Pion Spectrum in RadiativeKπ+Decay

The ${\pi }^{+}$ energy spectrum is calculated for the process $K^{+}\to {\pi }^{+}+{\pi }^0+\gamma$, taking into account the processes of internal bremsstrahlung and of direct dipole emission, both $E1\mathrm{}$ and $M1\mathrm{}$ transitions being permitted with parity nonconservation for weak decays. For the ${\pi }^{+}$ energy range 55-75 Mev, which has been examined in some recent investigations, the internal bremsstrahlung process alone leads to an expectation of 1.0 anomalous ${K_{\pi }}^{+}$ decay in the 8653 $K^{+}$ decays examined, quite compatible with the observation of two anomalous ${K_{\pi }}^{+}$ decays in these data. For reasonable values of the dimensionless parameters $A{\left(\frac{\mu }{M}\right)}^4$ and $B{\left(\frac{\mu }{M}\right)}^4$ which specify the dipole transition strengths, (that is, with $A=B=1\mathrm{}$ and $M$ equal to the $K$-particle mass), it appears that their main contribution will arise from the interference of the $E1\mathrm{}$ direct transition with the internal bremsstrahlung term, increasing or decreasing the above estimate by about 20%.