Dalitz plot analysis and branching fraction measurement of D+ and Ds+ -> pi+pi-pi+

Abstract

Fermilab fixed target experiment E791 obtained a sample of $1172 \pm 61$ events of $D^+ \to π^- π^+ π^+$ and 848 $\pm 44$ events of $D_s^+ \to π^- π^+ π^+$ decays. We find respectively $B (D^+ \to π^- π^+ π^+) / B (D^+ \to K^- π^+ π^+) = 0.0311 \pm 0.0018 ^ {+0.0016}_{-0.0026}$ and $B(D_s^+ \to π^+ π^- π^+) / B(D_s^+ \to ϕπ^+) = 0.245 \pm 0.028^{+0.019}_{-0.012}$. Using a coherent amplitude analysis to fit the Dalitz plot of the $D^+ \to π^- π^+ π^+$ decay, we find strong evidence for a scalar resonance of mass $478^{+24}_{-23} \pm 17 $MeV/$c^2$ and width $324^{+42}_{-40} \pm 21$ MeV/$c^2$, compatible with what is expected for the isoscalar meson $σ$ >. The $D^+ \to σ(500) π^+$ fraction accounts for approximately half of all three-charged-pion decays of the $D^+$ . From the Dalitz plot analysis of the $D_s^+ \to π^- π^+ π^+$ decay events, we find significant contributions from the channels $ρ^0(770)π^+$, $ρ^0(1450)π^+$, $f_0(980)π^+$, $f_2(1270)π^+$, and $f_0(1370)π^+$. We also present new measurement of the masses and widths of the isoscalar resonances $f_0(980)$ and $f_0(1370)$.