Mechanical properties of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> baryon from gravitational form factors

We present a comprehensive investigation of the mechanical properties of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mi mathvariant="normal">Ω</a:mi><a:mo>−</a:mo></a:msup></a:math> baryon by analyzing its gravitational form factors (GFFs) within the framework of QCD sum rules. These form factors encode rich information about the internal structure of hadrons and offer deep insights into the dynamics that govern their stability. The spin-<d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:mn>3</d:mn><d:mo>/</d:mo><d:mn>2</d:mn></d:mrow></d:math> nature of the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mi mathvariant="normal">Ω</f:mi><f:mo>−</f:mo></f:msup></f:math> baryon manifests in its gravitational form factors as intricate multipole structures, which encapsulate higher-order deformations and demonstrate the influence of intrinsic spin on internal dynamics. We extract the GFFs of the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi mathvariant="normal">Ω</i:mi><i:mo>−</i:mo></i:msup></i:math> baryon and apply their specific multipole combinations, gravitational multipole form factors (GMFFs), to quantify key mechanical observables—including energy density, angular momentum, pressure and shear force distributions, mass and mechanical radii, and D-terms—associated with different multipole orders. Notably, this work provides the first determination of several of these observables, such as the mechanical radii and the quadrupole contributions to the pressure and shear force distributions. Our analysis shows that the quadrupole contributions to the mechanical properties are generally subdominant compared to those from the monopole component. We further investigate the mechanical stability of the <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msup><l:mi mathvariant="normal">Ω</l:mi><l:mo>−</l:mo></l:msup></l:math> through a multipole analysis of its internal force distributions. These results enhance our understanding of the mechanical structure of spin-<o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mn>3</o:mn><o:mo>/</o:mo><o:mn>2</o:mn></o:mrow></o:math> hadrons and provide useful benchmarks for future theoretical and lattice QCD studies.