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.

Thanks already.

  • $\begingroup$ all figures have a paragraph describing what is displayed. you have not linked that $\endgroup$ – anna v Nov 14 '17 at 17:36
  • $\begingroup$ Apparently not. I took it from hep.ph.ic.ac.uk/~wstirlin/plots/plots.html and there is no detailed explanation what is shown. I searched as well for a publication where this appears but it does not seem to be the case especially since the author wants that one uses "private communication" for referencing his work. $\endgroup$ – Brian Nov 14 '17 at 18:34
  • $\begingroup$ physics is about accuracy, not about guessing what the variables shown display. I can guess that it is about inclusive crossections , thats all. If you go to the link you supplied, there is an archive reference link where the paper with the words exists. arxiv.org/abs/0901.0002 It turns out it is a theoretical/phenomenological paper with fits before even the LHC started. If the author says private communication maybe you should send an email and ask for explanation of symbols. My guess is that σ_b and σ_t are the inclusive crossections for the bottom and top. $\endgroup$ – anna v Nov 15 '17 at 5:09
  • $\begingroup$ I guess that the split in the b crossection must be related to CP violation by neutral bottom quark decays $\endgroup$ – anna v Nov 15 '17 at 5:28
  • $\begingroup$ I know that physics is about accuracy and to be 100% sure one has to ask the author of the plot. I just thought maybe someone in this community came across the problem already earlier and knows. The paper you referenced does not even show the plot. It is from 2009 and describes how they created their PDF set one often usess. The plot I referenced is from 2012 (the Higgs boson has already been found at that time). I agree with you that the sigmas are the pair production cross section (whatever they defined to go in there). $\endgroup$ – Brian Nov 15 '17 at 7:51

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...

  • $\begingroup$ are you saying that the split inthe sigma_b is because of two different data sets entering in the fit? $\endgroup$ – anna v Nov 15 '17 at 17:19
  • $\begingroup$ No, the split represents the uncertainty on the extrapolation. The dashed line is the mean value... $\endgroup$ – Brian Nov 15 '17 at 21:58
  • $\begingroup$ this is the reason why figures without their text are useless. $\endgroup$ – anna v Nov 16 '17 at 5:21
  • $\begingroup$ I totally agree :) $\endgroup$ – Brian Nov 16 '17 at 9:19

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