First observation of $D^0-\bar D^0$ oscillations in $D^0\to K^+\pi^-\pi^+\pi^-$ decays and measurement of the associated coherence parameters
Charm meson oscillations are observed in a time-dependent analysis of the ratio of D0 → K+π −π +π − to D0 → K−π +π −π + decay rates, using data corresponding to an integrated luminosity of 3.0 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 K3π D and the product of the coherence factor RK3π D and a charm mixing parameter y 0 K3π . The constraints measured are r K3π D = (5.67±0.12)×10−2 , which is the most precise determination to date, and RK3π D · y 0 K3π = (0.3 ± 1.8) × 10−3 , which provides useful input for determinations of the CP-violating phase γ in B±→ DK±, D→ K∓π ±π ∓π ± decays. The analysis also gives the most precise measurement of the D0 → K+π −π +π − branching fraction, and the first observation of D0–D0 oscillations in this decay mode, with a significance of 8.2 standard deviations.