Doubly heavy spin-$\frac {3}{2} $ baryons spectrum in the ground and excited states

This study employs QCD sum rules to predict the masses and residues of spin-$\frac {3}{2} $ doubly heavy baryons including two heavy quarks (c and/or b) and one light quark, specifically focusing on $ Ξ_{cc}^*$, $ Ξ_{bc}^*$, $ Ξ_{bb}^*$, $ Ω_{cc}^*$, $ Ω_{bc}^*$ and $ Ω_{bb}^*$. Our study provides results for the ground state ($1S$), first orbital excitation ($1P$), and the first radial excitation ($2S$), within a consistent theoretical framework. In addition to mass spectra, we provide residue calculations as well. The calculated residues are essential for estimating the decay widths and branching ratios of these baryons at different decay channels. Our analysis incorporates nonperturbative QCD effects through operators up to dimension ten, leading to improved precision in the mass and residue calculations. These predictions offer crucial guidance for ongoing and future experimental searches, particularly in light of the current lack of empirical data for the ground and excited states, and provide a basis for comparison with future experimental data.