Different approaches to calculate the $K^{\pm }\to {\pi }^{\pm }{\pi }^0{e}^{+}{e}^{-}$ decay width

Abstract

The rare $K^{\pm }\to {\pi }^{\pm }{\pi }^0{e}^{+}{e}^{-}$ decay, currently under analysis by the NA48/2 Collaboration, is considered. We have performed two theoretical approaches to calculate the differential decay width -- in the kaon rest frame, where we use Cabibbo-Maksimovicz variables, and in the center-of-mass system of the lepton pair. The latter essentially simplifies the computations. A comparison between the two approaches has been performed. We have also found the dependencies of the differential decay rate as a function of the virtual photon and dipion system masses

Comments: 10 pages,5 figures