Abstract
A resonance-like structure as narrow as 10 MeV is observed in the $K^-p$ invariant mass distributions in $\Lambda_c^+\to p K^- \pi^+$ at Belle. Based on the large data sample of about 1.5 million events and the small bin width of just 1 MeV for the $K^-p$ invariant mass spectrum, the narrow peak is found precisely lying at the $\Lambda\eta$ threshold. While lacking evidence for a quark model state with such a narrow width at this mass region, we find that this narrow structure can be naturally identified as a threshold cusp but enhanced by the nearby triangle singularity via the $\Lambda$-$a_0(980)^+$ or $\eta$-$\Sigma(1660)^+$ rescatterings.
Highlights
The discontinuation of the scattering amplitude caused by an S-wave open threshold generally will result in the cusp phenomenon in the energy spectrum
The PDG gives that the mass of Λð1670Þ is in the range of 1660 to 1680 MeV, with the averaged value MΛÃ ≈ 1670 MeV, and the width is in the range of 25 to 50 MeV, with the averaged value ΓΛÃ ≈ 35 MeV [23]
We investigate the Λþc → pK−πþ decays via the intermediate a0ð980ÞΛ and Σð1660Þη rescattering processes, and find that the narrow resonance-like structure observed by Belle in the K−p invariant mass spectrum can be identified as the cusp phenomenon caused by the Λη open threshold and closely related to the triangle singularity (TS) mechanism
Summary
The discontinuation of the scattering amplitude caused by an S-wave open threshold generally will result in the cusp phenomenon in the energy spectrum. This observation is based on a data sample of 2.287 × 107 events for the KÆ → πÆπ0π0 decays, and the excellent energy resolution for the π0π0 invariant mass spectrum [1] This measurement provided a precise determination of the ππ scattering length, which was suggested by Cabibbo [3]. One notices that the peak position of the structure in Λþc → pK−πþ is coincident with the Λη mass threshold ∼1663.5 MeV This could provide an important clue for understanding the narrow structure that may strongly be correlated with the Λη threshold cusp. As the leading singularity of the complex scattering amplitude, its association with the two-body cut near the physical boundary will strongly enhance the two-body cusp effects We find this mechanism can provide a natural explanation for the narrow cusp structure observed in Λþc → pK−πþ. − λ1=2ðM2Λþc ; m21; m22Þλ1=2ðm; m23; m2πþ Þ; ð1Þ with λðx; y; zÞ 1⁄4 ðx − y − zÞ2 − 4yz
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