Toward ab-initio nuclear theory calculations of δC

We propose a theory framework to study the isospin-symmetry breaking correction δC in superallowed nuclear β decays, crucial for the precise determination of |Vud|. Based on a general assumptions of the isovector dominance in isospin-symmetry breaking interactions, we construct a set of functions F_Tz which involve nuclear matrix elements of isovector monopole operators and the nuclear Green's function. Via the functions F_Tz, a connection of δC to measurable electroweak nuclear radii is established, providing an experimental gauge of the theory accuracy of δC. We outline a strategy to perform ab initio calculations of F_Tz based on the Lanczos algorithm, and discuss its similarity with other nuclear-structure-dependent inputs in nuclear β decays.