Linear realization of SU(3) parity doublet model for octet baryons with bad diquark

TL;DR

This paper develops a linear $SU(3)_L x SU(3)_R$ parity doublet model for the baryon octet, focusing on the representations $(3,\bar{3})+(\bar{3},3)$ and $(3,6)+(6,3)$ while excluding $(8,1)+(1,8)$. It demonstrates that the symmetric bad diquark content in $(3,6)+(6,3)$ is required to reproduce the correct mass hierarchy, particularly the Sigma Xi ordering, and incorporates explicit chiral breaking via bare quark masses to account for $SU(3)$ flavor breaking. The authors show that the ground-state spectrum is dominated by good diquark configurations, yet the bad diquark sector is crucial for the excited-state spectrum, and they achieve good reproduction of ground-state masses with predictions for excited states up to ~2.5 GeV, including a candidate Xi(1950) as a first positive-parity excitation. The numerical analysis ensures GMO compatibility and reveals a substantially reduced axial charge, suggesting the need for higher-order derivative terms or extended relations to reconcile with the experimental axial coupling. Overall, the work provides a predictive, tractable linear framework linking chiral representations, diquark dynamics, and explicit flavor breaking in the baryon octet.

Abstract

We construct a linear $SU(3)_L \times SU(3)_R$ parity doublet model for octet baryons. Our model employs the $(3,\bar{3}) + (\bar{3},3)$ and $(3,6) + (6,3)$ chiral representations while excluding the $(8,1) + (1,8)$ representation. Through systematic analysis, we demonstrate that the $(3,6) + (6,3)$ representation containing symmetric ``bad'' diquarks, despite being energetically disfavored, is essential for reproducing the correct baryon mass hierarchy, particularly the $Σ$$Ξ$ mass ordering. The model incorporates both spontaneous and explicit chiral symmetry breaking, with the latter implemented through bare quark mass terms that properly account for $SU(3)$ flavor breaking effects. Our numerical analysis successfully reproduces the ground-state octet baryon masses and predicts the spectrum of excited states up to 2.5 GeV. For the experimentally challenging $Ξ$ sector, we provide specific predictions for spin-parity assignments: identifying $Ξ(1950)$ as the first positive-parity excitation. The analysis reveals that ground states are dominated by the $(3,\bar{3}) + (\bar{3},3)$ representation, consistent with the preference for ``good'' diquark configurations, while the $(3,6) + (6,3)$ contribution remains crucial for the mass spectrum.

Figures (8)

• Figure 1: Phenomenological mass spectrum for the case with only $(3, \bar{3}) + (\bar{3}, 3)$ representation. In this scenario, there is a single physical state with one parameter $g$, and the mass ordering is $m_{\Sigma} > m_{N} = m_{\Xi} > m_{\Lambda}$.
• Figure 2: Phenomenological mass spectrum for the case with $(3, \bar{3}) + (\bar{3}, 3)$ and (8 , 1) + (1, 8) representation. In this scenario, with parameters $g$ and $h$ fixed, the predicted mass ordering of the ground state baryons is $m_{\Xi} > m_{\Lambda} > m_{N} > m_{\Sigma}$.
• Figure 3: Phenomenological mass spectrum for the case with only (3 , 6) + (6, 3) representation. The predicted mass ordering of the ground state baryons is $m_{\Xi} > m_{\Lambda} > m_{N} > m_{\Sigma}$.
• Figure 4: Numerical results for fitting the octet baryon masses with the combination of chiral invariant mass $( m_0^{(1)}, m_0^{(2)}) = (800, 1000)$ MeV. The red lines show the experimental values with $\delta m_i$ and the black lines show our numerical results for accumulating spectra from all parameter set satisfying $f_{{\rm min}}<1$.
• Figure 5: Parameters determined from fitting the octet baryon masses with chiral invariant mass $( m_0^{(1)}, m_0^{(2)}) = (800, 1000)$ MeV correspond to Fig. \ref{['fig-massspec']}.