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It was recently estimated that the strong isospin-symmetry breaking (ISB)corrections to the Fermi matrix element in free neutron decay could be of theorder $10^{-4}$, one order of magnitude larger than the na\"{\i}ve estimatebased on the Behrends-Sirlin-Ademollo-Gatto theorem. To investigate this claim,we derive a general expression of the leading ISB correction to hadronic Fermimatrix elements, which takes the form of a four-point correlation function inlattice gauge theory and is straightforward to compute from first principles.Our formalism paves the way for the first determination of such correction inthe neutron sector with fully-controlled theory uncertainties.

Quark mass difference effects in hadronic Fermi matrix elements from first principles