Suppose you have a massive spin one pseudo-vector particle. Is it allowed to decay into an electron-positron pair? I'm thinking it might be disallowed because of parity conservation.
If it is allowed, is a massive vector particle allowed to decay to a positron-electron pair ?
Or are they both allowed ?
Suppose you have a massive spin one pseudo-vector particle. Is it allowed to decay into an electron-positron pair?
Suppose you have fermion $\psi$ and pseudovector massive boson $G_{\mu}$. Phenomenologically you may write down two dimension-4 operators which mediate its decay on ff-pair: $$ L_{\text{decay}} = c_{1}G_{\mu}J^{\mu} + c_{2}G_{\mu}J_{5}^{\mu}, $$ where $$ J_{5}^{\mu} = \bar{\psi}\gamma^{\mu}\gamma_{5}\psi , \quad J_{\mu} = \bar{\psi}\gamma_{\mu}\psi $$ The first operator violates parity symmetry, while the second saves it. So there is no problem into pseudovector decay on ff pair even if you require that $L_{\text{decay}}$ has to be parity symmetrical (i.e., $c_{1} = 0$).
So the decay is, of course, possible.
As for the vector boson decay, then you even have examples from the Standard model - $Z-$boson decay on electron-positron pair, which is mediated by operators $$ L_{\text{decay}} = Z^{\mu}g^{e}_{L}\bar{e}_{L}\gamma_{\mu}e_{L} + Z^{\mu}g_{R}^{e}\bar{e}_{R}\gamma_{\mu}e_{R} $$
