Speaker
Description
We present a novel method that measures the relative strong phase, $\Delta \delta_D$, between $D^0$ and $\bar{D}^0$ amplitudes decaying to the $K_S^0 \pi^+ \pi^-$ final state measured from correlated $D\bar{D}$ pairs produced at the charm threshold, and its application to the measurement of $CP$ violating observables in $B^\pm \to DK^\pm$ decays which includes the measurement of the CKM angle, $\gamma$, from $B^\pm \to D(\to K_S^0 \pi^+ \pi^-) K^\pm$ decays.
We test this method using simulated correlated $\psi(3770) \to D^0\bar{D}^0$ decays with at least one $D$ decaying to the $K_S^0 \pi^+ \pi^-$ final state and simulated $B^\pm \to D(\to K_S^0 \pi^+ \pi^-)K^\pm$ decays, we perform simultaneous fits to the correcting polynomial to $\Delta \delta_D$ and the CKM parameters, $x_\pm = r_B \cos\left(\delta_B \pm \gamma\right), y_\pm = r_B \sin\left(\delta_B \pm \gamma\right)$.
This method has better statistical precision than the binned measurement of $\gamma$ using the binned measurements of $\Delta \delta_D$ from charm threshold data. We test the ability of our method against mis-modelling $\Delta \delta_D$ by performing pull studies with a predetermined bias applied to $\Delta \delta_D$, we show that our method is able to recover the original $\Delta \delta_D$ and avoid biasing the CKM parameters $x_\pm, y_\pm$ in contrast to the unbinned model dependent measurement.
