Inclusive Higgs boson production at large transverse momentum is induced by different production channels. We focus on the leading production through gluon fusion, and perform a consistent combination of the state of the art calculations obtained in the infinite-top-mass effective theory at next-to-next-to-leading order (NNLO) and in the full Standard Model (SM) at next-to-leading order (NLO). We thus present approximate QCD predictions for this process at NNLO, and a study of the corresponding perturbative uncertainties. This calculation is then compared with those obtained with commonly used event generators, and we observe that the description of the considered kinematic regime provided by these tools is in good agreement with state of the art calculations. Finally, we present accurate predictions for other production channels such as vector boson fusion, and associated production with a gauge boson, and with a $t\bar{t}$ pair. We find that, at large transverse momentum, the contribution of other production modes is substantial, and therefore must be included for a precise theory prediction of this observable.

Abstract We present a calculation of all matching coefficients for N-jettiness beam functions at next-to-next-to-next-to-leading order (N3LO) in perturbative quantum chromodynamics (QCD). Our computation is performed starting from the respective collinear splitting kernels, which we integrate using the axial gauge. We use reverse unitarity to map the relevant phase-space integrals to loop integrals, which allows us to employ multi-loop techniques including integration-by-parts identities and differential equations. We find a canonical basis and use an algorithm to establish non-trivial partial fraction relations among the resulting master integrals, which allows us to reduce their number substantially. By use of regularity conditions, we express all necessary boundary constants in terms of an independent set, which we compute by direct integration of the corresponding integrals in the soft limit. In this way, we provide an entirely independent calculation of the matching coefficients which were previously computed in ref. [1].

Over the last years, master integral families at one, two and three loops, with up to five external particles, including off-shell legs and internal masses have been computed analytically based on the Simplified Differential Equations approach. In this presentation we focus on the latest results for two-loop five-point Feynman Integrals with one off-shell leg. The three planar and one of the non-planar families have been fully expressed in terms of Goncharov polylogarithms. For the other two non-planar families, we introduce a new approach to obtain the boundary terms and establish a one-dimensional integral representation of the master integrals in terms of generalised polylogarithms, when the alphabet contains non-factorizable square roots. The results are relevant to the study of NNLO QCD corrections for $W,Z$ and Higgs-boson production in association with two hadronic jets.

In this contribution, we discuss the advancement made regarding multi-loop calculations within our group. In the first part, we discuss the progress made in the development of HELAC-2LOOP, a package for automated computations of two-loop scattering amplitudes, using the already working machinery of the HELAC framework. In the second part, we present recent results on two-loop five-point and three-loop four-point Feynman Integrals with one off-shell leg, using the Simplified Differential Equations approach.

Analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg are presented. The Simplified Differential Equations approach is the only known way to fulfil this task due to its unique factorisation property of the symbols of the canonical differential equation. The results are relevant to the study of many 2\to 32→3 scattering processes of interest at the LHC.

Based on the Simplified Differential Equations approach, we present results for the two-loop non-planar hexa-box families of master integrals. We introduce a new approach to obtain the boundary terms and establish a one-dimensional integral representation of the master integrals in terms of Generalised Polylogarithms, when the alphabet contains non-factorisable square roots. The results are relevant to the study of NNLO QCD corrections for $W,Z$ and Higgs-boson production in association with two hadronic jets.

We present recent results on two-loop five-point Feynman Integrals with one off-shell leg that are relevant to the study of many 2 → 3 scattering processes of interest at the LHC, especially for the leading-colour W + 2 jets production. The calculation is based on the Simplified Differential Equations approach.

The production of electroweak Z bosons that decay to neutrinos and recoil against jets with large transverse momentum p⊥ is an important background process to searches for dark matter at the Large Hadron Collider (LHC). To fully benefit from opportunities offered by the future high-luminosity LHC, the theoretical description of the pp → Z + j process should be extended to include mixed QCD-electroweak corrections. The goal of this paper is to initiate the computation of such corrections starting with the calculation of the Feynman integrals needed to describe two-loop QCD-electroweak contributions to $$ q\overline{q} $$→ Z + g scattering amplitudes. Making use of the hierarchy between the large transverse momenta of the recoiling jet, relevant for heavy dark matter searches, and the Z boson mass mZ , we present the relevant master integrals as a series expansion in mZ /p⊥.

A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of non-planar five-point two-loop Master Integrals with one external off-shell particle, relevant for instance for H + 2 jets production at the LHC, in both Euclidean and physical kinematical regions.

We compute the three-loop master integrals required for the calculation of the triple-real contribution to the N3LO quark beam function due to the splitting of a quark into a virtual quark and three collinear gluons, q → q* + ggg. This provides an important ingredient for the calculation of the leading-color contribution to the quark beam function at N3LO.

We compute the master integrals required for the calculation of the double-real emission contributions to the matching coefficients of 0-jettiness beam functions at next-to-next-to-next-to-leading order in perturbative QCD. As an application, we combine these integrals and derive the double-real gluon emission contribution to the matching coefficient I-qq (t, z) of the quark beam function.

We present the matching coefficient for the quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large N_c-approximation, N_c ∼ N_f ≫ 1. Although several refinements are still needed to make this result interesting for phenomenological applications, our computation shows that a fully-differential description of simple color singlet production processes at a hadron collider at N^3LO in perturbative QCD is within reach.

In this note we study the inclusive production of a Higgs boson with large transverse 23 momentum. We provide a recommendation for the inclusive cross section based on a combination of 24 state of the art QCD predictions for the gluon-fusion and vector-boson-fusion channels. Moreover, 25 we compare such predictions to those obtained with commonly used event generators. We observe 26 that the description of the considered kinematic regime provided by these tools is in good agreement 27 with state of the art QCD predictions. 28

The next-to-leading order QCD corrections to the top-bottom interference contribution to $H+j$ production at the LHC are presented. The QCD corrections to the interference are large and similar to the QCD corrections to the top-mediated Higgs production cross section. There is also a significant reduction in the mass-renormalization scheme uncertainty once the NLO QCD prediction for the interference is employed.

We compute the two-loop QCD corrections to amplitudes for processes gg → Hg, qg → Hq and \( q\overline{q}\to Hg \) in the limit when the Higgs transverse momentum is larger than the top quark mass, p⊥ ≫ m t . These amplitudes are important ingredients for understanding higher-order QCD effects on Higgs transverse momentum distribution at large p⊥.

We compute the next-to-leading order QCD corrections to the production of Higgs bosons with large transverse momentum p⊥≫2mt at the LHC. To accomplish this, we combine the two-loop amplitudes for processes gg→Hg, qg→Hq and qq¯→Hg, recently computed in the approximation of nearly massless top quarks, with the numerical calculation of the squared one-loop amplitudes for gg→Hgg, qg→Hqg and qq¯→Hgg processes. The latter computation is performed with OpenLoops. We find that the QCD corrections to the Higgs transverse momentum distribution at very high p⊥ are large but quite similar to the QCD corrections obtained for point-like Hgg coupling. Our result removes one of the largest sources of theoretical uncertainty in the description of high-p⊥ Higgs boson production and opens a way to use the high-p⊥ region to search for physics beyond the Standard Model.

We provide a precise description of the Higgs boson transverse momentum distribution including top and bottom quark contributions, that is valid for transverse momenta in the range mb ≲ p⊥ ≲ mt, where mb and mt are the bottom and top quark masses. This description is based on a combination of fixed next-to-leading order (NLO) results with next-to-next-to-leading logarithmic (NNLL) transverse momentum resummation. We show that ambiguities in the resummation procedure for the b-quark loops are of the same order as the related fixed-order uncertainties. We conclude that the current uncertainty in the top-bottom interference contribution to the Higgs transverse momentum spectrum is \( \mathcal{O}\left(20\%\right) \).

We compute the two-loop QCD corrections to amplitudes for processes gg → Hg, qg → Hq and qq→ Hg in the limit when the Higgs transverse momentum is larger than the top quark mass, p ⊥ ≫ m t . These amplitudes are important ingredients for understanding higher-order QCD effects on Higgs transverse momentum distribution at large p ⊥ .

A new approach to compute Feynman Integrals is presented. Based on it, we verify our previous results on planar five-point two-loop Master Integrals in the physical kinematical region. We also show how to obtain results for certain non-planar five-point two-loop Master Integrals in both Euclidean and physical regions.