The roles of three-nucleon force and continuum coupling in mirror symmetry breaking of oxygen mass region

With both three-nucleon force and continuum coupling included, we have developed a self-consistent {\it ab initio} Gamow shell model within the Gamow Hartree-Fock (GHF) basis obtained by the realistic interaction itself. With the chiral two-nucleon N$^3$LO and three-nucleon N$^2$LO interactions, the Gamow shell model has been applied to the mirror systems of $Z=8$ neutron-rich isotopes and $N=8$ proton-rich isotones, giving good agreements with data in binding energies, dripline positions and excitation spectra. The GHF calculated that the $0d_{3/2}$, $1s_{1/2}$ and $1p_{3/2}$ orbitals are resonances. The resonance states and their interplay with nonresonant continua play a crucial role in the descriptions of nuclei around driplines. Excitation spectra and Thomas-Ehrman shifts observed can be better described when both three-nucleon force and continuum coupling are considered in calculations. The three-nucleon force and continuum coupling produce a combined effect on the Thomas-Ehrman shift, e.g., for the ${1/2}^+$ resonance level of $^{19}$Na. The calculations help the understandings of related nuclear astrophysical processes.