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

We construct a linear <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>3</a:mn> <a:msub> <a:mo stretchy="false">)</a:mo> <a:mi>L</a:mi> </a:msub> <a:mo>×</a:mo> <a:mi>S</a:mi> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>3</a:mn> <a:msub> <a:mo stretchy="false">)</a:mo> <a:mi>R</a:mi> </a:msub> </a:math> parity doublet model for octet baryons. Our model employs the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mo stretchy="false">(</g:mo> <g:mn>3</g:mn> <g:mo>,</g:mo> <g:mover accent="true"> <g:mn>3</g:mn> <g:mo stretchy="false">¯</g:mo> </g:mover> <g:mo stretchy="false">)</g:mo> <g:mo>+</g:mo> <g:mo stretchy="false">(</g:mo> <g:mover accent="true"> <g:mn>3</g:mn> <g:mo stretchy="false">¯</g:mo> </g:mover> <g:mo>,</g:mo> <g:mn>3</g:mn> <g:mo stretchy="false">)</g:mo> </g:math> and <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mo stretchy="false">(</q:mo> <q:mn>3</q:mn> <q:mo>,</q:mo> <q:mn>6</q:mn> <q:mo stretchy="false">)</q:mo> <q:mo>+</q:mo> <q:mo stretchy="false">(</q:mo> <q:mn>6</q:mn> <q:mo>,</q:mo> <q:mn>3</q:mn> <q:mo stretchy="false">)</q:mo> </q:math> chiral representations while excluding the <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mo stretchy="false">(</w:mo> <w:mn>8</w:mn> <w:mo>,</w:mo> <w:mn>1</w:mn> <w:mo stretchy="false">)</w:mo> <w:mo>+</w:mo> <w:mo stretchy="false">(</w:mo> <w:mn>1</w:mn> <w:mo>,</w:mo> <w:mn>8</w:mn> <w:mo stretchy="false">)</w:mo> </w:math> representation. Through systematic analysis, we demonstrate that the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:mo stretchy="false">(</cb:mo> <cb:mn>3</cb:mn> <cb:mo>,</cb:mo> <cb:mn>6</cb:mn> <cb:mo stretchy="false">)</cb:mo> <cb:mo>+</cb:mo> <cb:mo stretchy="false">(</cb:mo> <cb:mn>6</cb:mn> <cb:mo>,</cb:mo> <cb:mn>3</cb:mn> <cb:mo stretchy="false">)</cb:mo> </cb:math> representation containing symmetric “bad” diquarks, despite being energetically disfavored, is essential for reproducing the correct baryon mass hierarchy—particularly the <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"> <ib:mi mathvariant="normal">Σ</ib:mi> <ib:mtext>−</ib:mtext> <ib:mi mathvariant="normal">Ξ</ib:mi> </ib:math> 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 <mb:math xmlns:mb="http://www.w3.org/1998/Math/MathML" display="inline"> <mb:mi>S</mb:mi> <mb:mi>U</mb:mi> <mb:mo stretchy="false">(</mb:mo> <mb:mn>3</mb:mn> <mb:mo stretchy="false">)</mb:mo> </mb:math> 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 <qb:math xmlns:qb="http://www.w3.org/1998/Math/MathML" display="inline"> <qb:mi mathvariant="normal">Ξ</qb:mi> </qb:math> sector, we identify <tb:math xmlns:tb="http://www.w3.org/1998/Math/MathML" display="inline"> <tb:mi mathvariant="normal">Ξ</tb:mi> <tb:mo stretchy="false">(</tb:mo> <tb:mn>1950</tb:mn> <tb:mo stretchy="false">)</tb:mo> </tb:math> as the first positive-parity excitation. The analysis reveals that ground states are dominated by the <yb:math xmlns:yb="http://www.w3.org/1998/Math/MathML" display="inline"> <yb:mo stretchy="false">(</yb:mo> <yb:mn>3</yb:mn> <yb:mo>,</yb:mo> <yb:mover accent="true"> <yb:mn>3</yb:mn> <yb:mo stretchy="false">¯</yb:mo> </yb:mover> <yb:mo stretchy="false">)</yb:mo> <yb:mo>+</yb:mo> <yb:mo stretchy="false">(</yb:mo> <yb:mover accent="true"> <yb:mn>3</yb:mn> <yb:mo stretchy="false">¯</yb:mo> </yb:mover> <yb:mo>,</yb:mo> <yb:mn>3</yb:mn> <yb:mo stretchy="false">)</yb:mo> </yb:math> representation, consistent with the preference for “good” diquark configurations, while the <ic:math xmlns:ic="http://www.w3.org/1998/Math/MathML" display="inline"> <ic:mo stretchy="false">(</ic:mo> <ic:mn>3</ic:mn> <ic:mo>,</ic:mo> <ic:mn>6</ic:mn> <ic:mo stretchy="false">)</ic:mo> <ic:mo>+</ic:mo> <ic:mo stretchy="false">(</ic:mo> <ic:mn>6</ic:mn> <ic:mo>,</ic:mo> <ic:mn>3</ic:mn> <ic:mo stretchy="false">)</ic:mo> </ic:math> contribution remains crucial for the mass spectrum.