Neutrino Electron Scattering In The Standard Model Approach

In summary, neutrino electron scattering is an interaction between a neutrino and an electron that results in a change in momentum and energy of the electron. The Standard Model approach is used to predict and study this interaction, and studying it is important for gaining insights into neutrino properties and fundamental interactions. It is measured using large detectors and current and future research directions include improving measurements, studying effects of neutrino properties, and using it to study astrophysical phenomena and develop new technologies.
  • #1
Radwan Parvez
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1
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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  • #3
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
 

1. What is neutrino electron scattering?

Neutrino electron scattering is a type of interaction between a neutrino and an electron where the neutrino exchanges a virtual W boson with the electron, resulting in a change in momentum and energy of the electron.

2. What is the Standard Model approach to studying neutrino electron scattering?

The Standard Model approach is a theoretical framework that describes the fundamental particles and their interactions through three of the four known fundamental forces: electromagnetism, strong nuclear force, and weak nuclear force. It provides a way to predict and study neutrino electron scattering based on the known properties of particles and their interactions.

3. Why is studying neutrino electron scattering important?

Studying neutrino electron scattering can provide valuable insights into the properties and behavior of neutrinos, which are elusive and difficult to detect particles. It can also help us understand the fundamental interactions between particles and contribute to our overall understanding of the universe.

4. How is neutrino electron scattering measured?

Neutrino electron scattering is usually measured using large detectors, such as the Super-Kamiokande or IceCube experiments, which are designed to detect the products of the interaction, such as electrons or photons. These detectors can also provide information about the energy and direction of the incoming neutrino.

5. What are some current and future research directions for studying neutrino electron scattering?

Current and future research in this field includes improving the precision of measurements, studying the effects of neutrino properties such as mass and flavor on the scattering process, and searching for new physics beyond the Standard Model. Other areas of interest include using neutrino electron scattering to study astrophysical phenomena, such as supernovae, and developing new technologies and techniques for detecting and studying neutrinos.

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