Event generation with exponential scaling in multiplicity using AmpliCol

TL;DR

The paper tackles the computational bottleneck of generating high-multiplicity LHC events due to QCD amplitude growth. It adopts a two-step LC→FC workflow in AmpliCol, sampling $\sigma_{\rm LC} \simeq \int \sum_i |\mathcal{A}_i|^2 C_{ii} \mathrm{d}\Phi$ and applying a reweight factor $r^{\rm LC\to FC} = \frac{|\mathcal{M}|^2}{\sum_i C_{ii} |\mathcal{A}_i|^2}$ to obtain FC accuracy, followed by secondary unweighting. Benchmarks for multi-jet, $t\bar t$+jets, $ZZ$+jets, and Drell–Yan+jets show the total runtime scales approximately as $b^n$ with $b\approx 5$, i.e., exponential in multiplicity, while the reweighting cost grows faster-than-exponential and can dominate at large $n$. This demonstrates that FC-accurate event generation becomes feasible at multiplicities previously intractable, and the approach remains extensible, with prospects for ML-based reweighting and integration into established frameworks.

Abstract

Efficient generation of LHC events is hindered by the rapidly rising cost of evaluating QCD matrix elements with increasing multiplicity. We build on a recently proposed two-step strategy in which unweighted events are first generated using the leading-colour (LC) approximation and then reweighted to full-colour (FC) accuracy, utilising the LC integration efficiency while recovering the exact FC prediction. In this work we extend the method to general Standard Model processes and present AmpliCol, a standalone implementation designed for LHC collisions. We benchmark multi-jet, $t\bar{t}$+jets, $ZZ$+jets, and Drell-Yan+jets production, measuring the time required to obtain a fixed number of unweighted events at FC accuracy. Across all processes, the runtime exhibits a stable exponential scaling with multiplicity, far milder than the factorial growth of conventional matrix-element generators. This demonstrates that the AmpliCol code enables efficient event generation at multiplicities that are otherwise computationally prohibitive.

Figures (2)

• Figure 1: Computational time (in seconds) for the four benchmark processes. Shown is the total computation time (circle with error bar) for $10^5$ unweighted events at FC accuracy (including the generation time of the LC events, the reweighting time, and accounting for the secondary unweighting loss), and separately the reweighting time (triangle). An exponential curve is fitted to the total timings and portrayed as a line in the plots, with the base $b$ of the exponential indicated in each of the four sub-plots.
• Figure 2: The unweighting efficiency $u^{\rm eff}$ for increasing jet multiplicity (left) and effective sample size ratio $f_{\text{ESS}}$ (right) for the four benchmark processes considered.