Study of the ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ decay

Study of the $D^{0} \to π^{-} π^{+} π^{-} π^{+}$ decay

J. M. Link et al.

Phys. Rev. D 75, 052003 – Published 26 March 2007

Abstract

Using data from the FOCUS (E831) experiment at Fermilab, we present new measurements for the Cabibbo-suppressed decay mode $D^{0} \to π^{-} π^{+} π^{-} π^{+}$ . We measure the branching ratio $Γ (D^{0} \to π^{+} π^{-} π^{+} π^{-}) / Γ (D^{0} \to K^{-} π^{+} π^{-} π^{+}) = 0.0914 \pm 0.0018 \pm 0.0022$ . An amplitude analysis has been performed, a first for this channel, in order to determine the resonant substructure of this decay mode. The dominant component is the decay $D^{0} \to a_{1} (1260)^{+} π^{-}$ , accounting for 60% of the decay rate. The second most dominant contribution comes from the decay $D^{0} \to ρ (770)^{0} ρ (770)^{0}$ , with a fraction of 25%. We also study the $a_{1} (1260)$ line shape and resonant substructure. Using the helicity formalism for the angular distribution of the decay $D^{0} \to ρ (770)^{0} ρ (770)^{0}$ , we measure a longitudinal polarization of $P_{L} = (71 \pm 4 \pm 2) %$ .