So-called radiative corrections

[humanino]

Hi all,

is anybody familiar with (QED for simplicity) radiative corrections for absolute cross section measurements in lepton (electron) DIS, or SIDIS, or exclusive reactions ? I'd be glad if someone can brainstorm even on elastic cross section. I think I understand they are fairly different, but I'm unsure about the interpretations of the respective contributions of real and virtual corrections. UV divergencies cancel each other, but how about infrared ones ? Is it correct to say that we publish a "classical" cross section with Planck constant's going to zero, which is strictly zero at the quantum level ?

Thanks in advance for sharing your thoughts.

 

[Bob_for_short]

Thanks in advance for sharing your thoughts.

Dear Humanino,

As soon as you invite to share thoughts, I can do it as I see it.

If we speak of QED, we have charges and photons in the initial and final states.
According to the QED's equations, charges and the quantized EMF are permanently coupled.
The calculation difficulties (UV and IR divergences) arise just because this coupling is strong rather than weak. Any charge scattering is accompanied with radiation so no elastic events are possible. It means the exact elastic cross section (or amplitude) is identically equal to zero. Now, as soon as in the zeroth-order the elastic amplitude is not equal to zero, the remaining perturbation series serves just to cancel it.

What is different from zero is the inelastic cross section which is the sum over any final photon state cross sections. It makes sense because experimentally one does not distinguish elastic from inelastic (in photons) cross sections - one observes only final charges whatever photon final states are. So experimentally it is the inelastic cross section which is usually measured. The most famous example is the Rutherford cross section. Rutherford could not observe the final target atom states but hey were excited ones. You can find details of this physics in my publication "Atom as a "dressed" nucleus" in arXiv or at the Central European Journal of Physics site. You will see that any particular excited (inelastic) cross section is quite particular - it depends on h_bar, but their sum is reduced to the elastic cross section from a point-like target (Rutherford cross section). There and in "Reformulation instead of Renormalizations" by Vladimir Kalitvianski you can find my thoughts about how it could be described naturally and without divergences.

Bob_for_short.

 

[sir-pinski]

Radiative corrections in quantum electrodynamics (QED) refer to the corrections that need to be applied to the measured cross section in order to account for the effects of virtual and real photon emission and absorption. These corrections are necessary in order to obtain accurate measurements of the cross section, as the presence of virtual and real photons can significantly affect the observed results.

In the context of lepton DIS, SIDIS, or exclusive reactions, radiative corrections are particularly important as they play a crucial role in understanding the underlying physics of these processes. The contributions of real and virtual corrections are different and need to be carefully considered in order to obtain a complete understanding of the measured cross section.

One important aspect of radiative corrections is the cancellation of divergences. In QED, UV divergences cancel each other, but infrared (IR) divergences can still remain. These IR divergences arise due to the emission and absorption of soft photons and need to be properly taken into account in order to obtain meaningful results. This is where the concept of the "classical" cross section with Planck's constant going to zero comes in. This cross section represents the limit of the quantum cross section as the IR divergences are removed. However, it is important to note that this limit is not physically meaningful and cannot be measured, as the quantum effects are still present.

In conclusion, radiative corrections are an essential aspect of cross section measurements in QED and need to be carefully considered in order to obtain accurate results. The contributions of real and virtual corrections, as well as the cancellation of divergences, are important concepts to understand in order to properly interpret the results.