SU(3)-Flavor Splittings of Heavy–Light Diquark Masses from QCD Sum Rules

We investigate the mass spectrum of heavy-light diquarks comprising a heavy quark (charm or bottom) and a light quark (up, down, or strange) using QCD Laplace sum rules. Our analysis focuses on the SU(3) flavor symmetry breaking effects, particularly the mass differences between strange and non-strange diquarks. By computing correlation functions up to next-to-leading order in perturbation theory and leading order in the strange quark mass, we isolate the contributions of the strange quark condensate parameter, κ (i.e., the ratio of the strange quark and light quark condensates) to the mass splittings. We find that the mass difference between the heavy-strange [Qs] and heavy-light [Qn] (where n = u or d) diquarks decreases with increasing κ, providing an upper bound on κ beyond which the mass hierarchy reverses. In the typical QCD sum-rule range 0.56 < κ < 0.74, we obtain 55 MeV < M[cs] - M[cn] < 100 MeV and 75 MeV < M[bs] - M[bn] < 150 MeV, with slightly larger splittings for the J^P = 1⁺ channels. These results provide insights into the constituent diquark masses required for modeling tetraquark and pentaquark states.