Unraveling weak radiative hyperon decays with broken flavor symmetry

We present a broken $SU(3)$ flavor analysis of weak radiative decays of spin-1/2 hyperons, incorporating current-current and electromagnetic-penguin contributions as well as charge- and mass-insertion effects. Six independent reduced amplitudes describe all decay channels, while a minimal relation between the parity-conserving and parity-violating form factors reduces to eight free parameters. A global fit to the ten available observables yields $\chi^2/\mathrm{d.o.f.}=0.98$ and accommodates the large negative asymmetry in $\Sigma^+\to p\gamma$. The resulting nonzero effective form factor $g_{b_8}$ provides a possible flavor-symmetry realization of the parity-violating amplitude while remaining compatible with Hara's theorem, which constrains the current-current contribution in the exact symmetry limit. Our analysis favors a sizable negative value of $\alpha_\gamma(\Xi^- \to \Sigma^- \gamma)$, which differs from the current experimental result by approximately $1.3\sigma$. Future precision measurements of this observable will provide a decisive test of this prediction.