Observation of an Altered $a_0(980)$ Line shape in $D^{+}\to {\pi }^{+}\eta \eta$

Abstract

Using $20.3{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected with the BESIII detector at $\sqrt{s}=3.773\mathrm{GeV}$, we perform the first amplitude analysis of the decay $D^{+}\to {\pi }^{+}\eta \eta$. The intermediate process $D^{+}\to a_0(980{)}^{+}\eta$, $a_0(980{)}^{+}\to {\pi }^{+}\eta$, is observed as the only significant component in the amplitude analysis, and its branching fraction is measured to be $(3.67\pm 0.12_{\mathrm{stat}}\pm 0.06_{\mathrm{syst}})\times 10^{-3}$. The ${\pi }^{+}\eta$ mass spectrum associated with $a_0(980{)}^{+}\eta$ production exhibits a line shape that differs substantially from those observed in $D_{(s)}\to a_0(980)\pi$ and $D^0\to a_0(980{)}^{-}{e}^{+}{\nu }_e$ decays. We examine several conventional descriptions of the $a_0(980)$ amplitude, including Flatté, dispersively modified Flatté, $T$-matrix, and $K$-matrix parameterizations. With reference $a_0(980)$ parameters, neither these models nor their extensions including additional small resonant or non-resonant amplitudes reproduce the observed line shape satisfactorily. When the $a_0(980)$ parameters are allowed to float, satisfactory fits can be obtained, but the pole mass is driven well above the $K\bar{K}$ threshold, inconsistent with the near-threshold character of the $a_0(980)$. The results reveal a tension between fit quality and the physical pole position in conventional direct-production amplitude models.