$CP$-violation studies with charm decays at LHCb

The LHCb detector [1] at the Large Hadron Collider (LHC) is a single arm spectrometer dedicated to studying the properties of charm ($D$) and beauty ($B$) hadrons. LHCb has two Ring Imaging Cherenkov (RICH) detectors, giving kaon-pion separation in the momentum range 2-100 GeV/$c$, a tracking system with a momentum resolution between 0.3% and 0.5% over the same range, and a silicon vertex detector able to measure $D$ and $B$ hadron lifetimes with a resolution of approximately 50 fs. The interest in studying $CP$-violation ($CPV$) in the charm sector stems from the fact that it is predicted to be small in the Standard Model. The arguments, summarized in [2], is that charm hadrons decay into quarks of the first two generations whose mixing matrix is real, and hence there is no $CPV$ possible in the dominant tree-level decays. $CPV$ can manifest itself through penguin or box diagrams, but since these are suppressed by $V_{cb}V_{ub}^*$ the allowed level of Standard Model $CPV$ does not exceed 1%. Although there is currently no evidence [3] for $CPV$ in the charm sector, effects of up to 1% level have not been completely ruled out by experiment. This makes it important to improve the precision of charm $CPV$ measurements to below the 0.1% level, in order to constrain the precise nature of $CPV$ in charm. LHCb is ideally poised to carry out such a programme because of the LHCb’s large open charm cross-section of 6.10 $\pm$ 0.93 mb [4]: one in every ten LHC interactions results in the production of a charm hadron. This amounts to approximately 1.5 MHz of produced events which contain a charm hadron, of which only about 1kHz can be written to storage for offline analysis. For this reason LHCb deploys a number of efficient real-time selection algorithms, called triggers, to select the most interesting charm events for later analysis. As a result, LHCb collects e.g. around 5 x 10$^3$ tagged $D^{*\pm} \to (D^{0} \to K^{+}K^{-})\pi^{\pm}$, or around 3 x 10$^5$ untagged $D^0 \to K^{-}\pi^{+}$, decays per pb$^{-1}$ of integrated luminosity; at the time of writing, it already has the world’s largest samples of two body $D^0$ decays on tape.