Triply heavy baryon spectroscopy revisited

We present a comprehensive study of triply heavy baryons (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi mathvariant="normal">Ω</a:mi></a:mrow><a:mrow><a:mi>c</a:mi><a:mi>c</a:mi><a:mi>c</a:mi></a:mrow></a:msub></a:mrow></a:math>, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi mathvariant="normal">Ω</d:mi><d:mrow><d:mi>b</d:mi><d:mi>b</d:mi><d:mi>b</d:mi></d:mrow></d:msub></d:math>, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi mathvariant="normal">Ω</g:mi><g:mrow><g:mi>b</g:mi><g:mi>c</g:mi><g:mi>c</g:mi></g:mrow></g:msub></g:math>, and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msub><j:mi mathvariant="normal">Ω</j:mi><j:mrow><j:mi>b</j:mi><j:mi>b</j:mi><j:mi>c</j:mi></j:mrow></j:msub></j:math>) within the nonrelativistic quark model, employing the Gaussian expansion method to calculate mass spectra up to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>D</m:mi></m:math>-wave states. Our analysis represents the most complete treatment to date for this model, incorporating full angular momentum mixing effects. While our predictions for low-lying states agree well with lattice quantum chromodynamics (QCD) results, we find systematically lower masses for excited states compared to lattice calculations. Using the obtained wave functions, we estimate radiative decay widths up to <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mn>1</o:mn><o:mi>D</o:mi></o:math> states, revealing significant differences from previous theoretical work. Additionally, we identify and resolve several misconceptions in prior treatments of triply heavy baryon spectroscopy, particularly symmetry constraint and wave function construction in three-quark systems. These results provide crucial information for future experimental searches and theoretical investigations of triply heavy baryon systems.