Model-independent measurement of mixing parameters in $D^0 \to K_S \pi^+ \pi^-$ decays

The first model-independent measurement of the charm mixing parameters in the decay $D^0 \to K_S \pi^+ \pi^-$ is reported, using a sample of $pp$ collision data recorded by the LHCb experiment, corresponding to an integrated luminosity of 1.0 fb$^{-1}$ at a centre-of-mass energy of 7 TeV. The measured values are \begin{eqnarray*} x &=& (+0.86 \pm 0.53 \pm 0.17) \times 10^{-2}, \\ y &=& (+0.03 \pm 0.46 \pm 0.13) \times 10^{-2}, \end{eqnarray*} where the first uncertainties are statistical and include small contributions due to the external input for the strong phase measured by the CLEO collaboration, and the second uncertainties are systematic. The results are consistent with the current world averages.