Model-independent determination of the strong phase difference between D 0 and D 0 → π + π − π + π − amplitudes

For the first time, the strong phase difference between D and D → π+π−π+π− amplitudes is determined in bins of the decay phase space. The measurement uses 818 pb−1 of e+e− collision data that is taken at the ψ(3770) resonance and collected by the CLEO-c experiment. The measurement is important for the determination of the CP -violating phase γ in B± → DK± (and similar) decays , where the D meson (which represents a superposition of D and D) subsequently decays to π+π−π+π−. To obtain optimal sensitivity to γ, the phase space of the D→ π+π−π+π− decay is divided into bins based on a recent amplitude model of the decay. Although an amplitude model is used to define the bins, the measurements obtained are modelindependent. The CP -even fraction of the D → π+π−π+π− decay is determined to be F 4π + = 0.769± 0.021± 0.010, where the uncertainties are statistical and systematic, respectively. Using simulated B±→ DK±, D→ π+π−π+π− decays, it is estimated that by the end of the current LHC run, the LHCb experiment could determine γ from this decay mode with an uncertainty of (±10± 7)◦, where the first uncertainty is statistical based on estimated LHCb event yields, and the second is due to the uncertainties on the parameters determined in this paper. ar X iv :1 70 9. 03 46 7v 1 [ he pex ] 1 1 Se p 20 17