arXiv subjects

Simon Badger

Publications and source records attributed to Simon Badger.

At least 37 records · Page 2Linked to original sources

arXiv2021

Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC

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.

hep-ph↗

arXiv2021

Optimising simulations for diphoton production at hadron colliders using amplitude neural networks

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 $2\to3$ and $2\to4$ 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.

hep-ph↗

arXiv2021

Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders

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.

hep-ph↗

arXiv2021

Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel

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.

hep-ph↗

arXiv2020

Using neural networks for efficient evaluation of high multiplicity scattering amplitudes

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 $e^+e^-\to$ 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.

hep-ph↗

arXiv2019

A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons

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.

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arXiv2018

Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case

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.

hep-ph↗

arXiv2018

Applications of integrand reduction to two-loop five-point scattering amplitudes in QCD

We review the current state-of-the-art in integrand level reduction for five-point scattering amplitudes at two loops in QCD. We present some benchmark results for the evaluation of the leading colour two-loop five-gluon amplitudes in the physical region as well as the partonic channels for two quarks and three gluons and four quarks and one gluon.

hep-ph↗

arXiv2017

A first look at two-loop five-gluon scattering in QCD

We compute the leading colour contributions to five-gluon scattering at two loops in massless QCD. The integrands of all independent helicity amplitudes are evaluated using d-dimensional generalised unitarity cuts and finite field reconstruction techniques. Numerical evaluation of the integral basis is performed with sector decomposition methods to obtain the first benchmark results for all helicity configurations of a 2 to 3 scattering process in QCD.

hep-ph↗

arXiv2017

A unitarity compatible approach to one-loop amplitudes with massive fermions

We explain how one-loop amplitudes with massive fermions can be computed using only on-shell information. We first use the spinor-helicity formalism in six dimensions to perform generalised unitarity cuts in $d$ dimensions. We then show that divergent wavefunction cuts can be avoided, and the remaining ambiguities in the renormalised amplitudes can be fixed, by matching to universal infrared poles in $4-2ε$ dimensions and ultraviolet poles in $6-2ε$ dimensions. In the latter case we construct an effective Lagrangian in six dimensions and reduce the additional constraint to an on-shell tree-level computation.

hep-ph↗

arXiv2016

Local integrands for two-loop all-plus Yang-Mills amplitudes

We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4-2epsilon dimensions.

hep-ph↗

arXiv2016

Local integrands for two-loop QCD amplitudes

In this talk we review the recent computation of the five- and six-gluon two-loop amplitudes in Yang-Mills theory using local integrands which make the infrared pole structure manifest. We make some remarks on the connection with BCJ relations and the all-multiplicity structure.

hep-ph↗

arXiv2016

Automating QCD amplitudes with on-shell methods

We review some of the modern approaches to scattering amplitude computations in QCD and their application to precision LHC phenomenology. We emphasise the usefulness of momentum twistor variables in parameterising general amplitudes.

hep-ph↗

arXiv2015

A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory

We compute the integrand of the full-colour, two-loop, five-gluon scattering amplitude in pure Yang-Mills theory with all helicities positive, using generalized unitarity cuts. Tree-level BCJ relations, satisfied by amplitudes appearing in the cuts, allow us to deduce all the necessary non-planar information for the full-colour amplitude from known planar data. We present our result in terms of irreducible numerators, with colour factors derived from the multi-peripheral colour decomposition. Finally, the leading soft divergences are checked to reproduce the expected infrared behaviour.

hep-ph↗

arXiv2015

A Two-Loop Five-Gluon Helicity Amplitude in QCD

We compute the planar part of the two-loop five gluon amplitude with all helicities positive. To perform the calculation we develop a D-dimensional generalized unitarity procedure allowing us to reconstruct the amplitude by cutting into products of six-dimensional trees. We find a compact form for the integrand which only requires topologies with six or more propagators. We perform cross checks of the universal infra-red structure using numerical integration techniques.

hep-ph↗

arXiv2015

One-loop triple collinear splitting amplitudes in QCD

We study the factorisation properties of one-loop scattering amplitudes in the triple collinear limit and extract the universal splitting amplitudes for processes initiated by a gluon. The splitting amplitudes are derived from the analytic Higgs plus four partons amplitudes. We present compact results for primitive helicity splitting amplitudes making use of super-symmetric decompositions. The universality of the collinear factorisation is checked numerically against the full colour six parton squared matrix elements.

hep-ph↗

arXiv2014

Multi-loop integrand reduction techniques

We review recent progress in D-dimensional integrand reduction algorithms for two loop amplitudes and give examples of their application to non-planar maximal cuts of the five-point all-plus helicity amplitude in QCD.

hep-ph↗

arXiv2014

Next-to-leading order QCD corrections to di-photon production in association with up to three jets at the Large Hadron Collider

We present the computation of next-to-leading order (NLO) QCD corrections to di-photon production in association with two or three hard jets in pp collisions at a center-of-mass energy of 8 TeV. The inclusion of NLO corrections is shown to substantially reduce the theoretical uncertainties estimated from scale variations on total cross section predictions. We study a range of differential distributions relevant for phenomenological studies of photon pair production in association with jets at the LHC. Using an efficient computational set-up we performed a detailed study of uncertainties due to parton distribution functions. The computation of the virtual corrections is performed using new features of the C++ library NJET.

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