The low energy neutron scattering lengths of He3 and T and their relation to the four-body problem

Udit Raha, Yuki Kamiya, Tetsuo Hyodo +1 more

We investigate the $s$-wave three-body system of two neutrons and one flavored meson with total spin-isospin $J=0,I=3/2$. The meson-neutron scattering length can become infinitely large in an unphysical region of the quark mass when extrapolated from strangeness to charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is manifest in the three-body system when the meson-neutron scattering length is extrapolated to the unitary limit of the two-body interaction. We thereby discuss the consequence of universal physics in the physical $K^{-}nn$ and $D^{0}nn$ systems.

Chih-Yuan Lin, Phillip C. Stancil, Heinz–Peter Liebermann +2 more

Lucas Platter

Udit Raha, Yuki Kamiya, Shung-Ichi Ando +1 more

We investigate the $s$-wave three-body system of two neutrons and one flavored meson with total spin-isospin $J=0,I=3/2$. The meson-neutron scattering length can become infinitely large when extrapolated to an unphysical region of the quark mass between strangeness and charm in the so-called zero coupling limit. Using a low-energy cluster effective field theory, we demonstrate that the Efimov effect is formally manifest in the three-body system when the meson-neutron scattering length approaches the unitary limit of the two-body interaction. We thereby discuss the consequence of remnant universal physics in the physical ${K}^{\ensuremath{-}}nn$ and ${D}^{0}nn$ systems.

Neeraj Vij

We consider the general two, three, and four neutron systems in a harmonic oscillator (HO) trap. By constructing a model for the 2, 3, and 4-neutron interactions, we make predictions about the theoretical conditions that produce a 2, 3, and 4 body bound state. We do so using an Effective Field Theory (EFT) in a No Core Shell Model (NCSM) basis space. The HO dependence is added to discretize the problem into a finite number of energy eigenstates in which the NCSM basis states are written. We find that as the width parameter (b) of the well tends to infinity, a bound 2-body state reproduces a bound 3 and 4-body state, that 2- body bound states do not reproduce 3 and 4 body bound states in the regime of 0.6760 < b/a < 1.7467, and we also show below scattering lengths of a = 4.438 X 10-15 m, 1.700 X 10- 15 m, and 1.866 X 10-15 m the 2, 3, and 4 body states are bound, respectively, for a width parameter of 3 Fermi’s.

H.‐W. Hammer, Lucas Platter