[Paper Review] The SysCalc code: A tool to derive theoretical systematic uncertainties

A. Kalogeropoulos, Johan Alwall|arXiv (Cornell University)|Jan 25, 2018

Particle physics theoretical and experimental studiesPhysics and Astronomy6 references49 citations

TL;DR

SysCalc derives weights for theoretical systematic uncertainties (scales, PDFs) from a central MC sample, avoiding extra MC generation and preserving statistical power.

ABSTRACT

Undisputedly, derivation of theoretical systematic uncertainties is an inseparable ingredient of any robust analysis dealing with experimental data. However, it is not uncommon, even for those analyses that use state of the art methods and tools to suffer from insufficient statistics when it comes to the simulated datasets used to estimate systematic uncertainties. This practically limits the power, and sometimes the robustness of the analysis. In this paper, we present SysCalc, a code which is able to derive weights for various important theoretical systematic uncertainties, including those related to the choice of the Parton Distribution Function sets and the various scale choices. SysCalc utilizes the central sample generated events to estimate the related systematic uncertainties, thus, omitting the need for generating dedicated systematics datasets, and with only a minimal added cost in terms of computing resources. In this paper we discuss the working principles of the code accompanied by various validation plots. We also discuss the structure of the code followed by a practical guide for how to use the tool.

Motivation & Objective

• Motivate the need to estimate theoretical systematic uncertainties without generating large dedicated samples.
• Introduce SysCalc as a reusable tool to compute weights for bcF, bcR scales, calpha_s variations, and PDFs.
• Demonstrate that SysCalc preserves the statistical power of the central sample while evaluating systematics.
• Provide a practical guide for installation, configuration, and usage of SysCalc.

Proposed method

• SysCalc processes central LO(MG5_aMC@NLO) events and outputs an XML-based weight file with weights for selected systematics.
• It reweights events via per-variation weights computed from scale and PDF variations (and, if applicable, matching) using event-level information from MadGraph5_aMC@NLO.
• The method includes explicit formulas for bmu_R and bmu_F scale weights, and PDF-weight calculations as ratios of PDFs and a_S terms (Equations 3, 4, 5).
• For matched/merged samples, SysCalc supports additional reweighting factors for ISR/FSR scales (Equations 6, 7).
• Output adheres to the LHEF v3 format, embedding weights in an initrwgt block and per-event rwgt entries.

Experimental results

Research questions

• RQ1 Can SysCalc derive accurate theoretical systematic weights (scales, PDFs) from a single central sample?
• RQ2 Do the SysCalc weights reproduce dedicated systematic samples within statistical fluctuations for processes like pp -> t tbar + xj and pp -> Z + xj?
• RQ3 How does SysCalc perform in matched/merged samples with showering (e.g., MG5_aMC@NLO + Pythia8) and what biases arise?
• RQ4 What practical guidance is needed to install, configure, and run SysCalc effectively?
• RQ5 What are future developments to extend SysCalc to MLM matching/merging scales?

Key findings

• SysCalc yields weights for scales (mu_R, mu_F) and PDFs that agree with dedicated samples within statistical fluctuations for test processes ttbar+0/1j and Z+0/1j.
• PDF variation weights (multiple PDF sets) reproduce dedicated samples within statistical fluctuations for ttbar+0/1j and Z+0/1j.
• In matching scenarios, SysCalc comparisons show general agreement with small biases due to SCALUP starting scale in parton showers, typically at the few percent level for ISR-related quantities.
• SysCalc outputs weights in LHEF v3, enabling analyses to incorporate theoretical systematics without regenerating large MC samples.
• The paper provides a practical installation and usage guide, including configuration syntax and example outputs.