QCD sum rule predictions on gluonic tetraquark states with JPC=0⁺⁻,0⁻⁻ and 1± ±

In this work, we present a systematic calculation of the mass spectrum for tetraquark hybrid states, focusing on the 8[cc̄]⊗ 8[G]⊗ 8[cc̄] 8 [ c c ¯ ] ⊗ 8 [ G ] ⊗ 8 [ c c ¯ ] color configuration, within the framework of QCD sum rules. As an extension of our previous work on 0⁺⁺ 0 + + and 0⁻⁺ 0 - + states, we now construct 18 distinct interpolating currents with JPC = 0⁺⁻ J PC = 0 + - , 0⁻⁻ 0 - - , and 1± ± 1 ± ± . Using operator product expansion (OPE) techniques and including nonperturbative contributions up to dimension six, we obtain key results: for the 0⁺⁻ 0 + - , 1⁻⁻ 1 - - , and 1⁻⁺ 1 - + states, the predicted masses lie in the range of $$7.2-7.3$$ 7.2 - 7.3 GeV, while the 1⁺⁻ 1 + -