Effect of direct CP violation in charm on γ extraction from B ±→DK ±, D→ K⁰Sπ⁺π⁻ Dalitz plot analysis

A possible effect of direct CP violation in D→ K⁰Sπ⁺π⁻ decay on the γ measurement from B ±→DK ±, D→ K⁰Sπ⁺π⁻ Dalitz plot analysis is considered. Systematic uncertainty of γ coming from the current limits on direct CP violation in D→ K⁰Sπ ⁺π⁻ is estimated, and a modified model-independent procedure of B ±→DK ±, D→ K⁰Sπ⁺π⁻ 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 D⁰→ KS⁰K⁺K⁻ , D 0→π + π − π 0, etc.