The $a_0(980)$ physics in semileptonic $D^0$ and $D^{+}$ decays

Abstract

The decays $D^0\to d\bar{u}{e}^{+}\nu \to a_0^{-}(980)e^{+}\nu \to {\pi }^{-}\eta e^{+}\nu$ and $D^{+}\to d\bar{d}{e}^{+}\nu \to a_0^0(980)e^{+}\nu \to {\pi }^0\eta e^{+}\nu$ (and the charge conjugated ones) is the direct probe of the two-quark components in the $a_0^{\pm }(980)$ and $a_0^0(980)$ wave functions. Recent BESIII experiment is the first step in experimental study of these decays. We present a possible variant of $\eta \pi$ invariant mass distribution when $a_0(980)$ has no $q\bar{q}$ component at all.

Comments: 16 pages, 9 figures. Updated version corresponding to PRD article. An essential upgrade, including taking into account the KLOE-2009 data on the phi-> eta pi0 gamma decay. arXiv admin note: text overlap with arXiv:1711.08777