# Amplitude analysis of $D^{0} \rightarrow K^{-} \pi^{+} \pi^{+} \pi^{-}$

## TL;DR

This paper performs a detailed amplitude analysis of the decay D0 to K- pi+ pi+ pi- using BESIII data, identifying key intermediate processes and their contributions.

## Contribution

It introduces a comprehensive amplitude model for the decay, including multiple intermediate states, and quantifies their relative fractions and phases.

## Key findings

- The dominant process is D0 to K- a1+(1260), with a 54.6% fit fraction.
- The analysis reveals the substructure and relative contributions of various intermediate states.
- Nearly background-free sample of 16,000 events enables precise amplitude modeling.

## Abstract

We present an amplitude analysis of the decay $D^{0} \rightarrow K^{-} \pi^{+} \pi^{+} \pi^{-}$ based on a data sample of 2.93 ${\mbox{\,fb}^{-1}}$ acquired by the BESIII detector at the $\psi(3770)$ resonance. With a nearly background free sample of about 16000 events, we investigate the substructure of the decay and determine the relative fractions and the phases among the different intermediate processes. Our amplitude model includes the two-body decays $D^{0} \rightarrow \bar{K}^{*0}\rho^{0}$, $D^{0} \rightarrow K^{-}a_{1}^{+}(1260)$ and $D^{0} \rightarrow K_{1}^{-}(1270)\pi^{+}$, the three-body decays $D^{0} \rightarrow \bar{K}^{*0}\pi^{+}\pi^{-}$ and $D^{0} \rightarrow K^{-}\pi^{+}\rho^{0}$, as well as the four-body decay $D^{0} \rightarrow K^{-}\pi^{+}\pi^{+}\pi^{-}$. The dominant intermediate process is $D^{0} \rightarrow K^{-}a_{1}^{+}(1260)$, accounting for a fit fraction of $54.6\%$.