Unraveling weak radiative hyperon decays with broken flavor symmetry

Abstract

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 ${\chi }^2/d.o.f.=0.98$ 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.

6 pages, 3 tables