Measurement of $\Delta m_d$ in $B^0 \rightarrow D^-(K^+\pi^-\pi^-)\pi^+$

We measure the $B^0-\overline{B^0}$ mixing frequency $\Delta m_d$ using $\sim$ 6000 $B^0~\rightarrow~D^-(K^+\pi^-\pi^-)\pi^+$ candidates from 36 pb$^{-1}$ of data taken in physics runs of the LHCb experiment in 2010. We use opposite and same side tagging algorithms which were optimized and calibrated in an independent analysis. The tagging performance on the $B^0 \rightarrow D^-(K^+\pi^-\pi^-)\pi^+$ candidates used in this analyses is found to be 4.3 $\pm$ 1.0 \%. The following result for the mixing frequency is obtained: $\Delta m_d$ = 0.499 $\pm$ 0.032 (stat.) $\pm$ 0.003 (sys.) ps$^{-1}$.