Sampling NNLO QCD phase space with normalizing flows

TL;DR

This paper demonstrates how neural importance sampling with normalizing flows can significantly improve the efficiency of NNLO QCD phase space integration, reducing computational costs and variance in top-quark pair production calculations.

Contribution

It introduces the application of neural importance sampling with normalizing flows to NNLO QCD phase space integration, enhancing efficiency over traditional methods.

Findings

Reduced cross-section variances

Increased unweighting efficiencies

Computational cost reduced by a factor of 8

Abstract

We showcase the application of neural importance sampling for the evaluation of NNLO QCD scattering cross sections. We consider Normalizing Flows in the form of discrete Coupling Layers and time continuous flows for the integration of the various cross-section contributions when using the sector-improved residue subtraction scheme. We thereby consider the stratification of the integrands into their positive and negative contributions, and separately optimize the phase-space sampler. We exemplify the novel methods for the case of gluonic top-quark pair production at the LHC at NNLO QCD accuracy. We find significant gains with respect to the current default methods used in STRIPPER in terms of reduced cross-section variances and increased unweighting efficiencies. In turn, the computational costs for evaluations of the integrand needed to achieve a certain statistical uncertainty for the cross section can be reduced by a factor 8.