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19 Jul 2024


Recommendation for LHC cross section calculations

The LHC experiments are now producing cross sections from 13 TeV data, after runs at 7 and 8TeV. The experiments need accurate predictions for these cross sections and their uncertainties at NNLO. Crucial to the predictions and their uncertainties are the parton distribution functions (PDFs) obtained from global fits to data from deep-inelastic scattering and increasing amounts of collider data. A number of groups have produced publicly available PDFs using different data sets and analysis frameworks. Given the necessity of having an official recommendation from the PDF4LHC working group available the prescription outlined at the the link below has been adopted. This is an update of two previous prescriptions.

Along with the presentation of the recommendation it is useful to highlight the differences between two cases in which PDFs are used:

  1. Assessment of the PDF uncertainty, such as required when computing the cross section for a process that hasn't been measured yet (e.g. the Higgs), or a process where acceptance corrections are required. This is also the case for measurements where the main requirement is a check as to whether a result is generally consistent with Standard Model expections.
  2. Assessement of the accuracy of one or more PDF sets, such as done when comparing precise data to the theory prediction, e.g. W and Z rapidity distributions or inlusive jet production
Clearly with time and increasing precision some processes will move from case (1) to case (2).

For the latter, it is clearly better to compare to predictions using individual PDFs (and their uncertainty bands). Such cross sections have the potential, for example, to provide information useful for modification and improvement of those PDFs, and also to discrimate between them. For the former, the need to provide a reliable estimate of the true uncertainty must take into account possible differences between the central values of predictions using different PDFs. From the results of benchmark studies it is clear that this uncertainty will generally be larger than that from any single PDF set, but it should not lose all connection to the individual PDF uncertainties (which would happen for some processes if the full spread of all PDFs were used), so some compromise is proposed.

The wish for a definite recommendation followed directly from the HERALHC workshop conclusions, and has always been one of the main goals of the PDF4LHC group since its creation in 2006, particularly as a wish of the LHC experiments. In order for the recommendation to be acceptable by the experiments, it has to be pragmatic and not unnecessarily complicated. It is also an advantage to try to keep close to the techniques or procedures that are already being used in the experiments up to now. This results in the prescription using presented here. However, it should be very clear that no general judgement is made on whether certain PDFs can or cannot be used; for any given particular analysis, different expert judgements can lead to different choices, maybe even the use of only a single PDF set. Also, the recommendation given evolves as a new level of understanding and development is reached, which follows from the ongoing discussions at the PDF4LHC forum.