Why Does the Top Quark Move More Sluggishly Than the Bottom Quark?

[Air]

The Question:
In their search for the top quark, physicists thought that another particle called the W might decay while stationary into one top and one bottom quark. They predicted “The resulting top quark moves off relatively sluggishly on one side while the lighter bottom quark travels more rapidly in the opposite direction”. Using an appropriate conservation law, explain why the top quark moves off more sluggishly than the bottom quark.


My Answer:
Momentum is conserved in all direction. The total momentum is zero. $p_t >> p_b \implies v_t << v_b$. Greater mass means slower speed hence the top quark was significantly slower that bottom quark to balance momentum.


My Problem:
The answer that I have given is correct according to the mark scheme and I would gain full marks. However, I want to know more about the theory in greater clarity hence didn't post this in homework help as the question is answered. I want a detailed explanation which would make my answer sound more powerful and convincing.

 

[humanino]

The total momentum is zero. $p_t >> p_b$

Hold on, there is something odd here. I guess you are mentionning an electron-positron collider if the total momentum is zero (in the initial state). But in the final state, the total momentum would be $p_b+p_t\neq 0$ according to your condition.

 

[daschaich]

Your answer (with "$$m_t \gg m_b$$" rather than "$$p_t \gg p_b$$", of course) is clearly what the question is driving at -- it really is that simple, all the power comes from momentum conservation. The whole weak interaction that describes just how a $$W$$ boson could decay to two quarks is much more complicated, but still has to obey that fundamental conservation law (typically repackaged as http://en.wikipedia.org/wiki/Lorentz_covariance" for notational simplicity).

If you don't mind a silly answer, you could point out that this particular decay is physically impossible because the top quark ended up being more than twice as heavy as the $$W$$.