QFT: differential cross section from center of mass to lab frame

In summary, the conversation discusses the process of computing |M|2 and the differential cross section in the center of mass frame, and the subsequent need to convert to the lab frame for an infinite massive nucleus. The speaker also mentions a general procedure for this conversion, involving the fact that the number of scattered particles passing through a cross section is the same in both frames. However, the speaker has encountered a discrepancy in their results.
  • #1
bnado
3
0
I have the following process: two ingoing particles, a photon hitting a nucleus, and two outgoing particles, the nucleus and a pion. I have computed |M|2 and the differential cross section in the center of mass frame dσ/dΩCM; I now have to go into the lab frame, where the nucleus is initially at rest, and consider the limit of a infinite massive nucleus MN→∞, and compute dσ/dΩlab.

Is there a general procedure to go from the first to the second? I first wrote dσ/dt and then multiplied it for a rather complicated expression that I found on a book to obtain dσ/dΩlab. However, taking the infinite massive nucleus limit, the result I get is not what I'm supposed to.
 
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  • #2
you should involve the fact
(dσ/dΩ')lab dΩ'=(dσ/dΩ)CM dΩ,which exploits the fact that the number of scattered particles passing through a cross section is same in both frames.
 

1. What is QFT and how does it relate to differential cross section?

QFT stands for Quantum Field Theory, which is a theoretical framework used to describe the interactions of particles in the subatomic world. Differential cross section is a measurement used to determine the probability of particles scattering during these interactions. QFT provides the mathematical tools and equations to calculate the differential cross section.

2. What is the center of mass frame and how is it related to the lab frame?

The center of mass frame is a reference frame where the total momentum of a system is equal to zero. In particle interactions, this frame is used to simplify calculations and make predictions about the behavior of particles. The lab frame, on the other hand, is the frame of reference in which the experiment is conducted. The differential cross section is calculated in the center of mass frame and then transformed to the lab frame for comparison to experimental data.

3. How is the differential cross section calculated in QFT?

The differential cross section is calculated using the Feynman diagrams, which represent the possible ways particles can interact in a given process. These diagrams are then used to write out mathematical equations that describe the amplitude of the interaction. The differential cross section is then obtained by taking the square of the amplitude and integrating it over all possible final states.

4. What factors affect the differential cross section in QFT?

The differential cross section is affected by various factors such as the type of particles involved in the interaction, the energy of the particles, and the angle at which they are scattered. It also depends on the nature of the interaction, whether it is a strong, weak, or electromagnetic interaction. Additionally, the differential cross section can be influenced by the presence of other particles or fields in the environment.

5. How is the differential cross section from the center of mass frame transformed to the lab frame?

The transformation from the center of mass frame to the lab frame involves a change in coordinates and momentum. This is done using special relativity equations, which take into account the relative velocities of the particles in the two frames. The transformation is necessary to compare the calculated differential cross section with experimental data, which is usually measured in the lab frame.

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