Model-independent measurement of charm mixing parameters in $\overline{B}\to D^0(\to K_S^0{\pi }^{+}{\pi }^{-}){\mu }^{-}{\overline{\nu }}_{\mu }X$ decays

A measurement of charm mixing and $CP$-violating parameters is reported, using $\overline{B}\to D^0(\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}){\mu }^{-}{\overline{\nu }}_{\mu }X$ decays reconstructed in proton-proton collisions collected by the LHCb experiment during the years 2016 to 2018, corresponding to an integrated luminosity of $5.4{\mathrm{fb}}^{-1}$. The measured mixing and $CP$-violating parameters are $x_{CP}=[4.29\pm 1.48(\mathrm{stat})\pm 0.26(\mathrm{syst})]\times {10}^{-3}$, $y_{CP}=[12.61\pm 3.12(\mathrm{stat})\pm 0.83(\mathrm{syst})]\times {10}^{-3}$, $\mathrm{\Delta }x=[-0.77\pm 0.93(\mathrm{stat})\pm 0.28(\mathrm{syst})]\times {10}^{-3}$, $\mathrm{\Delta }y=[3.01\pm 1.92(\mathrm{stat})\pm 0.26(\mathrm{syst})]\times {10}^{-3}$. The results are complementary to and consistent with previous measurements. A combination with the recent LHCb analysis of $D^{*+}\to D^0(\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}){\pi }^{+}$ decays is reported.

Figure 1

(Left) $D^0$ Dalitz plot of reconstructed $\overline{B}\to D^0(\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}){\mu }^{-}{\overline{\nu }}_{\mu }X$ decays for the $D^0$ flavor and (right) definition of the binning scheme proposed by CLEO [23].

Figure 2

$K_{\mathrm{S}}^0$${\pi }^{+}$${\pi }^{-}$ invariant-mass distribution of (left) DD and (right) LL $K_{\mathrm{S}}^0$ candidates after all selection requirements, with fit results superimposed.

Figure 3

Relative efficiency as a function of $D^0$ decay-time and $m^2({\pi }^{+}{\pi }^{-})$ as determined from $\overline{B}\to D^0(\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}){\mu }^{-}{\overline{\nu }}_{\mu }X$ candidates, separately for (left) DD and (right) LL $K_{\mathrm{S}}^0$ candidates. The distributions are smoothed using bilinear interpolation.

Figure 4

(Top) $CP$-averaged yield ratios and (bottom) difference of $D^0$ and ${\overline{D}}^0$ yield ratios as a function of $D^0$ decay-time for the different Dalitz bins. The solid blue line shows the nominal fit projections and the dashed red line shows the fit projections when $x_{CP}$ is fixed to zero.

Figure 5

Two-dimensional 68% and 95% confidence-level contours on (left) ($x$, $y$) and (right) ($|q/p|-1$, $\varphi$). Results from Run $2D^{*+}\to D^0(\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}){\pi }^{+}$ (Prompt) [9], $\overline{B}\to D^0(\to K_{\mathrm{S}}^0{\pi }^{+}{\pi }^{-}){\mu }^{-}{\overline{\nu }}_{\mu }X$ (SL), and their combination are shown.