Speaker
Dr
Benjamin Gibson
(Los Alamos National Laboratory)
Description
\begin{document}
\Large{Determining the Unknown $\Lambda n$ Interaction} \\
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\large{Benjamin F. Gibson\\
Theoretical Division\\ Los Alamos National Laboratory\\ Los Alamos, NM 87545}
\normalsize
No published data on $\Lambda n$ scattering exist. A relativistic heavy-ion experiment has suggested that a $\Lambda nn$ bound state has been seen [1]. Were that the case, our knowledge of the $nn$ interaction would permit us to use the $\Lambda nn$ bound state to provide strong constraints on the $\Lambda n$ interaction. JLab would be an ideal facility to obtain such data using the $^3$H(e,e'K$^+$)$^3_\Lambda$n reaction. However, four theoretical analyses based upon pairwise $nn$ and $\Lambda n$ interactions, including our own, have cast serious doubt on the bound-state assertion [2-5]. Nevertheless, there could exist a three-body resonance in the $\Lambda nn$ system. Such a resonance could also be used to rigorously constrain the $\Lambda n$ interaction.
We will discuss calculations of the $\Lambda nn$ system using pairwise interactions of rank one, separable form that fit effective range parameters of the $nn$ system and those predicted for the yet-to-be observed $\Lambda n$ system by two different Nijmegen one-boson exchange potentials [6,7], the J\"{u}lich one-boson exchange potential [8] and a chiral $\Lambda N$ potential [9] based upon the known $\Lambda p$ scattering data. The use of rank one separable potentials allows us to analytically continue the $\Lambda nn$ 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 potentials examined, based upon the nominal $\Lambda p$ scattering length and effective range, predict a true resonance pole, scaling of the $\Lambda n$ interaction by as little as $\sim$5\% (well within the $\Lambda p$ scattering data uncertainties), would produce a resonance in the $\Lambda nn$ system. This suggests that one may use photo (electro) production of the $\Lambda nn$ system as a tool to examine the strength of the $\Lambda n$ interaction. In particular, K$^+$ electro production from tritium at Jefferson Lab would be a means to explore the
$\Lambda nn$ final state (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 un-measured $\Lambda n$ interaction.
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\noindent
1. C. Rappold, \textit{et al.}, "Search for evidence of $^3_\Lambda n$ by observing $d+\pi^-$ and $t+\pi^-$ final states in the reaction of $^6$Li$+^{12}$C at $2A$ GeV", Phys. Rev. C \textbf{88}, 041001(R) (2013).\\
2. H. Garcilazo, and A.Valcarce, "Nonexistance of a $\Lambda nn$ bound state", Phys. Rev. C\textbf{89}, 057001 (2014).\\
3. E. Hiyama, S. Ohnishi, B. F. Gibson, and Th. A. Rijken, "Three-body structure of the
$nn\Lambda$ system with $\Lambda N-\Sigma N$ coupling", Phys. Rev. C \textbf{89}, 061302(R) (2014).\\
4. A. Gal, and H. Garcilazo, "Is there a bound $^3_\Lambda$n?", Phys. Lett. \textbf{B736}, 93 (2014).\\
5. I. R. Afnan and B. F. Gibson, "Resonances in the $\Lambda$n System", Phys. Rev. C. \textbf{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 \textbf{15}, 2547 (1977).\\
7. T. A. Rijken, V. G. J. Stoks, Y. Yamamoto, "Soft-core hypron-nucleon potentials", Phys. Rev. C \textbf{59}, 21 (1999).\\
8. J. Haidenbauer and Ulf-G. Mei\ss ner, "J\"ulich hypron-nucleon model revisited", Phys. Rev. C \textbf{72}, 044005 (2005).\\
9. J. Haidenbauer, \textit{et al.}, "Hypron-nucleon interaction at next-to-leading order in chiral effective field theory", Nucl. Phys. A \textbf{915}, 24 (2013).\\
\end{document}
Primary author
Dr
Benjamin Gibson
(Los Alamos National Laboratory)
