Study of the light scalar $a_{0}(980)$ through the decay $D^{0} \to a_{0}(980)^-e^{+} \nu_{e}$ with $a_{0}(980)^- \to \eta \pi^-$

TL;DR

This study measures the decay rate of $D^0$ to $a_0(980)^-$ and an electron-neutrino pair, analyzes the decay dynamics, and determines the product of the form factor and CKM matrix element for the first time.

Contribution

It provides the first measurement of the product of the form factor and CKM element in this decay channel and models the decay dynamics using a single-pole and Flatté parameterization.

Findings

Branching fraction of $D^0 o a_0(980)^- e^+ u_e$ measured as (0.86±0.17±0.05)×10^{-4}.

First determination of $f^{a_0}_+(0)|V_{cd}|$ as 0.126±0.013±0.003.

Decay dynamics modeled with single-pole and Flatté line shape.

Abstract

Using 7.93 ${\rm fb^{-1}}$ of $e^+e^-$ collision data collected at a center-of-mass energy of 3.773 ${\rm GeV}$ with the BESIII detector, we present an analysis of the decay $D^{0} \to \eta \pi^- e^+ \nu_{e}$. The branching fraction of the decay $D^{0} \to a_{0}(980)^{-} e^+ \nu_{e}$ with $a_{0}(980)^{-} \to \eta \pi^{-}$ is measured to be $(0.86\pm0.17_{\text{stat}}\pm0.05_{\text{syst}})\times 10^{-4}$. The decay dynamics of this process is studied with a single-pole parameterization of the hadronic form factor and the Flatt\'e formula describing the $a_0(980)$ line shape in the differential decay rate. The product of the form factor $f^{ a_0}_{+}(0)$ and the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ is determined for the first time with the result $f^{ a_0}_+(0)|V_{cd}|=0.126\pm0.013_{\rm stat}\pm0.003_{\rm syst}$.