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Massive spin one pseudovector decay?

Physics Asked by naomig on July 25, 2021

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 ?

One Answer

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 $$ L_{text{decay}} = Z^{mu}g^{e}_{L}bar{e}_{L}gamma_{mu}e_{L} + Z^{mu}g_{R}^{e}bar{e}_{R}gamma_{mu}e_{R} $$

Answered by Name YYY on July 25, 2021

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