Isospin symmetry breaking at high spin in the mirror nuclei $^{35}$Ar and $^{35}$Cl

High-spin states in $^{35}$Ar and $^{35}$Cl have been populated in the $^{24}$Mg($^{16}$O, $\alpha$n) and $^{24}$Mg($^{16}$O, $\alpha$p) reactions, respectively, at a beam energy of 70 MeV. The comparison between the level schemes of these mirror nuclei shows a striking asymmetry in the population yield of high-spin analog states of positive parity, which indicates different intensities of E1 transitions connecting positive- and negative-parity structures in both nuclei. Large energy differences are observed between analog states of negative parity with configurations of dominant pure single-particle character. This results from the comparison with large-scale shell-model calculations in the $s_{1/2}d_{3/2}f_{7/2}p_{3/2}$ valence space. It is shown that important contributions to the energy differences arise from the multipole Coulomb and the relativistic electromagnetic spin-orbit interactions