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A bstract Precision theoretical predictions for high multiplicity scattering rely on the evaluation of increasingly complicated scattering amplitudes which come with an extremely high CPU cost. For state-of-the-art processes this can cause technical bottlenecks in the production of fully differential distributions. In this article we explore the possibility of using neural networks to approximate multi-variable scattering amplitudes and provide efficient inputs for Monte Carlo integration. We focus on QCD corrections to e + e − → jets up to one-loop and up to five jets. We demonstrate reliable interpolation when a series of networks are trained to amplitudes that have been divided into sectors defined by their infrared singularity structure. Complete simulations for one-loop distributions show speed improvements of at least an order of magnitude over a standard approach.

A bstract We present the two-loop leading colour QCD helicity amplitudes for the process pp → W ( → lν ) γ + j . We implement a complete reduction of the amplitudes, including the leptonic decay of the W -boson, using finite field arithmetic, and extract the analytic finite remainders using a recently identified basis of special functions. Simplified analytic expressions are obtained after considering permutations of a rational kinematic parametrisation and multivariate partial fractioning. We demonstrate efficient numerical evaluation of the two-loop colour and helicity summed finite remainders for physical kinematics, and hence the suitability for phenomenological applications.

A bstract We compute the two-loop QCD helicity amplitudes for the production of a Higgs boson in association with a bottom quark pair at a hadron collider. We take the approximations of leading colour and work in the five flavour scheme, where the bottom quarks are massless while the Yukawa coupling is non-zero. We extract analytic expressions from multiple numerical evaluations over finite fields and present the results in terms of an independent set of special functions that can be reliably evaluated over the full phase space.

A bstract Machine learning technology has the potential to dramatically optimise event generation and simulations. We continue to investigate the use of neural networks to approximate matrix elements for high-multiplicity scattering processes. We focus on the case of loop-induced diphoton production through gluon fusion, and develop a realistic simulation method that can be applied to hadron collider observables. Neural networks are trained using the one-loop amplitudes implemented in the NJet C++ library, and interfaced to the Sherpa Monte Carlo event generator, where we perform a detailed study for 2 → 3 and 2 → 4 scattering problems. We also consider how the trained networks perform when varying the kinematic cuts effecting the phase space and the reliability of the neural network simulations.

A bstract We compute the two-loop QED helicity amplitudes for the scattering of a lepton pair with an off-shell and an on-shell photon, 0 → ℓ ℓ ¯ γγ * , using the approximation of massless leptons. We express all master integrals relevant for the scattering of four massless particles with a single external off-shell leg up to two loops in a basis of algebraically independent multiple polylogarithm, which guarantees an efficient numerical evaluation and compact analytic representations of the amplitudes. Analytic forms of the amplitudes are reconstructed from numerical evaluations over finite fields. Our results complete the amplitude-level ingredients contributing to the N 3 LO predictions of electron-muon scattering eμ → eμ , which are required to meet the precision goal of the future MUonE experiment.

A bstract We present a compact analytic expression for the leading colour two-loop five-gluon amplitude in Yang-Mills theory with a single negative helicity and four positive helicities. The analytic result is reconstructed from numerical evaluations over finite fields. The numerical method combines integrand reduction, integration-by-parts identities and Laurent expansion into a basis of pentagon functions to compute the coefficients directly from six-dimensional generalised unitarity cuts.

A bstract In this work, we provide a comprehensive set of differential cross-section distributions for photon + di-jet production in proton-proton collisions with next-to-next-to-leading order precision in massless QCD. The event selection corresponds to recent measurements by the ATLAS collaboration. We observe an improved description of data in comparison to lower-order calculations in the case of observables that are expected to be well described by perturbation theory. The results also show better agreement with data than parton-shower-matched and multi-jet-merged predictions generated for the ATLAS analysis using the S herpa Monte Carlo. A particular highlight of our study is the use of exact five-point two-loop virtual amplitudes. This is the first calculation of a complete two-to-three hadron-collider process at next-to-next-to-leading order in QCD that does not rely on the leading-colour approximation at two loops. We demonstrate, nevertheless, that the sub-leading-colour effects present in the infraredand ultraviolet-finite double-virtual contributions are negligible in view of the remaining scale uncertainties.

A bstract We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves. We present the results of the missing master integrals needed to compute the amplitude and obtain an analytic form for the finite remainders in terms of iterated integrals using rationalised kinematics and finite field sampling. We also study the numerical evaluation of the iterated integrals.

A bstract We present the first numerical results for the two-loop helicity amplitudes for the scattering of four partons and a W-boson in QCD. We use a finite field sampling method to reduce directly from Feynman diagrams to the coefficients of a set of master integrals after applying integration-by-parts identities. Since the basis of master integrals is not yet fully known analytically, we identify a set of master integrals with a simple divergence structure using local numerator insertions. This allows for accurate numerical evaluation of the amplitude using sector decomposition methods.

A bstract We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finite remainders from numerical evaluations over finite fields including all colour contributions. Compact expressions are found using the pentagon function basis. We provide a fast and stable implementation for the colour- and helicity-summed interference between the one-loop and two-loop finite remainders in C++ as part of the NJet library.