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