Particle collisions (4 momentum)

[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,

Any help at all please!
Thanks
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[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?

[Minus1]

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?

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

[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.

[Minus1]

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.

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?

[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.

[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