Neutrino Electron Scattering In The Standard Model Approach

[Radwan Parvez]

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.

I tried to do as following,
find out the value of |M_W|² , |M_Z|² and 2 M_W* M_Z and add them. The |M_W|² and the |M_Z|² were lengthy but easy, but the Interference Term 2 M_W* M_Z 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

* 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 for my poor way of describing the problem. i tried to insert some images but I just failed.

 

[Doc Al]

Links to images are broken. Instead of posting images, use Latex to present your calculations. (See: How to type mathematical equations using LaTeX)

 

[mfb]

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

 

[DrClaude]

Discussion continued in the thread https://www.physicsforums.com/threa...tering-in-the-standard-model-approach.960458/

Thread closed.