How to Calculate Cross Section for Scalar-Neutrino Interaction?

In summary, the conversation is about calculating the cross section for a process involving a massive neutral scalar, a massive Majorana neutrino, and a normal SM neutrino. The answer should be in the form of \frac{g^4}{4 \pi} \frac{m_N^2}{ {(m_\phi^2+m_N^2)}^2 }, where g is the coupling constant. The person asking for help is unsure which part of Eq. (4.5.13) corresponds to the diagram they are trying to calculate and how to deal with the \sigma \cdot k term. They are looking for assistance and have attempted the calculation but are unsure if it is correct.
  • #1
ryanwilk
57
0

Homework Statement



Hi. I'm trying to calculate the cross section for this process:

diag.jpg


where [itex]\phi[/itex] is a massive neutral scalar, N is a massive Majorana neutrino and [itex]\nu[/itex]L is the normal SM neutrino.

Homework Equations



N/A

The Attempt at a Solution


Apparently the answer should be something like: [tex] \frac{g^4}{4 \pi} \frac{m_N^2}{ {(m_\phi^2+m_N^2)}^2 } \>, [/tex]
where g is the coupling constant.

There’s a similar case in http://zippy.physics.niu.edu/spinors/DHMspinors.pdf, page 45. However, I’m not sure which part of Eq. (4.5.13) corresponds to the diagram above and I don’t know how to deal with the [tex] \sigma \cdot k [/tex] term (particularly when calculating the invariant amplitude squared)?

Any help would be appreciated,
Thanks!
 
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  • #2
So, I've attempted to do the calculation. Does this look correct? (there are lots of steps I'm unsure about):

blargleb.jpg
 
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FAQ: How to Calculate Cross Section for Scalar-Neutrino Interaction?

What is cross section calculation?

Cross section calculation is a method used by scientists to determine the probability of a particular reaction or process occurring during an experiment. It involves measuring the number of particles or events that interact with a target material, and calculating the ratio of these interactions to the total number of particles or events present. This gives a measure of the likelihood of the interaction occurring.

Why is cross section calculation important in scientific research?

Cross section calculation is important because it allows scientists to understand and predict the behavior of particles and materials in different environments. It also helps to validate theoretical models and provides a way to compare experimental results with existing data. Additionally, cross section calculation is essential for designing experiments and simulations, as well as for developing new technologies.

What factors influence the accuracy of cross section calculation?

There are several factors that can affect the accuracy of cross section calculation, including the experimental setup, the type and energy of particles involved, and the target material being used. Other factors such as background noise, uncertainties in measurements, and theoretical assumptions can also impact the accuracy of the calculation. It is important for scientists to carefully consider and control these factors in order to obtain reliable results.

How is cross section calculation performed in practice?

In practice, cross section calculation involves collecting data from experiments, analyzing and interpreting the data using statistical methods and theoretical models, and then calculating the cross section value. This process may involve multiple iterations and refinements to improve the accuracy of the calculation. Advanced techniques such as Monte Carlo simulations and Bayesian analysis are often used to aid in the calculation process.

Can cross section calculation be applied to different fields of research?

Yes, cross section calculation is a versatile tool that can be applied to various fields of research, including physics, chemistry, biology, and engineering. It is commonly used in nuclear and particle physics, material science, and radiation therapy, among others. The principles and methods of cross section calculation can also be adapted and applied to different types of interactions, such as chemical reactions, scattering processes, and radiation absorption.

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