Spectra and nonleptonic decays of multiply heavy baryons in a finite-size quark-diquark model

We investigate the mass spectra and two-body nonleptonic weak decays of ground-state doubly and triply heavy baryons in a nonrelativistic quark-diquark model. To account for the finite size of the diquark, we generalize the convoluted quark-diquark interaction to unequal-mass diquarks using mass-weighted constituent coordinates and distinct pairwise spin-spin couplings. The resulting Schr{ö}dinger equations provide the baryon masses and wave functions used consistently in the decay calculation. The predicted masses differ from existing lattice QCD results by less than $1.5\mathrm{\%}$, and our calculated mass of ${\mathrm{\Omega }}_{cc}^{+}$ is consistent with recent LHCb observations. The calculated hyperfine splittings are systematically slightly smaller than the lattice values, indicating a residual uncertainty in the spin-dependent interaction. Within the factorization approximation, we evaluate the $c\to s$ and $b\to c$ transitions with pion or kaon emission. At leading nonrelativistic order, the vector contribution vanishes for the $3\mathrm{/}{2}^{+}\to 1\mathrm{/}{2}^{+}$ transitions, while both vector and axial contributions enter the $3\mathrm{/}{2}^{+}\to 3\mathrm{/}{2}^{+}$ channels. The $b\to c$ spatial overlaps are substantially smaller than their $c\to s$ counterparts. Together with the Cabibbo-Kobayashi-Maskawa hierarchy, this reduces the corresponding $b\to c$ width by approximately two orders of magnitude. In the $3\mathrm{/}{2}^{+}\to 1\mathrm{/}{2}^{+}$ charm transitions, the leading $\mathrm{\mid }\mathit{k}{\mathrm{\mid }}^3$ dependence enhances the suppression of kaon emission. In bottom transitions with a larger energy release, the smaller relative phase-space difference brings the ratios close to the scaling determined by the Cabibbo-Kobayashi-Maskawa elements and meson decay constants. These results provide benchmark estimates for future studies of multiply heavy baryons and quantify the role of recoil dynamics within the finite-size quark-diquark framework.