Géometrie différentielle : une approche symplectique pour des théorémes de décomposition en géométrie ou relativité générale

Les théorémes de décomposition des tenseurs symétriques donnés par Ch. Barbance, Deser, Berger-Ebin, York et Moncrief peuvent tous étre obtenus á partir d'une construction générale de géométrie symplectique

Measurement of the ratios of branching fractions R(D∗)\mathcal{R}(D^{*}) and R(D0)\mathcal{R}(D^{0})

The ratios of branching fractions $\mathcal{R}(D^{*})\equiv\mathcal{B}(\bar{B}\to D^{*}\tau^{-}\bar{\nu}_{\tau})/\mathcal{B}(\bar{B}\to D^{*}\mu^{-}\bar{\nu}_{\mu})$ and $\mathcal{R}(D^{0})\equiv\mathcal{B}(B^{-}\to D^{0}\tau^{-}\bar{\nu}_{\tau})/\mathcal{B}(B^{-}\to D^{0}\mu^{-}\bar{\nu}_{\mu})$ are measured, assuming isospin symmetry, using a sample of proton-proton collision data corresponding to 3.0 fb${ }^{-1}$ of integrated luminosity recorded by the LHCb experiment during 2011 and 2012. The tau lepton is identified in the decay mode $\tau^{-}\to\mu^{-}\nu_{\tau}\bar{\nu}_{\mu}$. The measured values are $\mathcal{R}(D^{*})=0.281\pm0.018\pm0.024$ and $\mathcal{R}(D^{0})=0.441\pm0.060\pm0.066$, where the first uncertainty is statistical and the second is systematic. The correlation between these measurements is $\rho=-0.43$. Results are consistent with the current average of these quantities and are at a combined 1.9 standard deviations from the predictions based on lepton flavor universality in the Standard Model.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-039.html (LHCb public pages

Measurements of the branching fraction ratio B(ϕ→μ+μ−)/B(ϕ→e+e−)\cal{B}(\phi \to \mu^+\mu^-)/\cal{B}(\phi \to e^+e^-) with charm meson decays

International audienceMeasurements of the branching fraction ratio ${\cal{B}(\phi \to \mu^+ \mu^-)/\cal{B}(\phi\to e^+e^-)}$ with ${D_{s}^{+} \to \pi^{+} \phi}$ and ${D^{+} \to \pi^{+} \phi}$ decays, denoted $R^{s}_{\phi \pi}$ and $R^{d}_{\phi \pi}$, are presented. The analysis is performed using a dataset corresponding to an integrated luminosity of 5.4$\,\rm{fb}^{-1}$ of $pp$ collision data collected with the LHCb experiment. The branching fractions are normalised with respect to the ${B^{+} \to K^{+} J/\psi(\to e^+e^-)}$ and ${B^{+} \to K^{+} J/\psi(\to \mu^+\mu^-)}$ decay modes. The combination of the results yields $$R_{\phi \pi} = 1.022 \pm 0.012 \,({\rm stat}) \, \pm 0.048 \,({\rm syst}).$$ The result is compatible with previous measurements of the $\phi \to \ell^{+}\ell^{-}$ branching fractions and predictions based on the Standard Model

Observation of Cabibbo-suppressed two-body hadronic decays and precision mass measurement of the Ωc0\Omega_{c}^{0} baryon

International audienceThe first observation of the singly Cabibbo-suppressed $\Omega_{c}^{0}\to\Omega^{-}K^{+}$ and $\Omega_{c}^{0}\to\Xi^{-}\pi^{+}$ decays is reported, using proton-proton collision data at a centre-of-mass energy of $13\,{\rm TeV}$, corresponding to an integrated luminosity of $5.4\,{\rm fb}^{-1}$, collected with the LHCb detector between 2016 and 2018. The branching fraction ratios are measured to be $\frac{\mathcal{B}(\Omega_{c}^{0}\to\Omega^{-}K^{+})}{\mathcal{B}(\Omega_{c}^{0}\to\Omega^{-}\pi^{+})}=0.0608\pm0.0051({\rm stat})\pm 0.0040({\rm syst})$, $\frac{\mathcal{B}(\Omega_{c}^{0}\to\Xi^{-}\pi^{+})}{\mathcal{B}(\Omega_{c}^{0}\to\Omega^{-}\pi^{+})}=0.1581\pm0.0087({\rm stat})\pm0.0043({\rm syst})\pm0.0016({\rm ext})$. In addition, using the $\Omega_{c}^{0}\to\Omega^{-}\pi^{+}$ decay channel, the $\Omega_{c}^{0}$ baryon mass is measured to be $M(\Omega_{c}^{0})=2695.28\pm0.07({\rm stat})\pm0.27({\rm syst})\pm0.30({\rm ext})\,{\rm MeV}/c^{2}$, improving the precision of the previous world average by a factor of four