We report on ab initio no-core shell model calculations of the mirror $\mathrm{\Lambda }$ hypernuclei ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}$ and ${}_{\mathrm{\Lambda }}{}^4\mathrm{He}$, using the Bonn-Jülich leading-order chiral effective field theory hyperon-nucleon potentials plus a charge symmetry breaking $\mathrm{\Lambda }-{\mathrm{\Sigma }}^0$ mixing vertex. In addition to reproducing rather well the $0_{\mathrm{g}.\mathrm{s}.}^{+}$ and $1_{\mathrm{exc}}^{+}$ binding energies, these four-body calculations demonstrate for the first time that the observed charge symmetry breaking splitting of mirror levels, reaching hundreds of keV for $0_{\mathrm{g}.\mathrm{s}.}^{+}$, can be reproduced using realistic theoretical interaction models, although with a non-negligible momentum cutoff dependence. Our results are discussed in relation to recent measurements of the ${}_{\mathrm{\Lambda }}{}^4\mathrm{H}(0_{\mathrm{g}.\mathrm{s}.}^{+})$ binding energy at the Mainz Microtron [A. Esser et al. (A1 Collaboration), Phys. Rev. Lett. 114, 232501 (2015)] and the ${}_{\mathrm{\Lambda }}{}^4\mathrm{He}(1_{\mathrm{exc}}^{+})$ excitation energy [T.O. Yamamoto et al. (J-PARC E13 Collaboration), Phys. Rev. Lett. 115, 222501 (2015)].

• Received 7 December 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.122501