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$ψ$(4040) and $Y(4008)$ decay widths in hot and dense strange hadronic matter

In the present investigation, we evaluate the in-medium partial decay widths of exited states $ψ$(4040) and $Y$(4008) decaying to the pairs of non-strange pseudoscalar $D \bar{D}$ mesons, strange pseudoscalar $D_s \bar{D}_s$ mesons, non-strange vector $D^* \bar{D}^*$ meson and pseudoscalar-vector $D \bar{D}^*$ mesons using $^3P_0$ model. The in-medium effects are incorporated through the in-medium masses of daughter mesons (calculated using the chiral SU(3) model and QCD sum rule approach in our previous works). We consider $ψ$(4040) and $Y$(4008) states as 3$^3S_1$ states and observe the in-medium dominance of one state over the other for a given decay mode. The results of the present investigation will prove as one step forward in assigning the correct spectroscopic state to controversial $Y$(4008) state.