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We use supershadow methods to derive new expressions for superconformalblocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze thefour-point function $\langle\mathcal{A}_1 \mathcal{A}_2^\dagger \mathcal{B}_1\mathcal{B}_2^\dagger\rangle$, where $\mathcal{A}_i$ and $\mathcal{B}_i$ arescalar superconformal primary operators with arbitrary dimension and $R$-chargeand the exchanged operator is neutral under $R$-symmetry. Previously studiedsuperconformal blocks for chiral operators and conserved currents are specialcases of our general results.

$\mathcal{N}=1$ Superconformal Blocks for General Scalar Operators