# Particle collisions (4 momentum)

1. May 18, 2010

### Minus1

A particle accelerator collides 5000 GeV muon+ with 5000 GeV muon- particles, producing two massive particles in the final state, one with a mass of 800 GeV and another particle with unknown mass m.

a) write down the initial and final state momentum vectors

b) by using the conservation of 4-momentum, compute the maximum value m could be

c) without calculation explain why this maximum mass is reduced if a 10,000 GeV muon- is collided with a stationary muon+

I tried to attempt the question but i was put off by the way they have written mass, usually i see it as ...GeV/c^2 but there was no c^2, and secondly im not told about the final states or the velocities so basically im completely lost,

Thanks
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 18, 2010

### nickjer

Also, when the mass is given in units of eV, it is implied you divide the c^2 out.

First write out the 4-momentum final vector so we can see if you are doing it right. You can solve for the unknowns later.

EDIT: I am confused about the mass of your first product. I am assuming it is rest mass?

Last edited: May 18, 2010
3. May 18, 2010

### Minus1

this is what i would write as the 4 vectors, in the lab frame they would be,
P(1)=(5000GeV/c,5000GeV/c^2.v,0,0) =>first muon+
P(2)=(5000GeV/c,-5000GeV/c^2.v,0,0)=> 2nd muon-

i assumed the initial speeds were the same as they had identical energies
therefore P1+P2= (10000GeV/c,0,0,0)

and as for the product i havent been told whether it is rest mass or not, this is the full question

it doesnt feel right though, but to be honest anything i do doesnt feel right and ive got my exam in two days

4. May 18, 2010

### nickjer

Your momentum values are wrong. But since you know the muons are heading towards each other, then you have

$$\vec{p}_1+\vec{p}_2 = 0$$

So you get the same total initial 4 momentum as you wrote.

5. May 18, 2010

### Minus1

could you please tell me what im doing wrong, its really getting to me, i thought the momentum was (gamma).m.v, gamma.m=5000Gev and v is just the velocity, what am i doing wrong?

6. May 18, 2010

### nickjer

Alright, you can do it that way. It just looks odd with a 'v' term multiplied to a known value. Since you don't know what 'v' is. You could have just called the momentum 'p' since you don't know what that is either, and it is more simplified:

p_1 = (5000 GeV/c, p, 0, 0)
p_2 = (5000 GeV/c, -p, 0, 0)

It looks cleaner this way.

7. May 18, 2010

### nickjer

For the final total 4 momentum, I suggest using E1, E2, p1, p2 to start off before you start plugging in equations.

An equation that can be helpful is:

$$E^2 = p^2 c^2 + m^2 c^4$$