Weak Radiative Decays ofKMesons

The possibility of a unified description for several weak radiative decays of $K$ mesons is being investigated. In particular, those processes are considered in which the decay mechanism can be related to the strong (or electromagnetic) $\mathrm{PVV}$ vertex, namely $K^{+}\to e^{+}\nu \gamma$, $K_2^0\to {\pi }^{+}{\pi }^{-}\gamma$, and $K^{+}\to {\pi }^{+}\gamma \gamma$, in addition to the process $K_2^0\to \gamma \gamma$, which was treated before. Vector gauge fields with current mixing and octet breaking in the $\mathrm{PVV}$ vertex are used, as indicated from a phenomenological Lagrangian model fitting the data on strong and radiative meson decays. For the weak nonleptonic interaction we have considered two alternatives, the current-current "simplest" Hamiltonian suggested recently in connection with $K_2^0\to \gamma \gamma$ decay, as well as the current-current octet Hamiltonian in the form introduced by Sakurai, both satisfying the $\Delta S=1\mathrm{}$, $\Delta I=\frac{1}{2}$ rule. The experimental upper limit on $K^{+}\to e^{+}\nu \gamma$ imposes limits on a free parameter of the theory related to the SU(3) symmetry breaking in the $\mathrm{PVV}$ vertex. Within these limits we calculate the width for $K_2^0\to {\pi }^{+}{\pi }^{-}\gamma$, which differs considerably from the SU(3)-symmetric value and is predicted to be close to the present experimental upper limit. In the calculation of $K^{+}\to {\pi }^{+}\gamma \gamma$ we consider a new class of diagrams, which appear because of the use of vector gauge fields in the Lagrangian. These diagrams involving four-leg vertices are shown to give the dominant contribution to the decay. The calculated rate and spectrum differ from those of previous calculations.