QCD-based charge symmetry breaking interaction and the Okamoto-Nolen-Schiffer anomaly

An approach is proposed to link the charge symmetry breaking (CSB) nuclear interaction and the low-energy constants in quantum chromodynamics (QCD) by matching the CSB effect in nuclear matter. The resulting CSB interaction is applied to study the Okamoto-Nolen-Schiffer anomaly, still lacking a satisfactory microscopic understanding, on the energy differences of mirror nuclei by taking ${}^{17} \mathrm{F}$-${}^{17} \mathrm{O}$, ${}^{15} \mathrm{O}$-${}^{15} \mathrm{N}$, ${}^{41} \mathrm{Sc}$-${}^{41} \mathrm{Ca}$, and ${}^{39} \mathrm{Ca}$-${}^{39} \mathrm{K}$ as typical examples. The magnitude and sign of the QCD-based CSB interactions are found to resolve the anomaly successfully within theoretical uncertainties.