Momentum in a Head-on collision

[Rayan]

An electron and muon collide head-on, with energies 35 GeV and 50 GeV, the following reaction takes place:

$$ e^- + \mu^+ \rightarrow \nu_e + \nu_{\vec{\mu}} $$If the electron neutrino has energy of 25 GeV, and collides at angle 20 with respect to incoming electron direction, what is the muon neutrinos momentum?

Now I calculated the center of mass frame energy, which happened to be 84 GeV, and I was thinking that I can use energy conservation to determine muon neutrinos energy:

E = 60 GeV

and then since neutrinos mass is very small it can be neglected, so E ~ pc and therefore p~E/c .

But why is the angle between electron and electron neutrino given? Am I missing something here?

 

[mfb]

You calculated the magnitude of the momentum. The momentum is a vector and you should find its direction.

It's interesting that the problem statement gives you more information than required to solve the problem. Just giving the angle or the energy would be sufficient.

 

[Rayan]

You calculated the magnitude of the momentum. The momentum is a vector and you should find its direction.

It's interesting that the problem statement gives you more information than required to solve the problem. Just giving the angle or the energy would be sufficient.

You are totally right! I did calculate the angle and got

$$\theta=10.8^{\circ}$$

with respect to the direction of incoming muon.

But I did indeed use the energy in my calculation! I can't really think of a way to determine the angle without using it?