K 1 0 →γ+γ decay mode

Abstract

The mechanism for the rare radiative decay mode K10→2γ is treated as the virtual disassociation of K10 into a π+π− pair followed by internal annihilation of the pions into photons. Introducing a direct K10-2π interaction and using the techniques of dispersion theory, the branching ratioΓ(K10→2γ)/Γ(K10→π+π−) is expressed in terms of theI=0,s-wave pion-pion scattering phase shifts. With negative and small positive π-π scattering lengths, numerical estimates indicate no appreciable enhancement of the branching ratio from its perturbation-theory value: 0.24·10−5. Branching ratios of the order of 10−4 to 10−3 are obtained for large positive scattering lengths provided that the high-energy behaviour of the phase shifts has a specified character.