Effect of direct CP violation in charm on γ extraction from B ±→DK ±, $D\to K^{0}_{S}\pi^{+}\pi^{-}$ Dalitz plot analysis

Abstract

A possible effect of direct CP violation in $D\to K^{0}_{S}\pi^{+}\pi^{-}$ decay on the γ measurement from B ±→DK ±, $D\to K^{0}_{S}\pi^{+}\pi^{-}$ Dalitz plot analysis is considered. Systematic uncertainty of γ coming from the current limits on direct CP violation in $D\to K^{0}_{S}\pi ^{+}\pi^{-}$ is estimated, and a modified model-independent procedure of B ±→DK ±, $D\to K^{0}_{S}\pi^{+}\pi^{-}$ Dalitz plot analysis is proposed that gives an unbiased γ measurement even in presence of direct CP violation in charm decays. The technique is applicable to other three-body D decays such as $D^{0}\to K_{S}^{0}K^{+}K^{-}$ , D 0→π + π − π 0, etc.