Decays of $W$ bosons: possible mixing of spin $0$ and spin $1$ states

Abstract

We study decays of a spin $1$ boson within the formalism of Hagen-Hurley equations. Such particle can decay into two spin $\frac{1}{2}$ particles, a Weyl neutrino and a massive fermion, whose spins can couple to $S=0$ or $S=1$. Since spin $0$ and spin $1$ bosons can be described by the Dirac equation within the same representation of $\gamma ^{\mu }$ matrices mixing of $S=0$ and $S=1$ states is possible. We argue that the Hagen-Hurley equations describe $W$ boson with spin $S\in 0\oplus 1$ space and analyse mixed beta decays as well as top quark decays from this perspective.