Study of the Decay $D^{+}_{s}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ and Observation of the W-annihilation Decay $D^{+}_{s}\rightarrow a_0(980)^+\rho^0$

TL;DR

This paper reports the first observation of the decay $D^{+}_{s} ightarrow ext{pi}^+ ext{pi}^+ ext{pi}^- ext{eta}$, measures its branching fraction, analyzes its sub-structures, and observes a significant W-annihilation decay process.

Contribution

It provides the first measurement of the decay $D^{+}_{s} ightarrow ext{pi}^+ ext{pi}^+ ext{pi}^- ext{eta}$, performs an amplitude analysis, and reports the observation of a W-annihilation decay with a larger branching fraction than previous similar decays.

Findings

First observation of $D^{+}_{s} ightarrow ext{pi}^+ ext{pi}^+ ext{pi}^- ext{eta}$ decay

Branching fraction measured as (3.12 ± 0.13 ± 0.09)%

Observation of W-annihilation process with a branching fraction of (0.21 ± 0.08 ± 0.05)%

Abstract

The decay $D^{+}_{s}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ is observed for the first time, using $e^+e^-$ collision data corresponding to an integrated luminosity of 6.32 fb$^{-1}$, collected by the BESIII detector at center-of-mass energies between 4.178 and 4.226 GeV. The absolute branching fraction for this decay is measured to be $\mathcal{B}(D^+_s \to \pi^+ \pi^+ \pi^- \eta) = (3.12\pm0.13_{\rm stat.}\pm0.09_{\rm syst.})$%. The first amplitude analysis of this decay reveals the sub-structures in $D^{+}_{s}\rightarrow \pi^{+}\pi^{+}\pi^{-}\eta$ and determines the relative fractions and the phases among these sub-structures. The dominant intermediate process is $D^{+}_{s}\rightarrow a_1(1260)^+ \eta, a_1(1260)^+ \rightarrow \rho(770)^0\pi^+$ with a branching fraction of $(1.73 \pm 0.14_{\rm stat.} \pm 0.08_{\rm syst.})$%. We also observe the W-annihilation process $D^{+}_{s}\rightarrow a_0(980)^+\rho(770)^0$, $a_0(980)^+ \to \pi^+ \eta$ with a branching fraction of $(0.21\pm0.08_{\rm stat.}\pm0.05_{\rm syst.})$%, which is larger than the branching fractions of other measured pure W-annihilation decays by one order of magnitude.