Neutrino Electron Scattering In The Standard Model Approach

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Discussion Overview

The discussion centers around the calculation of the invariant amplitude for neutrino-electron scattering within the framework of the Standard Model, specifically addressing the complexities involved in the calculation without approximations. Participants explore various aspects of the calculation, including the use of Fierz Rearrangement and the challenges of manipulating gamma matrices.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant describes their approach to calculating the invariant amplitude, noting the difficulty in computing the interference term due to the arrangement of Lorentz indices in gamma matrices.
  • Another participant points out that perturbation theory is inherently an approximation, suggesting that the initial claim of not considering approximations may need reevaluation.
  • There is a suggestion to use LaTeX for presenting calculations instead of images, which may not be accessible to all participants.
  • Links to images are provided, but there are concerns about accessibility and security regarding private links.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the calculations and the use of approximations, indicating that there is no consensus on the approach or the validity of the initial claims. The discussion remains unresolved regarding the best methods to proceed with the calculations.

Contextual Notes

Participants highlight limitations related to the manipulation of gamma matrices and the potential need for clearer presentation of mathematical expressions. There are also unresolved issues regarding the accessibility of shared resources.

Radwan Parvez
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For a couple of months, I am trying to calculate the invariant amplitude of the Neutrino electron scattering in the standard model (SM) approach where I am not considering any kind of approximation and using the SM propagator for W Boson and Z Boson.
6623792828242533106


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I tried to do as following,
find out the value of |MW|2 , |MZ|2 and 2 MW* MZ and add them. The |MW|2 and the |MZ|2 were lengthy but easy, but the Interference Term 2 MW* MZ I was unable to calculate even after applying Fierz Rearrangement.

Since to apply Fierz Rearrangement one Lorentz index in the gamma matrix should be in the upper position and the same index should be lowered in another gamma matrix.

But, in my case, I had 4 gamma matrix with all the Lorentz index is in the upper position and I could not lower them using Metric Tensor
6623792992601953858
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* What should I do to calculate this invariant amplitude?
* Where can I find out any kind of hints and results of this calculation?
* Is my approach to solving the problem wrong?
* I am new in this Forum, so I don't know the perfect people who can help me. If someone can suggest me who can help, It will be a pleasure.
* Sorry :frown::frown: for my poor way of describing the problem. i tried to insert some images but I just failed.
 
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Radwan Parvez said:
where I am not considering any kind of approximation
Perturbation theory is always an approximation.

You can't directly link to images on your private google account. It would be a serious security flaw if others could access them. You can upload them here via the "upload" button or upload them in a visible place and then link to them.
LaTeX formulas here are even better, then others can copy them and add comments.

Two of the images are accessible via link:
https://plus.google.com/photos/photo/102407147815499061221/6623792828242533106
https://plus.google.com/photos/phot...1/6623792992601953858?authkey=COvZ97axwfjqggE
 

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