Global positioning of spin GPS scheme for half-spin massive spinors

Abstract

We present a simple and flexible method of keeping track of the complex phases and spin quantisation axes for half-spin initial- and final-state Weyl spinors in scattering amplitudes of Standard Model high energy physics processes. Both cases of massless and massive spinors are discussed. The method is demonstrated and checked numerically for spin correlations in $\tau \bar\tau$ production and decay. Its application is in our work of combining effects due to multiple photon emission (exponentiation) and spin, embodied in the Monte Carlo event generators for production and decay of unstable fermions such as the $\tau$ lepton, t-quark and hypothetical new heavy particles. In particular, the recurrent problem of combining, for such unstable fermions, one author's calculation of production and another author's calculation of decay, in the presence or absence of multiple photon effects, is there given a practical solution, both for Weyl spinor methods and for the traditional Jacob-Wick helicity methods. Moreover, for massive fermions we give a simple representation of the amplitude for $n(\gamma)$ emission ideally suited for numerical evaluation. No other method is known to us which for arbitrary n has been realized numerically for unstable, massive fermions. Our paper can contribute also, to the discussion on design principles of the phenomenology work for the future accelerators such as LHC or NLC.