Investigation of () hypernucleus in low-energy pionless halo effective theory

Ghanashyam Meher; Udit Raha

doi:10.1140/epjs/s11734-021-00007-1

2024 Impact factor 2.3

Special Topics

Nuclear Astrophysics in Our Time: Supernovae, Neutron Stars and Binary Neutron Star Mergers

Eur. Phys. J. Spec. Top. (2021) 230: 579-601
https://doi.org/10.1140/epjs/s11734-021-00007-1

Regular Article

Investigation of $Ξ^{-} n n$ $\varXi ^- nn$ ( $S = - 2$ ) hypernucleus in low-energy pionless halo effective theory

Ghanashyam Meher and Udit Raha^b

Department of Physics, Indian Institute of Technology Guwahati, 781 039, Guwahati, Assam, India

^b udit.raha@iitg.ac.in

Received: 1 October 2020
Accepted: 23 December 2020
Published online: 21 April 2021

Abstract

We study the $Ξ^{-} n n$ $\varXi ^- nn$ ( $S = - 2, I = 3 / 2, J^{P} = {1 / 2}^{+}$ $S=-2,\,I=3/2,\,J^P={1/2}^+$ ) three-body system using low-energy effective field theory (EFT). Due to the acute inadequacy of empirical information in this sector, there exists substantial degree of ambiguity in determining various few-body observables, some of which are expected to yield vital clues to resolving longstanding contentious issues in hypernuclear physics. Moreover, in astrophysical studies, a precise determination of neutron star equation of state (EoS) of putative hyperonic cores relies on essential input from the $S = - 2$ $$S=-2$$ sector. In this obscure current scenario, a pionless EFT analysis provides a systematic model-independent framework for assessing the feasibility of light three-particle-stable bound states, utilizing low-energy universality. Here we take recourse to a simplistic speculation of the three-body system by eliminating the repulsive spin-singlet $Ξ^{-} n$ $\varXi ^- n$ sub-system, while retaining the predominantly attractive (possibly bound) spin-triplet $Ξ^{-} n$ $\varXi ^- n$ and the virtual bound spin-singlet nn sub-systems. In particular, a qualitative leading order EFT investigation by introducing a sharp momentum ultraviolet cut-off parameter $Λ_{reg}$ $\varLambda _{\mathrm{reg}}$ into the coupled integral equations indicates a discrete scaling behavior akin to a renormalization group limit cycle, thereby suggesting the formal existence of Efimov states in the unitary limit, as $Λ_{reg} \to \infty$ $\varLambda _{\mathrm{reg}}\rightarrow \infty$ . Our subsequent non-asymptotic analysis indicates that the three-body binding energy $B_{3}$ $$B_3$$ is sensitively dependent on the cut-off without the inclusion of three-body contact interactions. Furthermore, our analysis reproduces several values of the binding energy $B_{3} \sim 3 - 4$ $B_3\sim 3{-}4$ MeV, predicted in context of existing potential models, with the regulator $Λ_{reg}$ $\varLambda _{\mathrm{reg}}$ in the range $\sim 350 - 460$ $\sim 350{-}460$ MeV. Finally, based on these model inputs for $B_{3}$ $$B_3$$ , a ballpark estimate of the three-body scattering length in the range $2.6 - 4.9$ $$2.6{-}4.9$$ fm, is naively constrained by our EFT analysis. Despite approximations, the resulting Phillips line is expected to yield a robust feature of the halo-bound $Ξ^{-} n n$ $\varXi ^- nn$ system. For pedagogical reasons, using a simple toy model interacting three-bosons system, we highlight in the appendices the typical universal features leading to emergence of RG limit cycle and Efimov states which are amenable to a low-energy EFT formalism.