Factorization Method in the Spontaneously Broken Gauge Theories

Abstract

We consider the factorization method in the spontaneously broken gauge theories such as the electroweak theory. Using the of\/f-shell $W$-boson density matrix formalism we demonstrate that the factorization conditions are completely under control. The main point of this paper is the presence of the "interference" or "crossed" terms in $WW$--scattering process which exhibits itself in the dependence on the relative azimuthal angle between two scattering planes. To illustrate our general consideration we use well-known example --- a single Higgs boson production. The origine of the quantitative failure of the $WW$--ef\/fective method, as originally propossed, is given and it is shown how to use it correctly.