Isospin Symmetry Breaking in the IMSRG and CKM Unitarity Tests

Unitarity of the quark mixing Cabibbo-Kobayashi-Maskawa (CKM) matrix provides one of the stringest tests of the Standard Model of particle physics, with violations of unitarity signaling physics beyond the Standard Model. One way to test CKM unitarity is through nuclear beta decay with so-called superallowed $0^+ o 0^+$ Fermi beta decays. Measurements of these transitions have become precise enough that the main source of uncertainty in calculations of elements of the CKM matrix, such as $V_{ud}$, stems from theoretical corrections. One such contributing correction is encoded in the term $delta_c$ which denotes corrections due to isospin symmetry breaking which are dependent on nuclear structure. Quantifying $delta_c$ can be done using nuclear structure calculations and ab initio nuclear many-body methods such as the In-Medium Renormalisation Group (IMSRG) method. We investigate and report on possible sources of error and uncertainty induced by basis truncation involving IMSRG methods and the nuclear shell model.