Missing Member of the \(J^{PC} = 2^{--}\) Nonet in Extreme Conditions

The isoscalar member of the axial-tensor family that should take place in the further states of the PDG is still absent. In this study, analyzes are made as to whether one of the X states whose quantum numbers are unknown in this group, is a candidate for the missing resonance under the assignment \( 2^3D_2 \). Moreover, replacing the time evolution operator with the thermal average one, we construct the modified correlator satisfying Thermal QCD sum rules approach. We determine that the hadronic parameters of the considered nonet member are sensitive to the increment of temperature. This knowledge can be helpful to complete the \(J^{PC} = 2^{--}\) light meson nonet and also explore the hot medium behaviors at upcoming heavy-ion collision experiments.