First determination of the CP content of D → π+π-π+π- and updated determination of the CP contents of D → π+π-π0 and D → K+K-π0

Quantum-correlated psi(3770) -> D (D) over bar decays collected by the CLEO-c experiment are used to perform a first measurement of F-+(4 pi), the fractional CP-even content of the self-conjugate decay D -> pi(+)pi(-)pi(+)pi(-), obtaining a value of 0.737 +/- 0.028. An important input to the measurement comes from the use of D -> K-S(0)pi(+)pi(-) and D -> K-L(0)pi(+)pi(-) decays to tag the signal mode. This same technique is applied to the channels D -> pi(+)pi(-)pi(0) and D -> K+K-pi(0), yielding F-+(pi pi pi 0) = 1.014 +/- 0.045 +/- 0.022 and F-+(KK pi 0) = 0.734 +/- 0.106 +/- 0.054, where the first uncertainty is statistical and the second systematic. These measurements are consistent with those of an earlier analysis, based on CP-eigenstate tags, and can be combined to give values of F-+(pi pi pi 0) = 0.973 +/- 0.017 and F-+(KK pi 0) = 0.732 +/- 0.055. The results will enable the three modes to be included in a model-independent manner in measurements of the unitarity triangle angle gamma using B--/+ -> DK -/+ decays, and in time-dependent studies of CP violation and mixing in the D-0(D) over bar (0) system. (C) 2015 The Authors. Published by Elsevier B.V.