppsi_2(3823)}=47.50\\pm 0.53\\pm 0.13\\;\\mathrm{MeV}/{c}^2,\\\ {}{m}_{\\uppsi_2(3823)}-{m}_{\\uppsi_2\\left(2\\mathrm{S}\\right)}=137.98\\pm 0.53\\pm 0.14\\;\\mathrm{MeV}/{c}^2,\\\ {}{m}_{\\upchi_{\\mathrm{c}1}(3872)}-{m}_{\\uppsi_2\\left(2\\mathrm{S}\\right)}=185.49\\pm 0.06\\pm 0.03\\;\\mathrm{MeV}/{c}^2,\\end{array}} $$resulting in the most precise determination of the χc1(3872) mass. The width of the ψ2(3823) state is found to be below 5.2 MeV at 90% confidence level. The Breit-Wigner width of the χc1(3872) state is measured to be Γ χ c 1 3872 BW = 0.96 − 0.18 + 0.19 ± 0.21 MeV$$ {\\Gamma}_{\\upchi_{\\mathrm{c}1}(3872)}^{\\mathrm{BW}}={0.96}_{-0.18}^{+0.19}\\pm 0.21\\;\\mathrm{MeV} $$which is inconsistent with zero by 5.5 standard deviations.

A bstract The production cross-section of J/ψ pairs is measured using a data sample of pp collisions collected by the LHCb experiment at a centre-of-mass energy of s = 13 TeV, corresponding to an integrated luminosity of 279 ±11 pb −1 . The measurement is performed for J/ψ mesons with a transverse momentum of less than 10 GeV/ c in the rapidity range 2 . 0 < y < 4 . 5. The production cross-section is measured to be 15 . 2 ± 1 . 0 ± 0 . 9 nb. The first uncertainty is statistical, and the second is systematic. The differential cross-sections as functions of several kinematic variables of the J/ψ pair are measured and compared to theoretical predictions.

Using proton-proton collision data, corresponding to an integrated luminosity of 9 fb −1 , collected with the LHCb detector between 2011 and 2018, a new narrow charmonium state, the X(3842) resonance, is observed in the decay modes$$ \\mathrm{X}(3842)\\to {D}^0{\\overline{D}}^0 $$X 3842 → D 0 D ¯ 0 and X(3842) → D + D − . The mass and the natural width of this state are measured to be$$ \\begin{array}{l}{m}_{X(3842)}=3842.71\\pm 0.16\\pm 0.12\\ MeV/{c}^2,\\hfill \\\ {}{\\varGamma}_{X(3842)}=2.79\\pm 0.51\\pm 0.35\\ MeV,\\hfill \\end{array} $$m X 3842 = 3842.71 ± 0.16 ± 0.12 M e V / c 2 , Γ X 3842 = 2.79 ± 0.51 ± 0.35 M e V , where the first uncertainty is statistical and the second is systematic. The observed mass and narrow natural width suggest the interpretation of the new state as the unobserved (spin-3 ψ 3 1 3 D 3 ) charmonium state. In addition, prompt hadroproduction of the ψ (3770) and χ 2 (3930) states is observed for the first time, and the parameters of these states are measured to be$$ \\begin{array}{l}{m}_{\\psi (3770)}=3778.1\\pm 0.7\\pm 0.6\\ MeV/{c}^2,\\hfill \\\ {}{m}_{\\chi_2(3930)}=3921.9\\pm 0.6\\pm 0.2\\ MeV/{c}^2,\\hfill \\\ {}{\\varGamma}_{\\chi_2(3930)}=36.6 \\pm 1.9 \\pm 0.9\\ MeV,\\hfill \\end{array} $$m ψ 3770 = 3778.1 ± 0.7 ± 0.6 M e V / c 2 , m χ 2 3930 = 3921.9 ± 0.6 ± 0.2 M e V / c 2 , Γ χ 2 3930 = 36.6 ± 1.9 ± 0.9 M e V , where the first uncertainty is statistical and the second is systematic.

The production of the η c ( 1 S ) state in proton-proton collisions is probed via its decay to the p p ¯ final state with the LHCb detector, in the rapidity range 2.0 < y < 4.5 and in the meson transverse-momentum range p T > 6.5 GeV / c . The cross-section for prompt production of η c ( 1 S ) mesons relative to the prompt J / ψ cross-section is measured, for the first time, to be σ η c ( 1 S ) / σ J / ψ = 1.74 ± 0.29 ± 0.28 ± 0 . 18 B at a centre-of-mass energy s = 7 TeV using data corresponding to an integrated luminosity of 0.7 fb - 1 , and σ η c ( 1 S ) / σ J / ψ = 1.60 ± 0.29 ± 0.25 ± 0 . 17 B at s = 8 TeV using 2.0 fb - 1 . The uncertainties quoted are, in order, statistical, systematic, and that on the ratio of branching fractions of the η c ( 1 S ) and J / ψ decays to the p p ¯ final state. In addition, the inclusive branching fraction of b -hadron decays into η c ( 1 S ) mesons is measured, for the first time, to be B ( b → η c X ) = ( 4.88 ± 0.64 ± 0.29 ± 0 . 67 B ) × 10 - 3 , where the third uncertainty includes also the uncertainty on the J / ψ inclusive branching fraction from b -hadron decays. The difference between the J / ψ and η c ( 1 S ) meson masses is determined to be 114.7 ± 1.5 ± 0.1 MeV / c 2 .

A bstract The differential branching fraction of the rare decay Λ b 0  →  Λμ + μ − is measured as a function of q 2 , the square of the dimuon invariant mass. The analysis is performed using proton-proton collision data, corresponding to an integrated luminosity of 3 . 0 fb −1 , collected by the LHCb experiment. Evidence of signal is observed in the q 2 region below the square of the J/ψ mass. Integrating over 15 < q 2 < 20 GeV 2 /c 4 the differential branching fraction is measured as d ℬ Λ b 0 → Λ μ + μ − / d q 2 = 1.18 − 0.08 + 0.09 ± 0.03 ± 0.27 × 10 − 7 GeV 2 / c 4 − 1 , where the uncertainties are statistical, systematic and due to the normalisation mode, Λ b 0  →  J / ψΛ , respectively. In the q 2 intervals where the signal is observed, angular distributions are studied and the forward-backward asymmetries in the dimuon ( A FB ℓ ) and hadron ( A FB h ) systems are measured for the first time. In the range 15 < q 2 < 20 GeV 2 /c 4 they are found to be A F B ℓ = − 0.05 ± 0.09 stat ± 0.03 syst and A F B h = − 0.29 ± 0.07 stat ± 0.03 syst .