Determination of the pi Sigma scattering lengths from the weak decays of Lambda_c

Abstract

The scattering lengths of the pi Sigma systems are key quantities in understanding the structure of the Lambda(1405) resonance and the subthreshold extrapolation of the barK N interaction. We demonstrate that the pi Sigma scattering lengths can be extracted from the threshold cusp phenomena in the weak Lambda_c -> pi pi Sigma decays, analogously with Cabibbo's method for determination of the pi pi scattering length. We show that the substantial cusp effect should be observed in the spectrum, when the pi Sigma interaction in I=0 is strongly attractive to generate a near-threshold singularity, such as a bound state or a virtual state.

13 pages, 13 figures, 3 tables, published version

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Cited by in corpus (20)

• Weak decays of heavy hadrons into dynamically generated resonances
• Antikaon-nucleon interaction and Lambda(1405) in chiral SU(3) dynamics
• Predictions for the ${\Lambda }_b\to J/\psi \Lambda (1405)$ decay
• Weak decay of Lambda_c^+ for the study of Lambda(1405) and Lambda(1670)
• QCD and the Strange Baryon Spectrum
• Hadron mass scaling near the s-wave threshold
• ${\Sigma }_{1/2^{-}}^{\ast }(1380)$ in the ${\Lambda }_c^{+}\to \eta {\pi }^{+}\Lambda$ decay
• The $a_0(980)$ and $\Lambda (1670)$ in the ${\Lambda }_c^{+}\to {\pi }^{+}\eta \Lambda$ decay
• Theoretical study of the $\Omega (2012)$ state in the ${\Omega }_c^0\to {\pi }^{+}\Omega (2012{)}^{-}\to {\pi }^{+}(\bar{K}\Xi {)}^{-}$ and ${\pi }^{+}(\bar{K}\Xi \pi {)}^{-}$ decays
• Anomalous enhancement of the isospin-violating $\Lambda (1405)$ production by a triangle singularity in ${\Lambda }_c\to {\pi }^{+}{\pi }^0{\pi }^0{\Sigma }^0$
• Roles of $a_0(980)$, $\Lambda (1670)$, and $\Sigma (1385)$ in the ${\Lambda }_c^{+}\to \eta \Lambda {\pi }^{+}$ decay
• Role of the $N^{\ast }(1535)$ in the ${\Lambda }_c^{+}\to {\bar{K}}^0\eta p$ decay
• Theoretical study of $N(1535)$ and ${\Sigma }^{\ast }(1/2^{-})$ in the Cabibbo-favored process ${\Lambda }_c^{+}\to p{\bar{K}}^0\eta$
• Search for the ${\Sigma }^{\ast }$ state in ${\Lambda }_c^{+}\to {\pi }^{+}{\pi }^0{\pi }^{-}{\Sigma }^{+}$ decay by triangle singularity
• Extraction of $ND$ scattering lengths from the ${\Lambda }_b\to {\pi }^{-}p{D}^0$ decay and properties of the ${\Sigma }_c(2800{)}^{+}$
• Production of $N^{\ast }(1535)$ and $N^{\ast }(1650)$ in ${\Lambda }_c\to {\bar{K}}^0\eta p$ $(\pi N)$ decay
• Recent developments in antikaon-nucleon dynamics
• Measurement of the Decays ${\Lambda }_c\to \Sigma \pi \pi$ at Belle
• New insights in \bar{K}N scattering and the Λ(1405)
• Antikaon-nucleon dynamics and its application to few-body systems