Finding Lorentz Vector? -Physics Noob

[godtripp]

I was given this as an extra-curricular activity... way over my understanding of physics, sophmore year undergraduate.

But I can use a bit of help.
I'm given data from a collision resulting in 2 muons.

(this is exactly how the text is written to me, if any of these definitions are not exactly correct please note)

For a muon, we measure
"pt", Transverse momentum = sqrt (px^2 + py^2)
"phi", angle in the x-y plane
"eta", pseudorapidity, which is another form of the angle from the z-axis
"mass", the mass of the muon

I need to find the Lorentz vector.

For the energy I figured out
E = sqrt ( mass^2 + momentum^2) where momentum should be the magnitude of the 3vector momentum.

What I'm having trouble with is finding Pz, momentum in the z axis.
Maybe I'm not quite understanding the definition of pseudorapidity?

I'd find Px and Py by
Px=Pt cos(phi) and Py = Pt sin(phi)

But how do I find the z component of momentum?

psuedorapidity only gives me an angle for the z component correct? and am I correct that Ptransverse doesn't contain any z component?

 

[tiny-tim]

Hi godtripp!

(have a phi: φ and an eta: η and try using the X² and X₂ icons just above the Reply box )

But how do I find the z component of momentum?

psuedorapidity only gives me an angle for the z component correct? and am I correct that Ptransverse doesn't contain any z component?

Yes, P_t is the component transverse to the z-direction, so it's only made up of P_x and P_y.

P_t = P.sinθ, where θ is the angle from the z-axis.

So you can get P (you don't need P_z) from P_t and η by using η = -logtan(θ/2) … see http://en.wikipedia.org/wiki/Pseudorapidity.

 

[godtripp]

Thank you so much tim. I was thinking of the angle from psuedorapidity in terms of the Pz vector component and not of the total momentum! Thanks!