SU(3)-flavor breaking as a structural probe of hidden-charm-strange $0^{--}$ tetraquarks in a color-octet basis

Abstract

We study hidden-charm-strange tetraquark candidates with the exotic quantum number $J^{PC}=0^{--}$ to test whether SU(3)-flavor breaking acts as a universal mass shift or as a structural probe of a fixed color-octet current basis. Using $[\bar c c]_{8_c}\otimes[\bar s s]_{8_c}$-type and $[\bar c s]_{8_c}\otimes[\bar s c]_{8_c}$-type color-octet currents within QCD sum rules, we keep the strange-quark mass and strange condensates explicitly in the operator product expansion through dimension eight so that the strange-sector response can be traced at fixed color and Dirac structure. The hidden-charm-strange system is treated as the primary phenomenological target, while the hidden-bottom-strange sector serves as a stability benchmark. The strange-sector spectrum remains ordered, but the induced charm-sector shifts are grouped rather than uniform, with relatively small shifts for the $[\bar c c]_{8_c}\otimes[\bar s s]_{8_c}$ configurations and substantially larger shifts for the $[\bar c s]_{8_c}\otimes[\bar s c]_{8_c}$ ones. The $[\bar c s]_{8_c}\otimes[\bar s c]_{8_c}$ solutions are shifted toward the $D_s^*\bar D_{s1}$ threshold region, with one overlapping this region within uncertainties and another showing the largest positive SU(3)-breaking shift. Taken together, these features indicate that hidden strangeness can serve as a useful discriminator of internal current structure in the exotic $0^{--}$ sector.