Sensitivity study of mirror energy differences in positive parity bands of T= 32 A=45 nuclei

Symmetry-conserving density-functional theory (DFT) based no-core-configuration-interaction framework (DFT-NCCI) is an excellent tool for precision calculation of diverse (pseudo-)observables related to isospin symmetry breaking from elusive isospin impurities through isospin corrections to superallowed beta decays to mirror- and triplet-displacement energies and mirror energy differences (MED) along rotational bands. In our recent work [Phys. Rev. C 106, 024327 (2022)2469-998510.1103/PhysRevC.106.024327] we performed axial DFT-NCCI calculations and failed to reproduce a sign of MED in positive-parity (π=+) bands of Sc45/Cr45, T=3/2 mirror pair what casts a shadow on credibility of the model. In this work we aim to perform a thorough analysis of this case with the focus on sensitivity of our predictions with respect to (i) low-energy constants (LECs) of our effective contact charge symmetry breaking force and (ii) nuclear shape. We demonstrate, among other things, that inclusion of triaxial π=+ ground state - which is actually the global π=+ minimum in our unconstrained mean-field calculation - in the DFT-NCCI calculations instead of the axial one used before leads to MED which are consistent with experimental data concerning both their sign as well as magnitude without any need for fine-tuning of the model's LECs.