First Calculation of Hyperon Axial Couplings from Lattice QCD

TL;DR

This paper addresses the poorly known hyperon axial couplings by performing the first lattice QCD calculation of $g_{\Sigma\Sigma}$ and $g_{\Xi\Xi}$ using 2+1-flavor MILC configurations with domain-wall valence quarks. The authors define axial charges via the zero-momentum limit of the axial form factor and extract them from renormalized three-point functions, achieving precise results: $g_{A,N}=1.18(4)$, $g_{\Sigma\Sigma}=0.450(21)$, and $g_{\Xi\Xi}=-0.277(15)$ at the physical point, with a detailed study of SU(3) breaking. They explore SU(3) breaking via an $x$ expansion and find quadratic behavior best describes the data, revealing about 20% SU(3) breaking at the physical point and receiving constraints on the low-energy constants $D$ and $F$. The work also shows limitations of leading-order SU(3) heavy-baryon chiral perturbation theory for these data, highlighting the need for higher-order terms or lighter pions. Overall, the results provide the first precise lattice QCD predictions for hyperon axial couplings, with controlled systematics, and have important implications for hyperon phenomenology and neutron-star physics.

Abstract

In this work, we report the first lattice calculation of hyperon axial couplings, using the 2+1-flavor MILC configurations and domain-wall fermion valence quarks. Both the $Σ$ and $Ξ$ axial couplings are computed for the first time in lattice QCD. In particular we find that $g_{ΣΣ} = 0.450(21)_{\rm stat}(27)_{\rm syst}$ and $g_{ΞΞ} = -0.277(15)_{\rm stat}(19)_{\rm syst}$.

Figures (2)

• Figure 1: (Top) The SU(3) symmetry breaking measure $\delta_{\rm SU(3)}$. The circles are the measured values at each pion mass, the square is the extrapolated value at the physical point, and the shaded region is the quadratic extrapolation and its error band. (Bottom) $\delta_{\rm SU(3)}/x^2$ plot. Symbols as above, but the band is a constant fit.
• Figure 2: Lattice data (circles) for $g_{A}$, $g_{\Sigma\Sigma}$ and $g_{\Xi\Xi}$ and chiral extrapolation (lines and bands). The square is the extrapolated value at the physical point.