24th European Conference on Few-Body Problems in Physics

Exploring the Unknown Λn Inteaction

3 Sept 2019, 16:15

25m

University of Surrey

Talk Invited Parallel Session Tuesday: Hyperon interactions and hypernuclei

Speaker

Dr Benjamin Gibson (Physical Review C)

Description

No published data for $\mathrm{\Lambda }n$ scattering exist. A relativistic heavy-ion experiment [1] has suggested that a $\mathrm{\Lambda }nn$ bound state has been seen. If that were the case, our knowledge of the $nn$ interaction would permit one to use that $\mathrm{\Lambda }nn$ bound state energy to generate strong constraints on the $\mathrm{\Lambda }n$ interaction. JLab would be an ideal facility to obtain such data using the ${}^3$H(e,e'K${}^{+}$)${}_{\mathrm{\Lambda }}^3$n reaction. However, at least four theoretical analyses based on a pairwise $nn$ and $\mathrm{\Lambda }n$ interaction hypothesis have cast serious doubt on the bound-state assertion [2-5]. However, there could exist a three-body $\mathrm{\Lambda }nn$ resonance. Such a resonance could be used to constrain the $\mathrm{\Lambda }n$ interaction.

We discuss calculations for the $\mathrm{\Lambda }nn$ system using pairwise interactions of rank-one, separable form that fit effective range parameters of the $nn$ system and those hypothesized for the as yet unobserved $\mathrm{\Lambda }n$ system based upon two different Nijmegen one-boson exchange potentials [6,7], a J\"{u}lich one-boson exchange potential [8] and a chiral $\mathrm{\Lambda }N$ potential [9], each of which is fit the known $\mathrm{\Lambda }p$ scattering data. The use of rank-one separable potentials allows us to analytically continue the $\mathrm{\Lambda }nn$ Faddeev equations into the second complex energy plane in search of resonance poles, by examining the eigenvalue spectrum of the kernel of the Faddeev equations.

Although none of the potential models utilized (each based upon the nominal $\mathrm{\Lambda }p$ scattering length and effective range) predict a physical resonance pole, scaling of the $\mathrm{\Lambda }n$ interaction by as little as $\sim$5\% (well within the $\mathrm{\Lambda }p$ scattering data uncertainties), does produce a resonance in the $\mathrm{\Lambda }nn$ system. This suggests that one may use photo (electro) production of the $\mathrm{\Lambda }nn$ system as a tool to examine the strength of the $\mathrm{\Lambda }n$ interaction. In particular, an experiment using K${}^{+}$ electro production from tritium at Jefferson Lab has been performed in an effort to explore the $\mathrm{\Lambda }nn$ final state (physical resonance or sub-threshold resonance); modeling the position and width of the spectrum would provide significant constraints on the scattering length and effective range of the heretofore unmeasured $\mathrm{\Lambda }n$ interaction.

1. C. Rappold, {et al.}, "Search for evidence of ${}_{\mathrm{\Lambda }}^{3}n$ by observing $d+{\pi }^{-}$ and $t+{\pi }^{-}$ final states in the reaction of ${}^6$Li${+}^{12}$C at $2A$ GeV", Phys. Rev. C {88}, 041001(R) (2013).
2. H. Garcilazo, and A.Valcarce, "Nonexistance of a $\mathrm{\Lambda }nn$ bound state", Phys. Rev. C {89}, 057001 (2014).
3. E. Hiyama, S. Ohnishi, B. F. Gibson, and Th. A. Rijken, "Three-body structure of the
   $nn\mathrm{\Lambda }$ system with $\mathrm{\Lambda }N-\mathrm{\Sigma }N$ coupling", Phys. Rev. C {89}, 061302(R) (2014).
4. A. Gal, and H. Garcilazo, "Is there a bound ${}_{\mathrm{\Lambda }}^3$n?", Phys. Lett. {B736}, 93 (2014).
5. I. R. Afnan and B. F. Gibson, "Resonances in the $\mathrm{\Lambda }$n System", Phys. Rev. C. {92}, 054608 (2015).
6. M. M. Nagels, T. A. Rijken, and J. J. de Swart, "Baryon-baryon scattering in a one-boson-exchange-potential approach, II. Hypron-nucleon scattering", Phys, Rev. D {15}, 2547 (1977).
7. T. A. Rijken, V. G. J. Stoks, Y. Yamamoto, "Soft-core hypron-nucleon potentials", Phys. Rev. C {59}, 21 (1999).
8. J. Haidenbauer and Ulf-G. Mei\ss ner, "J\"ulich hypron-nucleon model revisited", Phys. Rev. C {72}, 044005 (2005).
9. J. Haidenbauer, {et al.}, "Hypron-nucleon interaction at next-to-leading order in chiral effective field theory", Nucl. Phys. A {915}, 24 (2013).