Deep inelastic scattering: quention on the Hand convention for the flux.

[Einj]

Hi all. I'm studying deep inelastic cross section in parton model. In particular I'm referring to Halzen-Martin's "Quarks and leptons" section 8.5, but I think this is a quite generale procedure.
In studying the deep inelastic scattering by e- on proton it cuts off the electron part and work only on the virtual photon-proton part.
In doing so it's found out that the flux term is dependent on the photon virtuality by the relation:
$$4\sqrt{{(p_ap_b)}^2-m_a^2m_b^2}=4M\sqrt{K^2-q^2}$$
where K is the photon flux (unknow because of the virtuality), q is the photon quadri-momentum and M is the proton mass.
Now, it chooses the flux factor to satisfy the Hand convention:
$$K=\nu + \frac{q^2}{2M}$$
This choise is made in order to threat the photon as in the real case. But why we have such a freedom in defining the flux factor??

 

[AndyW]

Hello! It's great to see someone studying deep inelastic cross section in the parton model. Your question about the flux factor is a good one, and I'll try my best to explain it.

First, let's go over some background information. The parton model is a theoretical framework used to understand the structure of particles, specifically protons and neutrons. It describes these particles as being made up of smaller constituents called partons, which are quarks and gluons. Deep inelastic scattering is a process in which a high-energy electron is scattered off a proton, probing the internal structure of the proton.

Now, onto the flux factor. In deep inelastic scattering, the electron and proton are treated as point particles, and the interaction between them is mediated by a virtual photon. This virtual photon has a certain virtuality, which is related to its energy and momentum. However, since the photon is virtual, it cannot be directly measured. This is where the flux factor comes in - it is used to relate the virtual photon's virtuality to measurable quantities.

The Hand convention, which you mentioned, is a commonly used choice for the flux factor. It was originally proposed by physicist Richard Hand in the 1960s and has been widely used since then. The reason it is chosen is because it allows us to treat the virtual photon as if it were real, making calculations easier. This is because in the real case, the flux factor would simply be the energy of the photon, but in the virtual case, it is slightly more complicated.

Now, to answer your question about the freedom in defining the flux factor - while the Hand convention is commonly used, it is not the only choice. There are other conventions that can be used, but they may lead to more complicated calculations. The important thing is that the chosen flux factor should be consistent with the theoretical framework being used and should allow for the virtual photon to be treated as if it were real.

I hope this helps to answer your question. Keep up the good work with your studies on deep inelastic scattering!