Study of the D0 → π- π+π- π+ decay

Using data from the FOCUS (E831) experiment at Fermilab, we present new measurements for the Cabibbo-suppressed decay mode ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$. We measure the branching ratio $\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}})/\ensuremath{\Gamma}({D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+})=0.0914\ifmmode\pm\else\textpm\fi{}0.0018\ifmmode\pm\else\textpm\fi{}0.0022$. 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 ${D}^{0}\ensuremath{\rightarrow}{a}_{1}(1260{)}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$, accounting for 60% of the decay rate. The second most dominant contribution comes from the decay ${D}^{0}\ensuremath{\rightarrow}\ensuremath{\rho}(770{)}^{0}\ensuremath{\rho}(770{)}^{0}$, 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 ${D}^{0}\ensuremath{\rightarrow}\ensuremath{\rho}(770{)}^{0}\ensuremath{\rho}(770{)}^{0}$, we measure a longitudinal polarization of ${P}_{L}=(71\ifmmode\pm\else\textpm\fi{}4\ifmmode\pm\else\textpm\fi{}2)%$.