Time invariance of weak interaciton e-p->\nu n

[Phizzzzzik]

The question is rather simple, but I cannot seem to find a solid answer. I need the cross section of the following interaction:
[tex] e^- + p\rightarrow n+ \nu . [/tex]
I need the cross section using the form factors. There are many solutions for the interactions like:
[tex] n+ \nu\rightarrow e^- + p [/tex]
or
[tex] p+\overline{\nu}\rightarrow e^+ + n, [/tex]
but I am not sure which one of them is the right one for my case. I know that the lepton current is not T-invariant and I think that hadronic is, but I am not sure. I would be really thankful for some short explanation.

 

[AndyW]

Thank you for your question regarding the cross section of the interaction e^- + p -> n + v. The cross section for this interaction can be calculated using the form factors, which describe the internal structure of the proton and neutron.

Firstly, it is important to note that the interactions you have listed are all different processes involving different particles. In your case, the interaction involves an electron (e^-) and a proton (p) producing a neutron (n) and a neutrino (v). This is known as a charged current interaction, where the exchange of a W boson mediates the process.

In order to calculate the cross section for this interaction, we need to consider the form factors of the proton and neutron. These are functions that describe the distribution of charge and magnetism within the particles. The form factors are used to account for the fact that the proton and neutron are not point-like objects, but have a finite size and structure.

The form factors are usually expressed in terms of momentum transfer, which is the difference between the initial and final momenta of the particles involved in the interaction. In your case, the momentum transfer is given by the difference between the momenta of the initial electron and proton.

In order to calculate the cross section, we need to integrate over all possible values of momentum transfer, taking into account the form factors of the proton and neutron. This will give us the probability of the interaction occurring at a given momentum transfer.

Now, to address your question about T-invariance, it is true that the lepton current (e^-) is not T-invariant, while the hadronic current (p, n) is. However, in this particular interaction, we are only concerned with the hadronic current, as it is the proton and neutron that are involved in the form factors.

In conclusion, to calculate the cross section for the interaction e^- + p -> n + v, we need to integrate over all possible values of momentum transfer, taking into account the form factors of the proton and neutron. This will give us the cross section for this specific process. I hope this explanation helps to clarify the concept of form factors and their role in calculating cross sections.