Mirror-symmetry breaking in $\beta$ decays provides a sensitive probe of weak binding and halo structure in proton-rich nuclei. Motivated by the ongoing debate over a halo in ${}^{22}\mathrm{Al}$, we perform ab initio valence-space in-medium similarity renormalization group (VS-IMSRG) calculations, consistently evolving the Hamiltonian and Gamow-Teller (GT) operators. We compute mirror-energy differences (MEDs), GT transition strengths, the mirror-asymmetry parameter $\delta$, average orbital occupations, and relative proton radii $\delta R_p^2$ for the linked mirror $\beta$ decays ${}^{22}\mathrm{Si}/{}^{22}\mathrm{O}$ $\to$ ${}^{22}\mathrm{Al}/{}^{22}\mathrm{F}$ and ${}^{22}\mathrm{Al}/{}^{22}\mathrm{F}$ $\to$ ${}^{22}\mathrm{Mg}/{}^{22}\mathrm{Ne}$, as well as the benchmark mirror $\beta$ decays ${}^{26}\mathrm{P}/{}^{26}\mathrm{Na}$ $\to$ ${}^{26}\mathrm{Si}/{}^{26}\mathrm{Mg}$. Our VS-IMSRG calculations reproduce key experiments in MEDs, GT strengths, and the mirror-asymmetry parameter $\delta$. Based on MEDs and the mirror-asymmetry parameter $\delta$, our calculations support a halo in the ${}^{26}\mathrm{P}$ ground state and a halolike structure in the ${}^{22}\mathrm{Al}$ $1_1^{+}$ state, whereas the ${}^{22}\mathrm{Al}$ ground state retains good mirror symmetry and does not exhibit a halo. Moreover, we also predict halo features in the ${}^{22}\mathrm{Mg}$ $3_1^{+}$ state. These conclusions are corroborated by the calculated $\delta R_p^2$ values.

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• Beta decay
• Nuclear charge radii
• Nuclear structure & decays
• 20 ≤ A ≤ 38
• Ab initio calculations
• Nuclear many-body theory