Observation of the Mass Difference between Neutral Charm-Meson Eigenstates

A measurement of mixing and $CP$ violation in neutral charm mesons is performed using data reconstructed in proton-proton collisions collected by the LHCb experiment from 2016 to 2018, corresponding to an integrated luminosity of $5.4{\text{fb}}^{-1}$. A total of 30.6 million $D^0\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}$ decays are analyzed using a method optimized for the measurement of the mass difference between neutral charm-meson eigenstates. Allowing for $CP$ violation in mixing and in the interference between mixing and decay, the mass and decay-width differences are measured to be $x_{CP}=[3.97\pm 0.46(\text{stat})\pm 0.29(\text{syst})]\times 10^{-3}$ and $y_{CP}=[4.59\pm 1.20(\text{stat})\pm 0.85(\text{syst})]\times 10^{-3}$, respectively. The $CP$-violating parameters are measured as $\mathrm{\Delta }x=[-0.27\pm 0.18(\text{stat})\pm 0.01(\text{syst})]\times 10^{-3}$ and $\mathrm{\Delta }y=[0.20\pm 0.36(\text{stat})\pm 0.13(\text{syst})]\times 10^{-3}$. This is the first observation of a nonzero mass difference in the $D^0$ meson system, with a significance exceeding seven standard deviations. The data are consistent with $CP$ symmetry and improve existing constraints on the associated parameters.

Figure 1

Depiction of the interference of mixing and decay if a $D^0$ and a ${\overline{D}}^0$ meson decay to a common final state $f$.

Figure 2

“Binning” of the $D^0\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}$ Dalitz plot. Colors indicate the absolute value of the bin index $b$.

Figure 3

Distribution of $\mathrm{\Delta }m$ for the selected $D^{*+}\to D^0(\to K_S^0{\pi }^{+}{\pi }^{-}){\pi }^{+}$ candidates. The projection of the fit result is superimposed.

Figure 4

(Top) $CP$-averaged yield ratios and (bottom) differences of $D^0$ and ${\overline{D}}^0$ yield ratios as a function of $t/\tau$, shown for each Dalitz-plot bin with fit projections overlaid.