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We compute the superconformal partial waves of the four-point correlator$\langle JJJJ\rangle$, in which the external operator $J$ is the superconformalprimary of the $4D$ $\mathcal{N}=2$ stress-tensor multiplet $\mathcal{J}$. Wedevelop the superembedding formalism for the superconformal field theories(SCFTs) with extended supersymmetry. In $\mathcal{N}=2$ SCFTs, the three-pointfunctions $\langle \mathcal{J}\mathcal{J}\mathcal{O}\rangle$ with generalmultiplet $\mathcal{O}$ contain two independent nilpotent superconformalinvariants and new superconformal tensor structures, which can be nicelyconstructed from variables in superembedding space, and the three-pointfunctions can be solved in compact forms. We compute the superconformal partialwaves corresponding to the exchange of long multiplets using supershadowapproach. The results are consistent with the non-trivial constraints bydecomposing the $\mathcal{N}=2$ superconformal blocks into $\mathcal{N}=1$superconformal blocks. Our results provide the necessary ingredient to studythe fascinating $4D$ $\mathcal{N}=2$ SCFTs using conformal bootstrap.

Superconformal Partial Waves for Stress-tensor Multiplet Correlator in $4D$ $\mathcal{N}=2$ SCFTs