Visible narrow cusp structure in ${\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+}$ enhanced by triangle singularity

A resonance-like structure as narrow as 10 MeV is observed in the $K^{-}p$ invariant mass distributions in ${\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+}$ 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 $\mathrm{\Lambda }\eta$ 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 $\mathrm{\Lambda }\text{−}{a}_0(980{)}^{+}$ or $\eta \text{−}\mathrm{\Sigma }(1660{)}^{+}$ rescatterings.

Figure 1

Rescattering diagrams which contribute to ${\mathrm{\Lambda }}_c^{+}\to p{K}^{-}{\pi }^{+}$. Kinematic conventions for the intermediate states are (a) $\mathrm{\Lambda }(q_1,m_1)$, $a_0(q_2,m_2)$, $\eta (q_3,m_3)$ and (b) $\eta (q_1,m_1)$, ${\mathrm{\Sigma }}^{*}(q_2,m_2)$, $\mathrm{\Lambda }(q_3,m_3)$.

Figure 2

The TS location of $\mathcal{T}(s,m_2^2)$ in the complex $s$-plane. The thick line on the real axis represents the unitarity cut starting from $s_{\mathrm{th}}$. The trajectory marked with a triangle (box) is obtained by varying $M_{a_0}$ ($M_{{\mathrm{\Sigma }}^{*}}$) and fixing ${\mathrm{\Gamma }}_{a_0}=75\mathrm{MeV}$ (${\mathrm{\Gamma }}_{{\mathrm{\Sigma }}^{*}}=100\mathrm{MeV}$).

Figure 3

Invariant mass distribution of $K^{-}p$ via the rescattering processes in Fig. 1. The bands are obtained by taking into account uncertainties of the mass and width of $a_0(980)/\mathrm{\Sigma }(1660)$. The vertical dot-dashed line indicates the $\mathrm{\Lambda }\eta$ threshold.

Figure 4

Argand plot of the rescattering amplitude, with $s$ increasing from $(M_{K^{-}}+m_p{)}^2$ to $(M_{{\mathrm{\Lambda }}_c^{+}}-m_{{\pi }^{+}}{)}^2$ counterclockwise. The mass and width of $\mathrm{\Lambda }(1670)$ are taken to be PDG averaged values.