QCD Correction to DIS: Evaluating Trace & Lorentz Invariant Phase Space

In summary, the two Feynman diagrams representing the virtual correction to the DIS process between a quark and photon may appear to give different contributions. However, the trace of the corresponding Dirac matrices is Lorentz invariant, indicating that the two diagrams should give equal contributions to the overall amplitude. Techniques such as Feynman parameterization and loop integrals can be used to explicitly show the equivalence between the two diagrams. In quantum field theory, the overall amplitude is often more important than the individual contributions from each diagram.
  • #1
CAF123
Gold Member
2,948
88
I am considering the following virtual correction to the DIS process between a quark and photon. The process on the left in the attachment is one such QCD correction I can make but the diagram on the right is another (I just changed where the gluon vertices lie). It seems to me that both diagrams should give equal weighting as a correction, but I don't see this come through in the math.

In both cases, I need to evaluate a trace, where in case a) this is equal to $$\text{Tr}((\not p + \not q) \gamma^{\nu} \not p \gamma^{\sigma} (\not p - \not l) \gamma_{\nu} (\not p + \not q + \not l) \gamma_{\sigma})$$ and in case b) it is $$\text{Tr}(\not p \gamma^{\nu} (\not p + \not q) \gamma^{\sigma} (\not q + \not p - \not l) \gamma_{\nu} (\not p - \not l) \gamma_{\sigma})$$ and a lorentz invariant phase space for one final state species premultiplying it which is equal to ##\int d^{(d)} p \delta^{(d)}(p+q-p)## up to some factors. I am just trying to see if first my intuition about these giving same contributions is indeed correct and, if so, how I can see this explicitly - I thought about using the integral over all p to shift the momenta but shifting by such and such an amount did not give agreement.

Thanks for any tips!
 

Attachments

  • QCDcorrection.png
    QCDcorrection.png
    5.1 KB · Views: 407
Physics news on Phys.org
  • #2


Hello, as a scientist, I would like to address your question about the virtual correction to the DIS process between a quark and photon. It is important to note that in quantum field theory, Feynman diagrams represent a perturbative expansion of the amplitude for a given process. In this case, the two diagrams you mentioned are different Feynman diagrams that represent different contributions to the overall amplitude.

In order to determine the overall contribution of these diagrams, we need to evaluate the trace of the corresponding Dirac matrices. This trace represents the sum over all possible combinations of the external particle momenta. In your case, the difference between the two diagrams lies in the rearrangement of the gluon vertices, which results in a different ordering of the external momenta.

It is important to note that the trace of the Dirac matrices is Lorentz invariant, meaning it is independent of the choice of reference frame. Therefore, the two diagrams should indeed give equal contributions to the overall amplitude. However, this does not mean that the individual contributions from each diagram will be the same.

In order to explicitly show the equivalence between the two diagrams, you can use techniques such as Feynman parameterization and loop integrals to simplify the expressions. This will allow you to see the equivalence between the two diagrams more clearly.

I hope this helps to clarify your intuition about the contributions from these two diagrams. Keep in mind that in quantum field theory, it is often the overall amplitude that is important, rather than the individual contributions from each diagram. Thank you for bringing up this interesting topic for discussion.
 

1. What is QCD Correction to DIS?

QCD Correction to DIS (Deep Inelastic Scattering) is a theoretical framework used to study the interactions between quarks and gluons, which are the fundamental building blocks of protons and neutrons. It involves calculating the corrections to the basic equations of DIS in order to understand the underlying physics more accurately.

2. Why is it important to evaluate trace and Lorentz invariant phase space in QCD Correction to DIS?

Evaluating trace and Lorentz invariant phase space is crucial in QCD Correction to DIS because it allows us to accurately calculate the probability of various particle interactions and their corresponding energy and momentum distributions. This is essential in understanding the dynamics of quark-gluon interactions and improving our overall understanding of the strong nuclear force.

3. How is QCD Correction to DIS different from other theoretical frameworks in particle physics?

QCD Correction to DIS is specifically focused on studying the strong nuclear force and its effects on quarks and gluons. It is based on the theory of Quantum Chromodynamics (QCD), which describes the behavior of quarks and gluons. Other theoretical frameworks may focus on different aspects of particle physics, such as weak and electromagnetic forces.

4. What are some applications of QCD Correction to DIS in experimental particle physics?

QCD Correction to DIS has many practical applications in experimental particle physics, such as improving our understanding of hadron structure and interactions, testing the Standard Model of particle physics, and searching for new particles and phenomena beyond the Standard Model. It also plays a crucial role in accurately interpreting data from particle colliders like the Large Hadron Collider (LHC).

5. How do scientists evaluate trace and Lorentz invariant phase space in QCD Correction to DIS?

Scientists use a variety of mathematical techniques and computer simulations to evaluate trace and Lorentz invariant phase space in QCD Correction to DIS. These techniques involve taking into account the complex nature of quark-gluon interactions and their corresponding energy and momentum distributions, and are constantly being refined and improved upon as our understanding of the strong nuclear force grows.

Similar threads

  • High Energy, Nuclear, Particle Physics
2
Replies
38
Views
3K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
961
  • High Energy, Nuclear, Particle Physics
Replies
10
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
2
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
6
Views
2K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
6
Views
3K
  • High Energy, Nuclear, Particle Physics
Replies
4
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
13
Views
2K
Back
Top