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We study decays of a spin $1$ boson within the formalism of Hagen-Hurleyequations. Such particle can decay into two spin $\frac{1}{2}$ particles, aWeyl 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 equationwithin 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 astop quark decays from this perspective.

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