Realistic calculations for $c$-coefficients of the isobaric mass multiplet equation in $1p0f$ shell nuclei

We present calculations for the $c$-coefficients of the isobaric mass multiplet equation for nuclei from $A=42$ to $A=54$ based on two-body effective interactions derived from three realistic nucleon-nucleon interactions: CD-Bonn, N$^3$LO, and Argonne V18. The two-body effective interactions were derived using G-matrix or V$_{low~k}$ augmented by perturbation theory extended to third order. We demonstrate a clear dependence in the $c$-coefficients on the short-ranged charge-symmetry breaking (CSB) part of the strong interaction, which is required to reproduce their overall behavior as a function of excitation (angular momentum). We find, however, that the CSB component in all three realistic nucleon-nucleon interactions is too large when compared to experiment, and that, furthermore, there is significant disagreement between each of the three interactions. This implies either: 1) a deficiency in our understanding of isospin-symmetry breaking in the nucleon-nucleon interaction, 2) significant isospin-symmetry breaking in the initial three-nucleon interaction, or 3) large contributions to isospin-symmetry breaking in three-nucleon interactions induced by the renormalization procedure.