Observation of $\Lambda^+_c\to n\pi^+\eta$ and search for $\Lambda^+_c\to na_0(980)^+$

By analysing 6.1 ${\rm fb}^{-1}$ of data collected at center-of-mass energies between $\sqrt{s}=4.600$ and 4.843 $\rm GeV$ with the BESIII detector at the BEPCII collider, we observe the decay $\Lambda_c^+\to n\pi^+\eta$ for the first time with a statistical significance of $9.5\sigma$. The ratio of branching fractions $\mathcal{B}(\Lambda_c^+\to n\pi^+\eta)/\mathcal{B}(\Lambda_c^+\to \Lambda\pi^+\eta)$ is measured to be $0.155\pm0.031_{\rm stat.}\pm0.012_{\rm syst.}$ Taking the world average of $\mathcal{B}(\Lambda_c^+\to \Lambda\pi^+\eta)$ as reference, the absolute branching fraction is calculated to be $\mathcal{B}(\Lambda_c^+\to n\pi^+\eta)=(2.94\pm0.59_{\rm stat.}\pm0.23_{\rm syst.}\pm0.13_{\rm ref.})\times10^{-3}$. The intermediate process $\Lambda_c^+\to na_0(980)^+$ is also searched for in the $\pi^+\eta$ invariant mass spectrum. Since no significant signal is found, the upper limit on $\mathcal{B}(\Lambda_c^+\to na_0(980)^+)\times\mathcal{B}(a_0(980)^+\to\pi^+\eta)$ is set to $8.4\times10^{-4}$ at 90\% confidence level. A sophisticated deep learning approach using a Transformer-based architecture is employed to distinguish signals from prevalent hadronic backgrounds, complemented by thorough validation and systematic uncertainty quantification.