The recent experimental observation of Light-by-Light (LbL) scattering at the Large Hadron Collider has revived interest in this fundamental process, and especially of the accurate prediction of its cross-section, which we present here for the first time at Next-to-Leading Order (NLO) in both QCD and QED. We compare two radically different computational approaches, both exact in the fermion mass dependence, thus offering a strong cross-check of our results. The first approach is a fully analytic method to calculate compact and well-organized two-loop helicity amplitudes. The second one is entirely numerical and leverages the Local Unitarity construction. Our two calculations agree with each other and conclude that including the exact fermion mass contribution typically increases the size of the NLO corrections. Moreover, we find that the exact result converges slowly to the massless limit of the high-energy regime, thus emphasizing the importance of including the full mass dependence at NLO. We also compare our results with the ATLAS measurement of LbL in ultra-peripheral lead-lead collisions, and find that the inclusion of exact NLO corrections reduces, but does not eliminate, the existing tension with theoretical predictions.

France

Ajjath A H

Germany

Ekta Chaubey

Switzerland

Mathijs Fraaije

Valentin Hirschi

Hua-Sheng Shao

Light-by-light scattering at next-to-leading order in QCD and QED

We compute the next-to-leading-order (NLO) QCD corrections to the Higgs <math><msub><mrow><mi>p</mi></mrow><mrow><mi>T</mi></mrow></msub></math> distribution in Higgs production in association with a jet via gluon fusion at the LHC, with exact dependence on the mass of the quark circulating in the heavy-quark loops. The NLO corrections are presented including the top-quark mass, and for the first time, the bottom-quark mass as well. Further, besides the on-shell mass scheme, we consider for the first time a running mass renormalisation scheme. The computation is based on amplitudes which are valid for arbitrary heavy-quark masses.

Italy

Roberto Bonciani

Vittorio Del Duca

Denmark

Hjalte Frellesvig

Sweden

Martijn Hidding

CERN

Francesco Moriello

United States

Giulio Salvatori

Hungary

Gábor Somogyi

Francesco Tramontano

Next-to-leading-order QCD corrections to Higgs production in association with a jet

We present an update of the Universal FeynRules Output model format, commonly known as the UFO format, that is used by several automated matrix-element generators and high-energy physics software. We detail different features that have been proposed as extensions of the initial format during the last ten years, and collect them in the current second version of the model format that we coin the Universal Feynman Output format. Following the initial philosophy of the UFO, they consist of flexible and modular additions to address particle decays, custom propagators, form factors, the renormalisation group running of parameters and masses, and higher-order quantum corrections.

Luc Darmé

Belgium

Céline Degrande

Claude Duhr

Benjamin Fuks

Mark Goodsell

Gudrun Heinrich

Stefan Höche

Marius Höfer

Joshua Isaacson

Olivier Mattelaer

Thorsten Ohl

Davide Pagani

Jürgen Reuter

United Kingdom

Peter Richardson

Steffen Schumann

Frank Siegert

Marco Zaro

UFO 2.0: the ‘Universal Feynman Output’ format

The Local Unitarity (LU) representation of differential cross-sections locally realises the cancellations of infrared singularities predicted by the Kinoshita-Lee-Nauenberg theorem. In this work we solve the two remaining challenges to enable practical higher-loop computations within the LU formalism. The first concerns the generalisation of the LU representation to graphs with raised propagators. The solution to this problem results in a generalisation of distributional Cutkosky rules. The second concerns the regularisation of ultraviolet and spurious soft singularities, solved using a fully automated and local renormalisation procedure based on Bogoliubov’s R-operation. We detail an all-order construction for the hybrid   <math> <mover> <mi>MS</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\textrm{MS}} $$  and On-Shell scheme whose only analytic input is single-scale vacuum diagrams. We validate this novel technology by providing (semi-)inclusive results for two multi-leg processes at NLO, study limits of individual supergraphs up to N3LO and present the first physical NNLO cross-sections computed fully numerically in momentum-space, namely for the processes γ ∗ → jj and   <math> <msup> <mi>γ</mi> <mo>∗</mo> </msup> <mo>→</mo> <mi>t</mi> <mover> <mi>t</mi> <mo>¯</mo> </mover> </math>  $$ {\gamma}^{\ast}\to t\overline{t} $$ .

Zeno Capatti

Ben Ruijl

Local unitarity: cutting raised propagators and localising renormalisation

We propose a novel representation of differential scattering cross-sections that locally realises the direct cancellation of infrared singularities exhibited by its so-called real-emission and virtual degrees of freedom. We take advantage of the Loop-Tree Duality representation of each individual forward-scattering diagram and we prove that the ensuing expression is locally free of infrared divergences, applies at any perturbative order and for any process without initial-state collinear singularities. Divergences for loop momenta with large magnitudes are regulated using local ultraviolet counterterms that reproduce the usual Lagrangian renormalisation procedure of quantum field theories. Our representation is especially suited for a numerical implementation and we demonstrate its practical potential by computing fully numerically and without any IR counterterm the next-to-leading order accurate differential cross-section for the process e + e  −  →   <math> <mi>d</mi> <mover> <mi>d</mi> <mo>¯</mo> </mover> </math>  $$ d\overline{d} $$ . We also show first results beyond next-to-leading order by computing interference terms part of the N4LO-accurate inclusive cross-section of a 1 → 2 + X scalar scattering process.

Andrea Pelloni

Local Unitarity: a representation of differential cross-sections that is locally free of infrared singularities at any order

We present for the first time the exact next-to-leading-order QCD corrections to the light-quark part of the mixed QCD-EW contributions to Higgs production via gluon fusion at the Large Hadron Collider, for a center-of-mass energy of 13 TeV, with exact EW-boson mass dependence. The relevant two-loop real-emission matrix element is computed using a dynamic one-dimensional series expansion strategy whose stability and speed allows for a numerical phase-space integration using local IR subtraction counterterms. For the choice of renormalization (<math><msub><mi>μ</mi><mi>R</mi></msub></math>) and factorization (<math><msub><mi>μ</mi><mi>F</mi></msub></math>) scales, <math><msub><mi>μ</mi><mi>R</mi></msub><mo>=</mo><msub><mi>μ</mi><mi>F</mi></msub><mo>=</mo><msub><mi>M</mi><mi>H</mi></msub></math>, we find <math><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>g</mi><mi>g</mi><mo>→</mo><mi>H</mi><mo>+</mo><mi>X</mi></mrow><mrow><mo>(</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msubsup><mrow><mi>α</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>3</mn></mrow></msubsup><msup><mrow><mi>α</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></msubsup><mo>=</mo><mn>1.467</mn><mo>(</mo><mn>2</mn><msubsup><mrow><mo>)</mo></mrow><mrow><mo>−</mo><mn>14.6</mn><mo>%</mo></mrow><mrow><mo>+</mo><mn>18.7</mn><mo>%</mo></mrow></msubsup><mo>(</mo><msub><mrow><mi>μ</mi></mrow><mrow><mi>R</mi></mrow></msub><mtext> </mtext><mtext>var</mtext><mo>)</mo><mo>±</mo><mn>2</mn><mo>%</mo><mtext> </mtext><mo>(</mo><mi>PDF</mi><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>pb</mi></mrow></math>, which we use to provide the best result, including an estimate of suppressed contributions: <math><mrow><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>p</mi><mi>p</mi><mo>→</mo><mi>H</mi><mo>+</mo><mi>X</mi></mrow><mrow><mo>(</mo><mi>EW</mi><mo>,</mo><mtext>best</mtext><mo>)</mo></mrow></msubsup><mo>=</mo><mn>2.11</mn><mo>±</mo><mn>0.28</mn><mtext> </mtext><mo>(</mo><mtext>theory</mtext><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>pb</mi></mrow></math>.

Matteo Becchetti

Armin Schweitzer

Next-to-leading order corrections to light-quark mixed QCD-EW contributions to Higgs boson production

We present analytic results for the partonic cross sections for the production of a Higgs boson via the fusion of two bottom quarks at N LO in QCD perturbation theory in the five-flavour scheme. We combine this perturbative result with NLO accurate predictions in the four-flavour scheme that include the full bottom quark mass dependence by appropriately removing any double-counting stemming from contributions included in both predictions. We thereby obtain state-of-the-art predictions for the inclusive production probability of a Higgs boson via bottom quark fusion at hadron colliders.

Falko Dulat

Bernhard Mistlberger

Higgs production in bottom quark fusion: matching the 4- and 5-flavour schemes to third order in the strong coupling

We introduce a novel construction of a contour deformation within the framework of Loop-Tree Duality for the numerical computation of loop integrals featuring threshold singularities in momentum space. The functional form of our contour deformation automatically satisfies all constraints without the need for fine-tuning. We demonstrate that our construction is systematic and efficient by applying it to more than 100 examples of finite scalar integrals featuring up to six loops. We also showcase a first step towards handling non-integrable singularities by applying our work to one-loop infrared divergent scalar integrals and to the one-loop amplitude for the ordered production of two and three photons. This requires the combination of our contour deformation with local counterterms that regulate soft, collinear and ultraviolet divergences. This work is an important step towards computing higher-order corrections to relevant scattering cross-sections in a fully numerical fashion.

Dario Kermanschah

Numerical Loop-Tree Duality: contour deformation and subtraction

The MadGraph5_aMC@NLO framework aims to automate all types of leading- and next-to-leading-order-accurate simulations for any user-defined model that stems from a renormalisable Lagrangian. In this paper, we present all of the key ingredients of such models in the context of supersymmetric theories. In order to do so, we extend the FeynRules package by giving it the possibility of dealing with different renormalisation options that are relevant to supersymmetric models. We also show how to deal with the problem posed by the presence of narrow resonances, thus generalising the so-called on-shell subtraction approaches. We extensively compare our total rate results with those of both Prospino2 and Resummino, and present illustrative applications relevant to the 13 TeV LHC, both at the total-rate and differential levels. The computer programmes that we have used to obtain the predictions presented here are all publicly available.

Stefano Frixione

Japan

Kentarou Mawatari

Marthijn Sunder

Netherlands

Automated simulations beyond the Standard Model: supersymmetry

Loop-tree duality (LTD) offers a promising avenue to numerically integrate multiloop integrals directly in momentum space. It is well established at one loop, but there have been only sparse numerical results at two loops. We provide a formal derivation for a novel multiloop LTD expression and study its threshold singularity structure. We apply our findings numerically to a diverse set of up to four-loop finite topologies with kinematics for which no contour deformation is needed. We also lay down the ground work for constructing such a deformation. Our results serve as an important stepping stone towards a generalized and efficient numerical implementation of LTD, which is applicable to the computation of virtual corrections.

Loop-Tree Duality for Multiloop Numerical Integration