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) ${\Sigma }^{+}(uus)\Rightarrow p(uud)+\gamma$ decay amplitude does not vanish but just transforms into another PV decay amplitude, namely, of the ${\Omega }_{cc}^{+}(ccs)\to {\Xi }_{cc}^{+}(ccd)+\gamma$ 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 ${\Sigma }^{+}\Rightarrow p+\gamma$ 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 ${\Xi }^{-}\Rightarrow {\Sigma }^{-}+\gamma$ decay.

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