Spin-orbit amplitudes for decays with arbitrary spin

Abstract

In this paper, we propose a method to construct the decay amplitudes in the orbital ($L$) and spin ($S$) coupling scheme for particles with arbitrary spins. For the $1\to 2$ decay with only massive particles involved, the angular dependence is completely encoded in the angular momentum part, and the spins of daughter particles are coupled in the rest frame of the mother particle, which contributes only a constant factor. For the sequential decay, the total amplitude is constructed by the two $1\to2$ amplitudes evaluated in the rest frame of their own mother particles, and then they are transformed to the common frame, usually chosen as the laboratory frame, by certain Lorentz transformations. In this way, it is easy to add the amplitudes of possible different decay chains coherently. If massless particles show up in the final states, the polarizations are expressed in helicity basis and the amplitudes are modified correspondingly.