Why cannot the $W$ and $Z$ bosons decay into a pair of quarks where one is a top or anti-top quark?

Question

Now I can understand its unlikely to see a $W$ or $Z$ boson decay into a pair of quarks that involve a top or anti-top quark simply because of the amount of energy it would require, but find it well within the realm of a theoretical possibility unbound by practical limitations considering that any particle can have enough velocity to obtain any energy level.

Wikipedia states that the branching ratios can be derived theoretically from coupling constants, so it appears that somehow the $W$ and $Z$ boson energy levels are limited. Im thinking maybe there are some assumptions that are taken to derive the branching ratios that include assuming the energy level of these bosons thereby excluding the top quark from the branching ratios.

Can someone confirm that it is or is not possible for a top or anti-top quark from being involved in a $W$ or $Z$ boson decay by stating what theoretical mechanism allows or prevents this?

Note: It sounds like since the reference frame of the boson and the decay products are the same then the total mass-energy of the products is limited to the rest mass of the Boson.

Answer 1

The top quark mass, $m_\text{top} = 173\,\mathrm{GeV}/c^2$, is much heavier than the masses of either the charged ($m_W = 80\,\mathrm{GeV}/c^2$) or neutral ($m_Z = 91\,\mathrm{GeV}/c^2$) weak boson. So a weak boson in its rest frame does not have enough energy to decay to a final state involving top quarks.

Any particle can have enough velocity to obtain any energy

Give it any velocity you want. I'll run alongside the weak boson and observe the decay in its rest frame. (I am very fast.) There is not enough energy for the decay to happen in my reference frame, so you don't observe it either.

It appears that somehow the Z and W boson energy levels are limited.

You seem to be thinking that perhaps the $Z$ and $W$ have internal degrees of freedom and can store energy in an excited state. That's a good idea: we see that atoms and nuclei can store energy internally. Even nucleons will vibrate if you hit them hard enough, giving rise the the baryon spectrum. However, the $Z$ and $W$ (along with the quarks and the leptons) are structureless, fundamental particles. So far as we know, they don't have any internal degrees of freedom to excite.