Finding Lorentz Vector? -Physics Noob

In summary, the conversation revolves around finding the Lorentz vector for a collision resulting in two muons. The key measurements needed are "pt" for transverse momentum, "phi" for angle in the x-y plane, "eta" for pseudorapidity, and "mass" for the muon's mass. The formula for energy is also provided and the main difficulty is in finding the z component of momentum. It is clarified that pseudorapidity only gives an angle for the z component and that Pt only contains Px and Py components. A helpful tip is given for calculating P using Pt and η.
  • #1
godtripp
54
0
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?
 
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  • #2
Hi godtripp! :smile:

(have a phi: φ and an eta: η and try using the X2 and X2 icons just above the Reply box :wink:)
godtripp said:
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, Pt is the component transverse to the z-direction, so it's only made up of Px and Py.

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

So you can get P (you don't need Pz) from Pt and η by using η = -logtan(θ/2) … see http://en.wikipedia.org/wiki/Pseudorapidity. :wink:
 
  • #3
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!
 

Related to Finding Lorentz Vector? -Physics Noob

1. What is a Lorentz vector in physics?

A Lorentz vector is a mathematical quantity that describes the position, velocity, and acceleration of an object in special relativity. It takes into account the effects of time dilation and length contraction at high speeds.

2. How do you calculate a Lorentz vector?

The formula for calculating a Lorentz vector is given by V = (γc, γv), where γ is the Lorentz factor, c is the speed of light, and v is the velocity of the object. The Lorentz factor is equal to 1 divided by the square root of 1 minus the squared velocity divided by the speed of light squared.

3. What is the significance of the Lorentz vector in special relativity?

The Lorentz vector is significant in special relativity because it allows us to describe the motion of objects at high speeds, where the laws of classical mechanics no longer apply. It helps us understand the effects of time dilation and length contraction, which are important concepts in Einstein's theory of special relativity.

4. How is the Lorentz vector related to the Lorentz transformation?

The Lorentz vector is closely related to the Lorentz transformation, which is a set of equations that describe how space and time coordinates change between observers in different frames of reference. The Lorentz vector is used to calculate the Lorentz transformation, and it represents the four-dimensional space-time coordinates of an object.

5. What are some real-world applications of the Lorentz vector?

The Lorentz vector has many applications in modern physics, including particle accelerators, nuclear physics, and astrophysics. It is also used in engineering and technology, such as in the design of high-speed trains and spacecraft. Additionally, the Lorentz vector is used in GPS systems to correct for the effects of time dilation on satellite clocks.

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