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

We construct a linear S U ( 3 ) L × S U ( 3 ) R parity doublet model for octet baryons. Our model employs the ( 3 , 3 ¯ ) + ( 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 S U ( 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 identify Ξ ( 1950 ) as the first positive-parity excitation. The analysis reveals that ground states are dominated by the ( 3 , 3 ¯ ) + ( 3 ¯ , 3 ) representation, consistent with the preference for “good” diquark configurations, while the ( 3 , 6 ) + ( 6 , 3 ) contribution remains crucial for the mass spectrum.