Reweighting QCD matrix-element and parton-shower calculations

TL;DR

This work develops and validates a comprehensive on-the-fly reweighting framework within Sherpa to efficiently estimate parametric (PDF, $α_s$) and perturbative (scale) uncertainties, extending from fixed-order calculations to parton showers and multijet merging. By explicitly tracing $α_s$ and PDF dependences and employing trial emissions with Sudakov factors, the method yields variational event weights for LO/NLO, shower variations, and merging across multiple jet multiplicities from a single run. Extensive closure tests against dedicated variations demonstrate accurate uncertainty bands for observables like $p_T$ of gauge bosons and thrust, while achieving substantial CPU savings. The resulting framework enables consistent, comprehensive uncertainty studies and is poised for extensions to NNLO+shower accuracy and grid-based uncertainty propagation for PDF fits and $oldsymbol{α_s}$ determinations.

Abstract

We present the implementation and validation of the techniques used to efficiently evaluate parametric and perturbative theoretical uncertainties in matrix-element plus parton-shower simulations within the Sherpa event-generator framework. By tracing the full $α_s$ and PDF dependences, including the parton-shower component, as well as the fixed-order scale uncertainties, we compute variational event weights on-the-fly, thereby greatly reducing the computational costs to obtain theoretical-uncertainty estimates.

Figures (9)

• Figure 1: The gauge-boson and lepton transverse momenta in off-shell production at the LHC with independent variations of $\mu_{F,R}$ (green), $\alpha_\text{s}$ (red) and the PDF (blue). In the right-hand panels, the individual uncertainty bands, calculated via an on-the-fly reweighting, are compared to uncertainty bands from dedicated calculations (yellow). They are found to be equal.
• Figure 2: Uncertainty band for the Thrust event shape in dijet production in $\Pelectron\Ppositron$ annihilation for a variation of $\alpha_\text{s}$. The left panel shows the nominal distribution and the ratio to the central value. The uncertainty band calculated using reweighting (including all emissions, i.e. $n_\text{PS}=\infty$) is compared to the one obtained from dedicated calculations. The comparison is repeated in the three panels on the right for different maximum number of reweighted emission $n_\text{PS}$.
• Figure 3: The same as in Fig. \ref{['fig:nlo-w-pt']}, but for LO + parton-shower (PS) generation. The uncertainty bands are calculated by reweighting the ME and up to $n_\text{PS}$ shower emissions. In the upper four plots, $n_\text{PS}=3$. In the lower plots, $n_\text{PS}$ is varied for comparison. The scale uncertainties do not change with $n_\text{PS}$ and are therefore not repeated.
• Figure 4: The same as in Fig. \ref{['fig:lops-w-pt']}, but for NLO + parton-shower (PS) generation. The uncertainty bands are calculated by reweighting the ME and a maximum number of emissions from the Mc@Nlo ($n_\textsc{NloPs}\xspace$) and the ordinary PS ($n_\text{PS}$). $n_\textsc{NloPs}\xspace$ is constrained to 0 or 1, as the Mc@Nlo prescription only affects the first emission. In the upper four plots we consider $n_\textsc{NloPs}\xspace=1$ and $n_\text{PS}=2$, thus up to three emissions get reweighted. In the lower plots, we consider variations of $n_\textsc{NloPs}\xspace$ and $n_\text{PS}$.
• Figure 5: Possible parton-shower histories of a $qg\to Zgqq^\prime\bar{q}^\prime$ matrix element allowing only QCD splittings (left) and also including electroweak splittings (right).