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We compute the most general superconformal blocks for scalar operators in$4\mathcal{D}$ $\mathcal{N}=1$ superconformal field theories. Specifically weemploy the supershadow formalism to study the four-point correlator$\langle\Phi_1 \Phi_2 \Phi_3 \Phi_4\rangle$, in which the four scalars $\Phi_i$have arbitrary scaling dimensions and R-charges with the only constraint fromR-symmetry invariance of the four-point function. The exchanged operators canhave arbitrary R-charges. Our results extend previous studies on $4\mathcal{D}$$\mathcal{N}=1$ superconmformal blocks to the most general case, which are theessential ingredient for superconformal bootstrap, especially for bootstrappingmixed correlators of scalars with independent scaling dimensions and R-charges.

The Most General $4\mathcal{D}$ $\mathcal{N}=1$ Superconformal Blocks for Scalar Operators