Hara Theorem, GIM model, and Asymmetry in Weak Radiative Hyperon Decays

Abstract

It is shown that in the framework of GIM model,the parity-violating (PV) $Σ^{+}(uus) \Rightarrow p(uud) + γ$ decay amplitude does not vanish but just transforms into another PV decay amplitude, namely, of the $Ω^{+}_{cc}(ccs)\to Ξ^{+}_{cc}(ccd)+γ$ decay. The known result is used that the relevant part of the CP-invariant effective current$\times$ current Hamiltonian changes sign under simultaneous quark changes $d\leftrightarrow s$ and $u\leftrightarrow c$. So, asymmetry of $Σ^{+} \Rightarrow p + γ$ decay should not vanish in contrast to the Hara result of the old-fashioned $SU(3)_{f}$ model. At the same time, the zero asymmetry prediction persists for the $ Ξ^{-} \Rightarrow Σ^{-} + γ$ decay.