Search for new physics in CP violation with beauty and charm decays at LHCb

LHCb is one of the four big experiments operating at LHC and it's mainly dedicated to measurements of $C\!P$ violation and to the search for new physics in the decays of rare hadrons containing heavy quarks. The LHCb collaboration has recently published a result which shows for the first time a compelling 5.3 $\sigma$ evidence of $C\!P$ violation in the two-body meson $D^{0}\rightarrow K^{+}K^{-}$ and $D^{0}\rightarrow \pi^{+}\pi^{-}$ decays. $C\!P$ violation in the Cabibbo-suppressed decays $D^{+}_{s} \rightarrow K^{0}_{S}\pi^{+}$, $D^{+} \rightarrow K^{0}_{S}K^{+}$, $D^{+} \rightarrow \phi \pi^{+}$ is expected to be small ($\sim10^{-3}$) due to interference between tree and penguin diagrams and thus sensible to contributions Beyond Standard Model (BSM). The last measurement by LHCb of direct $C\!P$ asymmetries in the aforementioned decay channels shows consistency with the hypothesis of $C\!P$ conservation. In the $B_{s}$ sector the $C\!P$ violating phase $\phi_{s}$ receives contributions from direct decay and mixing and may also be sensitive to BSM contributions. The last two published measurements of $\phi_{s}$ using the $B_{s}\rightarrow J/\psi K^{+}K^{-}$ and $B_{s}\rightarrow J/\psi \pi^{+} \pi^{-}$ decay channels show a combined 2 $\sigma$ hint of $C\!P$ violation.