Measurement of the Mass Difference Between Neutral Charm-Meson Eigenstates

We report a measurement of the mass difference between neutral charm-meson eigenstates using a novel approach that enhances sensitivity to this parameter. We use $2.3\times {10}^6$ $D^0\to K_{\mathit{S}}^0{\pi }^{+}{\pi }^{-}$ decays reconstructed in proton-proton collisions collected by the LHCb experiment in 2011 and 2012. Allowing for $CP$ violation in mixing and in the interference between mixing and decay, we measure the $CP$-averaged normalized mass difference $x_{CP}=[2.7\pm 1.6(\text{stat})\pm 0.4(\text{syst})]\times {10}^{-3}$ and the $CP$-violating parameter $\mathrm{\Delta }x=[-0.53\pm 0.70(\text{stat})\pm 0.22(\text{syst})]\times {10}^{-3}$. The results are consistent with $CP$ symmetry. These determinations are the most precise from a single experiment and, combined with current world-average results, yield the first evidence that the masses of the neutral charm-meson eigenstates differ.

Figure 1

Distribution of (left) the difference between $D^{*+}$ and $D^0$ masses for $D^{*+}\to D^0(\to K_{\mathit{S}}^0{\pi }^{+}{\pi }^{-}){\pi }^{+}$ candidates and (right) $D^0$ mass for $\overline{B}\to D^0(\to K_{\mathit{S}}^0{\pi }^{+}{\pi }^{-}){\mu }^{-}X$ candidates.

Figure 2

Smoothed efficiency as a function of $m^2({\pi }^{+}{\pi }^{-})$ and $t/\tau$ in $D^{*+}\to D^0(\to K_{\mathit{S}}^0{\pi }^{+}{\pi }^{-}){\pi }^{+}$ decays, as determined from the data with downstream $K_{\mathit{S}}^0$ candidates.

Figure 3

(Top) $CP$-averaged yield ratios and (bottom) differences of $D^0$ and ${\overline{D}}^0$ yield ratios as functions of $t/\tau$ for each Dalitz bin. Prompt (closed points) and semileptonic (open points) data are shown separately. Fit projections over the prompt (solid line) and semileptonic (dashed line) data are overlaid.