Determination of the D{sup 0}{yields}K{sup -}{pi}{sup +}{pi}{sup 0} and D{sup 0}{yields}K{sup -}{pi}{sup +}{pi}{sup +}{pi}{sup -} coherence factors and average strong-phase differences using quantum-correlated measurements

The first measurements of the coherence factors (R{sub K{pi}}{sub {pi}{sup 0}} and R{sub K3{pi}}) and the average strong-phase differences ({delta}{sub D}{sup K{pi}}{sup {pi}{sup 0}} and {delta}{sub D}{sup K3{pi}}) for D{sup 0}{yields}K{sup -}{pi}{sup +}{pi}{sup 0} and D{sup 0}{yields}K{sup -}{pi}{sup +}{pi}{sup +}{pi}{sup -} are presented. These parameters can be used to improve the determination of the unitarity triangle angle {gamma} in B{sup -}{yields}DK{sup -} decays, where D is a D{sup 0} or D{sup 0} meson decaying to the same final state. The measurements are made using quantum-correlated, fully reconstructed D{sup 0}D{sup 0} pairs produced in e{sup +}e{sup -} collisions at the {psi}(3770) resonance. The measured values are: R{sub K{pi}}{sub {pi}{sup 0}}=0.84{+-}0.07, {delta}{sub D}{sup K{pi}}{sup {pi}{sup 0}}=(227{sub -17}{sup +14}) deg., R{sub K3{pi}}=0.33{sub -0.23}{sup +0.20}, and {delta}{sub D}{sup K3{pi}}=(114{sub -23}{sup +26}) deg. These results indicate significant coherence in the decay D{sup 0}{yields}K{sup -}{pi}{sup +}{pi}{sup 0}, whereas lower coherence is observed in the decay D{sup 0}{yields}K{sup -}{pi}{sup +}{pi}{sup +}{pi}{sup -}. The analysis also results in a small improvement in the knowledge of other D-meson parameters, in particular, the strong-phase difference for D{sup 0}{yields}K{sup -}{pi}{sup +}, {delta}{sub D}{sup K{pi}}, and the mixing parameter y.