Charm: Mixing, CP Violation and Rare Decays at LHCb

Recent results on mixing, CP violation and rare decays in charm physics from the LHCb experiment are presented. Study of ''wrong-sign'' $D^{0} \rightarrow K^+ \pi^-$ decays provides the highest precision measurements to date of the mixing parameters $x^{\prime 2}$ and $y^{\prime}$, and of CP violation in this decay mode. Direct and indirect CP violation in the $D^0$ system are probed to a sensitivity of around $10^{-3}$ using $D^0 \rightarrow K^+K^-$ and $D^0 \rightarrow \pi^+\pi^-$ decays and found to be consistent with zero. Searches for the rare decays $D^+_{(s)} \rightarrow \pi^+\mu^+\mu^-$, $D^+_{(s)} \rightarrow \pi^-\mu^+\mu^+$ and $D^0 \rightarrow \mu^+\mu^-$ find no evidence of signal, but set the best limits on branching fractions to date. Thus, despite many excellent results in charm physics from LHCb, no evidence for physics beyond the Standard Model is found.