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We have computed superconformal partial wave for the mixed correlatorsinvolving $J$, $\phi$ and $\phi^\dagger$, where $J$ is the superconformalprimary of 4D ${\mathcal N} = 2$ multiplet, $\phi$ and $\phi^\dagger$ arechiral and anti-chiral scalars respectively. We have used the super embeddingformalism and compute conformal partial wave corresponding to the exchange oflong multiplet using supershadow approach. This study provides part of theingredients necessary for the study of conformal bootstrap for mixed correlatorin 4D ${\mathcal N} = 2$ superconformal field theories.

Superconformal blocks for stress-tensor and chiral operators for 4D $\mathcal{N}=2$ superconformal field theories