First model-independent determination of the relative strong phase between D{sup 0} and D{sup 0}{yields}K{sub S}{sup 0}{pi}{sup +}{pi}{sup -} and its impact on the CKM angle {gamma}/{phi}{sub 3} measurement

We exploit the quantum coherence between pair-produced D{sup 0} and D{sup 0} in {psi}(3770) decays to make a first determination of the relative strong phase differences between D{sup 0}{yields}K{sub S}{sup 0}{pi}{sup +}{pi}{sup -} and D{sup 0}{yields}K{sub S}{sup 0}{pi}{sup +}{pi}{sup -}, which are of great importance in determining the Cabibbo-Kobayashi-Maskawa angle {gamma}/{phi}{sub 3} in B{sup -}{yields}D{sup 0}(D{sup 0})K{sup -} decays. Using 818 pb{sup -1} of e{sup +}e{sup -} collision data collected with the CLEO-c detector at E{sub cm}=3.77 GeV, we employ a binned Dalitz-plot analysis of K{sub S}{sup 0}{pi}{sup +}{pi}{sup -} and K{sub L}{sup 0}{pi}{sup +}{pi}{sup -} decays recoiling against flavor-tagged, CP-tagged, and K{sub S}{sup 0}{pi}{sup +}{pi}{sup -}-tagged events to determine these strong phase differences.