Recent Progress in Ab-Initio Nuclear Theory for Precision Physics Searches in Muonic Atoms and Superallowed $β$ Decays

Abstract

Precision tests of the Standard Model at low energy are increasingly limited by nuclear-structure theory rather than by experiment. We review two such cases: the two-photon-exchange correction to the Lamb shift in muonic atoms, and the \texorpdfstring{$γW$}{gamma-W} box radiative correction to superallowed \texorpdfstring{$β$}{beta} decays. Although they probe different physics, both are governed by the same generalized hadronic tensor, so that the chiral effective field theory Hamiltonians and currents, Lanczos-based response methods, and Bayesian uncertainty quantification developed for one carry over directly to the other. We summarize recent ab initio progress in light nuclei and its impact on nuclear charge radii, on the helium isotope-shift puzzle, and on the extraction of \texorpdfstring{$V_{ud}$}{Vud} for the top-row CKM unitarity test, and state a future outlook.