MadNIS at NLO

Abstract

We combine fast amplitude surrogates with neural importance sampling to accelerate NLO calculations. For virtual corrections, a learned ratio to the Born matrix element with calibrated uncertainties guarantees reliable precision across phase space. For real emission, we stick to the standard FKS subtraction and train sector-conditioned surrogates of the regularized integrands away from divergences. MadNIS then uses multi-channel mappings and FKS sectors as conditions. We validate our approach for electron-positron scattering to three and four jets and find significant speed-ups and variance reduction in the integration.

Figures (12)

• Figure 1: Left to right: representative Feynman diagrams for the Born, virtual, and real-emission contribution for the NLO predictions of the $\mathrm{e}\xspace^{+} \mathrm{e}\xspace^{-} \to \mathrm{u}\xspace \mathrm{\bar{u}}\xspace \mathrm{g}\xspace \mathrm{g}\xspace$ process.
• Figure 2: Learned Born, combination of Born and virtual contributions without the integrated subtraction term, and full Born-like amplitudes. We show result for 3-jet (left) and 4-jet (right) production. The solid lines indicate surrogates, the dashed lines the truth.
• Figure 3: Ratios of the learned amplitudes to the Born contribution, shown for the combined virtual and integrated subtraction term (left) and for the virtual contribution alone (right). The solid lines indicate the surrogates, the dashed lines the truth.
• Figure 4: Relative accuracies for the virtual amplitudes defined in Eq.\ref{['eq:def_delta']} (upper) and systematic pulls defined in Eq.\ref{['eq:pull']} (lower) for the different options. We show results for 3-jet (left) and 4-jets (right) production.
• Figure 5: Learned real emission amplitudes for the NLO corrections to 3-jet (left) and 4-jet (right) production. We denote the target function $\Sigma$ without subscripts since we are considering all the FKS sectors at the same time.