Proton-proton collisions cross section plot by Stirling

Question

I am struggling to understand some details of the cross section plot by Stirling that is very often shown when talking about LHC physics. See e.g. here: http://www.hep.ph.ic.ac.uk/~wstirlin/plots/crosssections2012_v5.pdf

I understand very well the discontinuity when switching from $p\bar{p}$ to pp collisions, however, what I don't get is what is meant with $\sigma_{b}$ and $\sigma_{t}$. Is this only referring to pair production, like $gg \rightarrow g \rightarrow b\bar{b}$ ? Or are processes that are experimenatally often called single-top production, like $qq' \rightarrow W \rightarrow tb$ included as well?

Moreover, what I completely miss is the meaning of the two lines splitting for the $\sigma_{b}$ cross section. Is this due to uncertainties as pdfs or different calculation schemes?

I would appreciate any help or kick into the right direction.

Answer 1

This is the inclusive cross section for b-quark pair-production which is something experiments can not really measure very precisely due to limited acceptance. The main way a b-quark pair is produced at the LHC is two initial state gluons fuse to one intermediate one that then splits into a final state b-quark pair. This is due to the fact that the gluon contribution dominates amongst the proton's pdf at very low Bjorken x. However, at very low x, the pdfs have huge uncertainties, e.g. for the pdf set Stirling used in the calculation (it can be seen here: https://mstwpdf.hepforge.org/). If you e.g. consider the case of having a momentum transfer just right to produce two b-Quarks at rest (~9 GeV) - at the Tevatron that corresponded to a larger x value than it does at the LHC. Unfortunately for a given set of PDFs with associated uncertainties one can only use the DGLAP equations to go from one Q^2 to another but not to move from one x to another. Therefore, one would need to include more data at low x in order to constrain these uncertainties, but they only used data mainly collected at HERA and the Tevatron. However, the set is as well outdated and newer PDF sets including LHC data exist (see e.g. https://arxiv.org/abs/1706.00428). This is the reason why the line starts to split at really high sqrt(s) - schematically x ~ M_x/sqrt(s). This is also the reason why you don't see it e.g. for top-quark pair-production because to produce them at rest a much higher x is needed, which in turn has lower uncertainties. In addition to the pdf-related uncertainties, there are as well large contribution coming from the Matrix element itself, however, I do not elaborate much more on that...