Neutrino Electron Scattering In The Standard Model Approach

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SUMMARY

The discussion focuses on calculating the invariant amplitude of neutrino-electron scattering using the Standard Model (SM) approach, specifically addressing the W and Z boson propagators. The user successfully calculated the squared masses |MW|² and |MZ|² but struggled with the interference term 2MW*MZ due to difficulties in applying Fierz Rearrangement with four gamma matrices, all having upper Lorentz indices. The user seeks guidance on resolving this calculation issue and improving their understanding of the topic.

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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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