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The Gell-Mann -- Okubo mass relation among baryons from fully-dynamical mixed-action lattice QCD

Silas R. Beane, Kostas Orginos, Martin J. Savage

TL;DR

The paper tests the Gell-Mann–Okubo mass relation for the lowest-lying baryon octet using fully-dynamical lattice QCD with a mixed-action setup (domain-wall valence quarks on rooted-staggered MILC configurations) at $b\approx0.125$ fm and four light-quark masses corresponding to $m_\pi\approx290$–$590$ MeV. Deviations from GMO are extracted via correlator ratios $G^{\rm GMO}(t)$ and the fractional violation $\delta_{\rm GMO}$, revealing small violations across all masses and consistency with the experimental value $\delta_{\rm GMO}^{\rm expt}=0.00761\pm0.00007$, as well as with leading-order HB$\chi$PT predictions. The results support the idea that higher-dimensional $SU(3)$ representations are suppressed and align with large-$N_c$ expectations, while providing validation that finite-volume and mixed-action artifacts are under control. This work reinforces GMO as a robust feature of QCD spectroscopy beyond the physical point, with implications for understanding flavor symmetry breaking in the baryon spectrum.

Abstract

We explore the Gell-Mann--Okubo mass relation among the octet baryons using fully-dynamical, mixed-action (domain-wall on rooted-staggered) lattice QCD calculations at a lattice spacing of b ~ 0.125 fm and pion masses of m_pi ~ 290 MeV, 350 MeV, 490 MeV and 590 MeV. Deviations from the Gell-Mann--Okubo mass relation are found to be small at each quark mass.

The Gell-Mann -- Okubo mass relation among baryons from fully-dynamical mixed-action lattice QCD

TL;DR

The paper tests the Gell-Mann–Okubo mass relation for the lowest-lying baryon octet using fully-dynamical lattice QCD with a mixed-action setup (domain-wall valence quarks on rooted-staggered MILC configurations) at fm and four light-quark masses corresponding to – MeV. Deviations from GMO are extracted via correlator ratios and the fractional violation , revealing small violations across all masses and consistency with the experimental value , as well as with leading-order HBPT predictions. The results support the idea that higher-dimensional representations are suppressed and align with large- expectations, while providing validation that finite-volume and mixed-action artifacts are under control. This work reinforces GMO as a robust feature of QCD spectroscopy beyond the physical point, with implications for understanding flavor symmetry breaking in the baryon spectrum.

Abstract

We explore the Gell-Mann--Okubo mass relation among the octet baryons using fully-dynamical, mixed-action (domain-wall on rooted-staggered) lattice QCD calculations at a lattice spacing of b ~ 0.125 fm and pion masses of m_pi ~ 290 MeV, 350 MeV, 490 MeV and 590 MeV. Deviations from the Gell-Mann--Okubo mass relation are found to be small at each quark mass.

Paper Structure

This paper contains 2 sections, 9 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Conclusions

Figures (4)

  • Figure 1: The logarithm of the correlation function $G^{\rm GMO}(t)$ for the four quark masses employed in this work. Each has been off-set vertically for display purposes.
  • Figure 2: Effective mass plots for the correlation function $G^{\rm GMO}(t)$ at the four quark masses employed in this work.
  • Figure 3: Deviations from the Gell-Mann--Okubo mass relation for the lowest-lying baryon octet. The red diamond corresponds to the experimental value. The brown band corresponds to the leading-order one-loop $SU(3)$ HB$\chi$PT prediction, and its expected $\sim 30\%$ uncertainty. The black data points are the results of our fully-dynamical lattice QCD calculation at pion masses of $m_\pi\sim$$293~{\rm MeV}$, $354~{\rm MeV}$, $493~{\rm MeV}$ and $592~{\rm MeV}$.
  • Figure :