$\Lambda (1405)$ mediated triangle singularity in the $K^{-}d\to p{\Sigma }^{-}$ reaction

Abstract

We study for the first time the $p{\Sigma }^{-}\to K^{-}d$ and $K^{-}d\to p{\Sigma }^{-}$ reactions close to threshold and show that they are driven by a triangle mechanism, with the $\Lambda (1405)$, a proton and a neutron as intermediate states, which develops a triangle singularity close to the $\bar{K}d$ threshold. We find that a mechanism involving virtual pion exchange and the $K^{-}p\to {\pi }^{+}{\Sigma }^{-}$ amplitude dominates over another one involving kaon exchange and the $K^{-}p\to K^{-}p$ amplitude. Moreover, of the two $\Lambda (1405)$ states, the one with higher mass around $1420$ MeV, gives the largest contribution to the process. We show that the cross section, well within measurable range, is very sensitive to different models that, while reproducing $\bar{K}N$ observables above threshold, provide different extrapolations of the $\bar{K}N$ amplitudes below threshold. The observables of this reaction will provide new constraints on the theoretical models, leading to more reliable extrapolations of the $\bar{K}N$ amplitudes below threshold and to more accurate predictions of the $\Lambda (1405)$ state of lower mass.

12 pages and 10 figures

References in corpus (14)

• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Effective Kbar N interaction based on chiral SU(3) dynamics
• A Discussion on Triangle Singularities in the ${\Lambda }_b\to J/\psi K^{-}p$ Reaction
• Constraints on the chiral unitary $\bar{K}N$ amplitude from $\pi \Sigma K^{+}$ photoproduction data
• Measurement of the Sigma pi photoproduction line shapes near the Lambda(1405)
• $\bar{K}$ nuclear bound states in a dynamical model
• On the nature of $a_1(1420)$
• Kaonic production of Lambda(1405) off deuteron target in chiral dynamics
• Two-pole structures in QCD: Facts, not fantasy!
• The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$
• Triangle singularity in the $J/\psi \to K^{+}{K}^{-}{f}_0(980)(a_0(980))$ decays
• Triangle singularity mechanism for the $pp\to {\pi }^{+}d$ fusion reaction
• Antineutrino induced Lambda(1405) production off the proton
• Kaon induced Lambda(1405) production on a deuteron target at DAFNE

Cited by in corpus (1)

• The role of triangle singularity in the decay process $D^0\to {\pi }^{+}{\pi }^{-}{f}_0(980),f_0\to {\pi }^{+}{\pi }^{-}$