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

We use supershadow methods to derive new expressions for superconformal blocks in 4d $\mathcal{N}=1$ superconformal field theories. We analyze the four-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}$_i$ are scalar superconformal primary operators with arbitrary dimension and $R$-charge and the exchanged operator is neutral under $R$-symmetry. Previously studied superconformal blocks for chiral operators and conserved currents are special cases of our general results.