Observation of the Semileptonic Decay $D^0 to a_0(980)^- e^+ u_e$ and Evidence for $D^+ to a_0(980)^0 e^+ u_e$

Using an $e^+e^-$ collision data sample of 2.93 fb$^{-1}$ collected at a center-of-mass energy of 3.773 GeV by the BESIII detector at BEPCII, we report the observation of $D^0 to a_0(980)^- e^+ u_e$ and evidence for $D^+ to a_0(980)^0 e^+ u_e~$ with significances of $6.4sigma$ and $2.9sigma$, respectively. The absolute branching fractions are determined to be $mathcal{B}(D^0 to a_0(980)^- e^+ u_e)timesmathcal{B}(a_0(980)^- to eta pi^-) = (1.33_{-0.29}^{+0.33}({rm stat})pm0.09({rm syst}))times10^{-4}~$ and $mathcal{B}(D^+ to a_0(980)^0 e^+ u_e)timesmathcal{B}(a_0(980)^0 to eta pi^0) = (1.66_{-0.66}^{+0.81}({rm stat})pm0.11({rm syst}))times10^{-4}~$. An upper limit of $mathcal{B}(D^+ to a_0(980)^0 e^+ u_e)timesmathcal{B}(a_0(980)^0 to eta pi^0)<3.0times10^{-4}~$ is also determined at the $90%~$ confidence level.