  In this work we present the first steps towards benchmarking isospin symmetry
breaking in ab initio nuclear theory for calculations of superallowed Fermi
$\beta$-decay. Using the valence-space in-medium similarity renormalization
group, we calculate b and c coefficients of the isobaric multiplet mass
equation, starting from two different Hamiltonians constructed from chiral
effective field theory. We compare results to experimental measurements for all
T=1 isobaric analogue triplets of relevance to superallowed $\beta$-decay for
masses A=10 to A=74 and find an overall agreement within approximately 250 keV
of experimental data for both b and c coefficients. A greater level of
accuracy, however, is obtained by a phenomenological Skyrme interaction or a
classical charged-sphere estimate. Finally, we show that evolution of the
valence-space operator does not meaningfully improve the quality of the
coefficients with respect to experimental data, which indicates that
higher-order many-body effects are likely not responsible for the observed
discrepancies.
