The massless limit for massive amplitudes and the contraction of the little group

Abstract

This paper is devoted to study the spin-spinor formalism to deal with amplitudes for massive particles. After presenting the basic formulae and conventions, we evaluate in detail the amplitudes for two specific examples, namely the decay W -> l ν_l and the reaction e+ e- -> mu+ mu-. For each case, we display the amplitudes using charts that represent the flow of spin/helicities from the initial to the final particles, which can be used to calculate the total squared amplitude. One can also study the symmetries of the process by comparing different branches along the charts, which are related by those symmetries. Finally, we study the massless limit of the massive theory, employing the concept of Little Group Contraction (LGC), which was used first by Inonu and Wigner to derive the algebra of the Little Group (LG) for the massless case as the limit of the massive one.