First observation of $D^0-\bar D^0$ oscillations in $D^0\to K^+π^-π^+π^-$ decays and measurement of the associated coherence parameters

Charm meson oscillations are observed in a time-dependent analysis of the ratio of $D^0\to K^+π^-π^+π^-$ to $D^0\to K^-π^+π^-π^+$ decay rates, using data corresponding to an integrated luminosity of $3.0\,{\rm fb}^{-1}$ recorded by the LHCb experiment. The measurements presented are sensitive to the phase-space averaged ratio of doubly Cabibbo-suppressed to Cabibbo-favoured amplitudes $r_{D}^{K3π}$ and the product of the coherence factor $R_{D}^{K3π}$ and a charm mixing parameter $y^{'}_{K3π}$. The constraints measured are $r_{D}^{K3π}=(5.67 \pm 0.12)\times10^{-2}$, which is the most precise determination to date, and $R_{D}^{K3π} \cdot y^{'}_{K3π} = (0.3 \pm 1.8)\times 10^{-3}$, which provides useful input for determinations of the CP-violating phase $γ$ in $B^\pm \to D K^\pm, D \to K^\mpπ^\pmπ^\mpπ^\pm$ decays. The analysis also gives the most precise measurement of the $D^0\to K^+π^-π^+π^-$ branching fraction, and the first observation of $D^0-\bar D^0$ oscillations in this decay mode, with a significance of 8.2 standard deviations.