Calculation ofK20→π+π−γDecay as a Consistency Test of a Current-Current Quark Model

The $CP$-conserving decay $K_2^0\to {\pi }^{+}{\pi }^{-}\gamma$ 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 $r=\frac{R(K_2^0\to {\pi }^{+}{\pi }^{-}\gamma )}{R(K_2^0\to \mathrm{all}\mathrm{modes})=3.0\mathrm{}\times {10}^{-4\mathrm{}}}$ is below the present experimental upper limits of Thatcher et al. ($r<\mathrm{}4\mathrm{}\times {10}^{-4\mathrm{}}$) and may be compared with the tree-graph estimate $2.6\times {10}^{-4\mathrm{}}<r<\mathrm{}4\mathrm{}\times {10}^{-4\mathrm{}}$ of Moshe and Singer; however, the present model has no adjustable parameters.