Calculation of K20 → π+π-γ decay as a consistency test of a current--current quark model

The CP-conserving decay K₂⁰→π⁺π⁻γ is studied in a modified fermion-loop model as a consistency test of a current-current quark model. The weak Hamiltonian is phenomenologically constructed from one-baryon octet matrix elements. The predicted branching ratio $r=\frac{R(K_2^0\to {\pi }^{+}{\pi }^{-}\gamma )}{R(K_2^0\to allmodes)=3.0\times {10}^{-4}}$ is below the present experimental upper limits of Thatcher et al. (r<4×10⁻⁴) and may be compared with the tree-graph estimate 2.6×10⁻⁴<r<4×10⁻⁴ of Moshe and Singer; however, the present model has no adjustable parameters.