– 1 – Review of Charm Dalitz Plot Analyses

The formalism of Dalitz-Plot analysis is reviewed in the preceeding note. Table 1 lists reported analyses of D mesons. In the following, we discuss a number of subjects of current interest: (1) D0 → K0 Sππ; (2) D → πππ: a σ(500) or f0(600); (3) D+ → K−π+π+: a κ(800)? (4) the f0(980), f0(1370) and f0(1500); (5) doubly Cabibbo-suppressed decays; and (6) CP violation. D0 → K0 Sππ: Several experiments have analyzed D0 → K0 Sπ +π− decay (see Table 1). The most precise results are from CLEO (BABAR and Belle, discussed below, have not yet evaluated systematic uncertainties). The CLEO analysis included ten resonances: K0 Sρ 0, K0 Sω, K 0 Sf0(980), K 0 Sf2(1270), K0 Sf0(1370), K ∗(892)−π+, K∗ 0(1430)−π+, K∗ 2(1430)−π+, K∗(1680)−π+, and the doubly Cabibbo-suppressed mode K∗(892)+π−. CLEO found a much smaller nonresonant contribution than did the earliest experiments. The source of the nonresonant component found in the early experiments has been attributed to the broad scalar resonances, the K∗ 0(1430)− and f0(1370), found in the later, larger data samples. The observation of a small but significant nonresonant component in the largest data samples suggests the presence of additional broad scalar resonances, the κ(800) and σ(500). The CLEO analysis could accommodate the σ(500) in lieu of the nonresonant component, but found no evidence for the κ(800). The ten quasi-two-body intermediate states in the CLEO analysis include both CP -even and CP -odd eigenstates and one doubly Cabibbo-suppressed channel. A time-dependent analysis of the Dalitz plot allows simultaneous determination of the strong transition amplitudes and phases and the mixing parameters x and y without phase or sign ambiguity. Using 9 fb−1, CLEO obtained (−4.5 < x < 9.3)% and (−6.4 < y < 3.6)% [1].