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

TL;DR

This paper presents new measurements of the decay mode D^0 to four pions, including a first amplitude analysis revealing dominant resonant substructures and polarization measurements, based on Fermilab data.

Contribution

It provides the first amplitude analysis of D^0 to four pions decay, identifying key resonant contributions and polarization, with precise branching ratio measurements.

Findings

Dominant decay component is D^0 to a_1(1260)^+ pi^- (60%)

Second dominant is D^0 to rho(770)^0 rho(770)^0 (25%)

Longitudinal polarization of D^0 to rho^0 rho^0 is 71%

Abstract

Using data from the FOCUS (E831) experiment at Fermilab, we present new measurements for the Cabibbo-suppressed decay mode $D^0 \to \pi^-\pi^+\pi^-\pi^+$. We measure the branching ratio $\Gamma(D^0 \to\pi^+\pi^- \pi^+\pi^-)/\Gamma(D^0 \to K^-\pi^+\pi^-\pi^+) = 0.0914 \pm 0.0018 \pm 0.0022$. 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 $D^0 \to a_1(1260)^+ \pi^-$, accounting for 60% of the decay rate. The second most dominant contribution comes from the decay $D^0 \to \rho(770)^0\rho(770)^0$, 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 $D^0 \to \rho(770)^0\rho(770)^0$, we measure a longitudinal polarization of $P_L = (71 \pm 4\pm 2)$%.