Study of the D^0 \to pi^-pi^+pi^-pi^+ decay

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 $Γ(D^0 \toπ^+π^- π^+π^-)/Γ(D^0 \to K^-π^+π^-π^+) = 0.0914 \pm 0.0018 \pm 0.0022$. 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 $D^0 \to ρ(770)^0ρ(770)^0$, 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 $D^0 \to ρ(770)^0ρ(770)^0$, we measure a longitudinal polarization of $P_L = (71 \pm 4\pm 2)$%.

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