The first ab initio calculations for p-shell single-Lambda hypernuclei (Wirth et al., Phys. Rev. Lett. 113, 192502 (2014)) used leading-order (LO) chiral hyperon-nucleon (YN) interactions and left a five-part open program: inclusion and validation of next-to-leading-order (NLO) chiral YN interactions; consistent construction and inclusion of initial chiral and SRG-induced YNN three-body forces; control of SRG-induced four-nucleon terms in the nucleonic parents; controlled convergence for long-range observables such as B(E2)B(\mathrm{E2}); and clarification of the origin of the strong induced YNN terms. Later literature has resolved much of this for light systems: the induced-YNN origin and machinery are established, NLO/N2LO YN potentials exist and have been validated up to A≈7A\approx 7 together with consistent chiral Λ\LambdaNN/Σ\SigmaNN three-body forces. The surviving open core, explicitly identified as the next step in a 2026 review, is the extension of this consistent two- plus three-baryon chiral treatment into the mid p-shell for Λ9Be_\Lambda^9\mathrm{Be} and Λ13C_\Lambda^{13}\mathrm{C}, with spectroscopic validation of spin doublets and negative-parity states and quantified uncertainties, so that hypernuclear data can constrain the YN higher partial waves and the YNN low-energy constants of chiral effective field theory.

Background

A hypernucleus is a bound nuclear system in which one or more nucleons are replaced by a hyperon, a baryon containing a strange quark; in single-Λ\Lambda hypernuclei the added hyperon is the Λ\Lambda (neutral, isospin zero), which binds to the nucleons through the hyperon-nucleon (YN) interaction. Because the Λ\Lambda and Σ\Sigma hyperons (the Σ\Sigma has isospin one) differ in mass by only about 77 MeV, a faithful Hamiltonian must treat the Λ\Lambda and Σ\Sigma as coupled channels, including Λ\Lambda-Σ\Sigma conversion terms. The YN interaction is far less constrained than the nucleon-nucleon (NN) one: low-energy Λp\Lambda p scattering data amount to only a few hundred differential-cross-section points and there are essentially no ΣN\Sigma N data of comparable quality. Chiral effective field theory (EFT), the systematic low-momentum expansion of QCD, extended to the baryon octet through approximate SU(3) flavor symmetry, provides YN potentials at leading order (LO), next-to-leading order (NLO), and next-to-next-to-leading order (N2LO), each order adding one- and two-meson-exchange topologies and contact terms (short-range operators with fitted low-energy constants, LECs). In the strangeness sector, irreducible three-baryon forces with one hyperon (YNN, i.e. Λ\LambdaNN and Σ\SigmaNN) formally enter at N2LO; their leading structure was derived from SU(3) chiral EFT by Petschauer et al. (2016).

On the many-body side, the no-core shell model (NCSM) diagonalizes the Hamiltonian in a harmonic-oscillator basis with all nucleons and hyperons treated as active particles; convergence is accelerated by the similarity renormalization group (SRG), a continuous unitary transformation that decouples low from high momenta. The SRG transformation conserves the spectrum but induces interaction terms of higher particle rank than the initial Hamiltonian: evolving NN and YN two-body terms generates induced three-nucleon (3N), YNN, and four-nucleon (4N) components that must either be included or demonstrably neglected. Hypernuclear observables include the Λ\Lambda separation energy BΛB_\Lambda (the energy needed to remove the hyperon), excitation spectra, spin-doublet splittings (pairs of levels that would be degenerate if the Λ\Lambda were a spinless spectator), and electromagnetic transition strengths such as B(E2)B(\mathrm{E2}), a long-range observable that converges slowly in oscillator bases.

In this setting, Wirth, Gazda, Navrátil, Calci, Langhammer, and Roth (2014) performed the first ab initio calculations of p-shell single-Λ\Lambda hypernuclei (Λ7Li{}^7_\Lambda\mathrm{Li}, Λ9Be{}^9_\Lambda\mathrm{Be}, Λ13C{}^{13}_\Lambda\mathrm{C}), using two NCSM implementations with explicit Λ\Lambda and Σ\Sigma hyperons, chiral NN+3N interactions, and YN interactions at LO in chiral EFT (NLO YN potentials existed since Haidenbauer et al. 2013 but had not been used in such calculations). LO chiral YN interactions reproduced ground-state and excitation energies within cutoff dependence up to the mid p-shell, but both LO chiral and phenomenological YN interactions failed for the first negative-parity doublet of Λ13C{}^{13}_\Lambda\mathrm{C}, pointing to deficiencies in the higher relative partial waves of the YN interaction; the 12C{}^{12}\mathrm{C} parent was overbound by about 6 MeV because of SRG-induced 4N interactions omitted in the upper p-shell; and B(E2)B(\mathrm{E2}) in Λ7Li{}^7_\Lambda\mathrm{Li} showed problematic convergence. The paper's outlook posed the coherent program examined here: include and validate NLO chiral YN interactions; consistently construct, SRG-evolve, and include initial chiral and SRG-induced YNN three-body forces (the induced YNN terms were found to be large); quantify SRG-induced 4N contributions; establish systematic extrapolations for long-range observables; and explain the origin and operator structure of the strong induced YNN terms. The single overarching objective is a quantitatively predictive ab initio description of p-shell hypernuclei whose comparison with data constrains the YN and YNN sectors of chiral EFT. Repulsive YNN forces are also a leading candidate mechanism for the 'hyperon puzzle', the apparent absence of hyperons in the cores of the heaviest neutron stars, so a quantitative handle on YNN forces from hypernuclei has implications for dense-matter physics.

Problem Statement

The problem, as posed by the source paper and narrowed by subsequent progress, is to complete the Hamiltonian and methodology of ab initio p-shell hypernucleus spectroscopy so that it becomes quantitatively predictive and informative about the underlying interactions. Concretely, within no-core-shell-model-type calculations with explicit Λ and Σ hyperons and Λ-Σ coupling, using chiral NN+3N nucleonic interactions and SRG-evolved Hamiltonians: (a) use chiral YN interactions beyond leading order (NLO/N2LO) rather than LO, validating them against p-shell spectra — especially spin-doublet splittings and the negative-parity states that probe the higher relative partial waves of the YN interaction, such as the observed 1/2−/3/2− doublet of Λ13C{}^{13}_{\Lambda}\mathrm{C}, which the LO YN interaction fails to reproduce; (b) include, consistently in the chiral power counting, the initial chiral YNN three-body forces (ΛNN, ΣNN) together with the YNN terms induced by the SRG evolution; (c) keep SRG-induced 4N (and higher-rank) contributions in the nucleonic parents demonstrably under control; and (d) establish controlled model-space and frequency extrapolations, including for long-range observables such as B(E2)B(\mathrm{E2}) in Λ7Li{}^7_{\Lambda}\mathrm{Li}. The components serve one objective: reliable, uncertainty-quantified predictions of p-shell hypernuclear binding energies, spectra, and transitions that can be confronted with data to constrain the YN (in particular its poorly known higher partial waves) and YNN sectors of chiral EFT. Items (b) (both chiral and induced YNN, for A ≤ 7), the origin of the induced YNN terms, and much of the convergence methodology have been demonstrated for light hypernuclei up to A=7A=7 and are background supplied by the cited literature, not deliverables to be reproduced at those masses. The surviving open core, explicitly identified as the next step in the 2026 literature, is the extension of this consistent two- plus three-baryon chiral treatment into the mid p-shell for Λ9Be{}^9_{\Lambda}\mathrm{Be} and Λ13C{}^{13}_{\Lambda}\mathrm{C}. Completing it requires, for each system, the realization of all four components (a)–(d) together with the spectroscopic validation and quantified uncertainties, and the inference about whether hypernuclear data constrain the YN higher partial waves and the YNN low-energy constants; a partial realization of (a)–(d), or the inference step alone, does not resolve the task.

References

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