Observation of a Threshold Cusp at the $\Lambda\eta$ Threshold in the $pK^{-}$ Mass Spectrum with $\Lambda_{c}^{+} \rightarrow p K^{-} \pi^{+}$ Decays

We observe a narrow peaking structure in the $pK^{-}$ invariant-mass spectrum near the $\Lambda\eta$ threshold. The peak is clearly seen in 1.5 million events of $\Lambda_{c}^{+} \rightarrow p K^{-} \pi^{+}$ decay using the $980~{\rm fb^{-1}}$ data sample collected by the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. We try two approaches to explain this structure: as a new resonance and as a cusp at the $\Lambda\eta$ threshold. The best fit is obtained with a coherent sum of a Flatt$\rm{\acute{e}}$ function and a constant background amplitude with the $\chi^2/{\rm n.d.f}=257/243$ ($p = 0.25$), while the fits to Breit-Wigner functions are unfavored by more than 7$\sigma$. The best fit explains the structure as a cusp at the $\Lambda\eta$ threshold, and the obtained parameters are consistent with the known properties of $\Lambda(1670)$. The observation gives the first identification of a threshold cusp in hadrons from the spectrum shape.