Cross section in muon pair production from electron positron annihilat

In summary, the textbook discusses the calculation of the cross section in muon pair production from electron positron annihilation. After some calculations, the differential cross section is found to be (1+cos(theta)^2)alpha^2/(4*s). The total cross section is then calculated by integrating over the angular variables theta and phi, resulting in 4*pi*alpha^2/(3*s). However, the author forgot to include the sine term in the differential angle, which changes the result to 8*pi*alpha^2/(3*s). This mistake is corrected and the correct steps from the differential cross section to the total cross section are clarified.
  • #1
villsen
2
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I have a question regarding the calculation of the cross section in muon pair production from electron positron annihilation.

After some calculations the textbook comes to the conclusion that the differential cross section is approximately equal to:

(1+cos(theta)^2)alpha^2/(4*s)

where alpha is a constant and theta is the angle of the outgoing muons and s is the center of mass energy squared.

The author then proceeds to calculate the total cross section from the differential by integrating over the angular variables theta (from 0 to pi) and phi (from 0 to 2*pi). Since phi is not in the differential cross section it only gives a contribution of 2*pi. left to calculate is the integral over theta. After doing that the result is the total cross section:

4*pi*alpha^2/(3*s)

I just can't seem to get this result and I don't know what I am doing wrong. I want to integrate:

1+cos(theta)^2

giving an indefinite integral:

3*theta/2 + sin(2*theta)/4 + constant

which should give a contribution of 4*pi/3. But from what I can understand this integral should be 8/3. If I try to integrate not on theta but on cos(theta) I get something more like the correct answer but I don't understand why I can't just do the simple integration.

Could someone please make more clear the steps from the differential cross section to the total cross section.

Thank you!
 
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  • #2
Nevermind i figured it out myself. Just forgot the sine in the differential angle:

dΩ=sin(θ)dθdϕ
 

1. What is cross section in muon pair production from electron positron annihilat?

The cross section in muon pair production from electron positron annihilat is a measure of the probability of producing a muon pair (a positively charged muon and a negatively charged muon) from the annihilation of an electron and a positron. It is an important quantity in particle physics as it helps to understand the underlying interactions and processes involved in the production of these particles.

2. How is the cross section in muon pair production from electron positron annihilat measured?

The cross section in muon pair production from electron positron annihilat is typically measured using particle detectors, such as a collider detector, which can detect and track the produced muons. The number of detected muon pairs is then compared to the number of expected muon pairs based on theoretical calculations, allowing for the determination of the cross section.

3. What factors influence the cross section in muon pair production from electron positron annihilat?

Several factors can influence the cross section in muon pair production from electron positron annihilat, including the energy of the electron and positron beams, the angle at which the muon pairs are produced, and the type of interaction involved (e.g. electromagnetic or weak). The cross section can also be affected by the presence of other particles in the collision, such as photons or other hadrons.

4. What is the significance of studying the cross section in muon pair production from electron positron annihilat?

Studying the cross section in muon pair production from electron positron annihilat allows scientists to test and refine theories and models of particle interactions, as well as to search for new particles and phenomena. It also provides important information about the properties and behavior of muons, which are fundamental particles in the Standard Model of particle physics.

5. How does the cross section in muon pair production from electron positron annihilat differ from other types of cross sections?

The cross section in muon pair production from electron positron annihilat is specific to the production of muon pairs and is only applicable to electron-positron collisions. Other types of cross sections, such as those involving protons or other particles, are measured and interpreted differently. Additionally, the cross section can vary depending on the energy and other parameters of the collision, making it a versatile and dynamic quantity in particle physics research.

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