Calculation methods and sources
How to read the figures: definitions, uncertainty methods and the sources behind each example.
Calculation methods
Fixed order: LO and NLO QCD
Leading order provides the lowest-order contribution for the selected process. Next-to-leading order includes virtual and real-emission QCD contributions. Their combination gives an infrared-finite prediction for an appropriate observable. The fixed-order and shower-matching framework is described in Alwall et al., JHEP 07 (2014) 079.
- LO (Born)
- NLO
Matching to a parton shower
Matching combines a fixed-order prediction with successive emissions generated by a parton shower, while accounting for overlap between their descriptions of radiation. The transverse-momentum example compares LO and NLO calculations matched to Pythia 8.
Threshold resummation
Near partonic threshold, logarithmically enhanced soft-radiation terms can become important. The aNNLO+NNLL method combines approximate NNLO QCD with threshold resummation at next-to-next-to-leading logarithmic accuracy. It is distinct from a full NNLO calculation and is applied to compatible processes.
Understanding uncertainties
Scale variation probes residual dependence on renormalisation and factorisation scales. A seven-point envelope is a prescription for variation, not a statistical confidence interval.
PDF uncertainty describes uncertainty associated with the parton-distribution input. Monte Carlo integration uncertainty measures numerical sampling error. The examples identify the components actually displayed.
Examples and data sources
The examples use different calculation setups. The LO and NLO figures show particle pair production at 14 TeV, with the central LO value held fixed in the K-factor denominator. The showered distribution comes from a separate calculation at 100 TeV with a particle mass of 1800 GeV. For the invariant-mass ratio, the recorded Resummino calculation uses 13 TeV and a particle mass of 1000 GeV.
These examples therefore cannot be read as four perturbative orders of the same benchmark. Nor do they provide an accuracy ranking that applies to every process.
Published reference
This mass scan comes from a published study of electroweak pair production at 13 TeV, with threshold resummation included. It covers masses from 200 to 1500 GeV under the assumptions given in the paper. The shaded band shows the published scale variations; PDF uncertainties are listed separately in the data table.
Redrawn from Fiaschi et al., EPJC 83 (2023) 707, Table 6. CC BY 4.0. Central values and scale variations are transcribed from the printed table; layout and typography are adapted.
The reference figure is redrawn from the published numeric table. Its source specifies the full benchmark and the uncertainty prescription.
Data and figures to download
For each observable in the Calculations section, you can inspect the numerical table or download the CSV data and SVG figure. Units appear in the CSV headers; figure labels and source details are included.
Figure presentation and validation
The main panel shows the same recorded values in 3D and 2D. Depth separates the calculation series without adding a physical observable. In 2D, the native HwU figure also includes the relative MC uncertainty and AUX diagnostic panels.
The fixed-order calculation uses CT18NNLO, MG5_aMC 3.5.17 and pair-mass scales. It has not yet been validated for publication. Read the validation scope.
Working with Particael
We are developing Particael for collider simulation and analysis on macOS. The methods you can use depend on the model, process and observable. Sign up for release emails to hear when it becomes available.