The odd-parity strange baryons $Σ\,(\frac{1}{2}^-)$ below 1.8 GeV with Hamiltonian effective field theory

TL;DR

This work probes the Σ(1/2−) spectrum below 1.8 GeV by combining experimental K−p scattering data with lattice QCD finite-volume spectra within the Hamiltonian Effective Field Theory (HEFT). Two scenarios are examined: a bare strange triquark core Σ_0 plus meson–baryon channels versus purely dynamically generated states; the lattice data favor the former. The analysis reveals two near-1.7 GeV resonances with poles at around $1687-110i$ MeV and $1714-14i$ MeV on appropriate Riemann sheets, along with a cusp near the $K̄N$ threshold in the T-matrices. These results demonstrate that a bare core plays a significant role in the Σ(1/2−) spectrum and illustrate HEFT’s power to bridge experimental data and lattice QCD, guiding future experimental and lattice investigations toward a more definitive picture of the Σ hyperon family.

Abstract

We examine the spectrum of the $Σ\,(\frac{1}{2}^-)$ family based on the experimental $K^-p$ scattering data and lattice QCD simulations within the Hamiltonian Effective Field Theory. Especially, two different scenarios are constructed in order to clarify whether there is one or two $Σ\,(\frac{1}{2}^-)$ resonances with masses around 1.5$\sim$1.7 GeV. The relevant lattice QCD data support our scenario with two resonance poles at $1687-110\,i$ and $1714-14\,i$ MeV in which the bare strange triquark core plays an important role. We also show an extra clear cusp structure around 1.4 GeV in our scattering T matrices associated with the odd-parity strange baryons.

Figures (8)

• Figure 1: The experimental data and fitted results for the $K^-p$ scattering cross sections. The red solid and the blue dot-dashed lines represent our results with and without the bare baryon component $\Sigma_0$, respectively. The experimental data points are taken from Refs. Piscicchia:2022wmdAbrams:1965zzSakitt:1965khKim:1965zzdMast:1975pvBangerter:1980pxCiborowski:1982etEvans:1983hzMast:1974sxNordin:1961zzBerley:1996zhFerroLuzzi:1962zzaWatson:1963zzEberhard:1959zz. The peaks near 400 MeV are associated with the $I=0$ D-wave $\Lambda(1520)$ resonance which is not included in this work as discussed in the text.
• Figure 2: Finite-volume energy spectra in two scenarios compared to the lattice QCD data with Ensemble A ($L = 2.118\,\text{fm}$) from the BGR group Engel:2013ig. The broken lines denote noninteracting meson-baryon energies, while the solid lines denote the eigenenergies obtained from the finite-volume Hamiltonian matrix. The pink shaded area illustrates the uncertainty of the HEFT results obtained by varying the Hamiltonian parameters within the allowed range as described in Sec. \ref{['jia']}. For clarity, we shift the higher (lower) lattice QCD datum to the left (right) a little while keeping middle datum unchanged on each pion mass.
• Figure 3: The dependence of the Hamiltonian eigenvector components on the pion mass for the first six eigenstates under the hypothesis with a bare baryon $\Sigma_0$ .
• Figure 4: Finite-volume energy spectrum with the bare baryon $\Sigma_0$ compared to the lattice QCD data with Ensemble B ($L = 2.186\,\text{fm}$) from the BGR group Engel:2013ig. The pink shaded area illustrates the uncertainty of the HEFT results obtained by varying the Hamiltonian parameters within the allowed range as described in Sec. \ref{['jia']}. See Fig. \ref{['withoutbaresp']} for other captions.
• Figure 5: Finite-volume energy spectrum with the bare baryon $\Sigma_0$ compared to the lattice QCD data with Ensemble C ($L = 2.237\,\text{fm}$) from the BGR group Engel:2013ig. The pink shaded area illustrates the uncertainty of the HEFT results obtained by varying the Hamiltonian parameters within the allowed range as described in Sec. \ref{['jia']}. See Fig. \ref{['withoutbaresp']} for other captions.