# Vacuum polarization and initial state radiation correction for the cross section

I saw that the experimental Born cross section measured for (e+e- -> Hadrons) for positron-electron particle physics experiments such as the (BESIII or BaBar experiments) is corrected by initial state radiation and vacuum polarization factors. The cross section is given by: $$\sigma^B=\frac{N^\text{obs}}{\mathcal{L}_\text{int}(1+\delta^r)(1+\delta^\upsilon)\varepsilon \mathcal{B}}$$

where $$(1+\delta)$$ stands for the correction factors.

Can anyone give me a simplified explanation on why the cross sections are corrected like this? or maybe provide me an easy to understand (without having a strong background in theory) reference?

• Are you asking why there is such a thing as radiative corrections? Or why it would have this form? Commented Jan 3, 2021 at 8:11
• @kaylimekay I am asking why there is radiative correction to the cross section? what would be the difference if it's not corrected ? would the observed cross section (without the corrections) considered to be wrong ? Commented Jan 3, 2021 at 8:20

The other issue that requires approximation is that if we want to measure the production of, say, a certain B meson at an experiment, we can never force the scattering process to produce only that B meson and nothing else. In general, when we detect a B meson there will also be any number of other particles that were also produced in the same interaction. So the total cross section for B meson production is the sum of $$\sigma_B + \sigma_{B, X} + \sigma_{B, X, Y}+\dots$$ where $$X,Y,\dots$$ are anything else. These other things could be initial or final state radiation (extra gauge bosons coming off the initial or final particles), other baryons from the hard scattering, etc. In practice, it's only feasible to compute the cross section including up to some finite number of extra particles. Including these extra particles is again a correction to the no-extra-particle approximation that corrects our calculation to be closer to the true total cross section that includes all possible additions.