We present integrated subtraction terms and finite remainders for $\textit{arbitrary}$ processes with massless partons at hadron and lepton colliders in the context of the nested soft-collinear subtraction scheme. These results provide the very last ingredients needed to make this scheme a fully local, analytic and process-independent framework for treating infrared singularities at next-to-next-to-leading order in perturbative QCD. The explicit infrared finiteness of all required contributions, as well as their process-independence, puts these results on par with subtraction schemes developed for next-to-leading order computations and opens up a clear path towards the automation of next-to-next-to-leading order computations in QCD.

United States

Federica Devoto

Germany

Kirill Melnikov

Italy

Raoul Röntsch

Chiara Signorile-Signorile

Davide Tagliabue

Matteo Tresoldi

Integrated subtraction terms and finite remainders for arbitrary processes with massless partons at colliders in the nested soft-collinear subtraction scheme

<p>We study the impact of the pointlike <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><msup><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><mi>W</mi><mi>H</mi></math> interactions originating from a subset of dimension-six operators of the Standard Model effective field theory (SMEFT) on the Higgs boson associated production <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>p</mi><mi>p</mi><mo stretchy="false">→</mo><msup><mi>W</mi><mo>+</mo></msup><mi>H</mi></math> at the LHC. For consistency, we also take into account the corresponding <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>q</mi><msup><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mo>′</mo></msup><mi>W</mi></math> vertices implied by these operators. We compute the next-to-next-to-leading order quantum chromodynamics (QCD) corrections to this process and compare these corrections in the Standard Model and SMEFT production mechanisms.</p>

Marco Bonetti

Robert V. Harlander

Dmitrii Korneev

Ming-Ming Long

Davide Maria Tagliabue

<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>W</mi><mi>H</mi></math> production at the LHC within SMEFT at next-to-next-to-leading order QCD

We describe the calculation of integrated subtraction terms in the nested soft-collinear subtraction scheme for hadron collider processes with quarks and gluons, thereby extending the results presented in ref. [1]. Although this extension eventually proves to be straightforward, it requires a more careful treatment of certain collinear limits to achieve a compact and physically-transparent final result. We also show that the cancellation of infrared divergences can be organized in such a way that, once soft contributions are removed, it occurs independently for each of the external partons. We consider these results to be important stepping stones on the way to deriving finite remainders of the integrated subtraction terms for fully-general hadron collider processes in the context of the nested soft-collinear subtraction scheme.

Towards a general subtraction formula for NNLO QCD corrections to processes at hadron colliders: final states with quarks and gluons

We study QCD corrections to the process where a Higgs boson is produced in weak boson fusion and then decays into a pair of massive <math><mi>b</mi></math> quarks. We find that typical experimental criteria used to identify <math><mi>b</mi></math> jets in this process affect QCD corrections to the decay, making it necessary to account for them in the proper description of this process. Indeed, if corrections to the production and decay are combined, the fiducial cross section of the weak boson fusion process <math><mi>p</mi><mi>p</mi><mo>→</mo><mi>H</mi><mo>(</mo><mo>→</mo><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover><mo>)</mo><mi>j</mi><mi>j</mi></math> is reduced by about 40% relative to leading-order predictions, compared to just about 8% if only corrections to the production process are considered. We investigate the origin of these large corrections through next-to-next-to-leading order and conclude that they appear because a number of independent moderately large effects conspire to significantly reduce the fiducial cross section for this process.

Konstantin Asteriadis

CERN

Arnd Behring

Ivan Novikov

QCD corrections to Higgs boson production and <math><mi>H</mi><mo>→</mo><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> decay in weak boson fusion

We describe how the nested soft-collinear subtraction scheme [1] can be used to compute the next-to-next-to-leading order (NNLO) QCD corrections to the production of an arbitrary number of gluonic jets in hadron collisions. We show that the infrared subtraction terms can be combined into recurring structures that in many cases are simple iterations of those terms known from next-to-leading order. The way that these recurring structures are identified and computed is fairly general, and can be applied to any partonic process. As an example, we explicitly demonstrate the cancellation of all singularities in the fully-differential cross section for the   <math> <mi>q</mi> <mover> <mi>q</mi> <mo>¯</mo> </mover> </math>  $$ q\overline{q} $$  → X + Ng process at NNLO in QCD. The finite remainder of the NNLO QCD contribution, which arises upon cancellation of all ϵ-poles, is expressed via relatively simple formulas, which can be implemented in a numerical code in a straightforward way. Our approach can be extended to describe arbitrary processes at NNLO in QCD; the largest remaining challenge at this point is the combinatorics of quark and gluon collinear limits.

United Kingdom

A fresh look at the nested soft-collinear subtraction scheme: NNLO QCD corrections to N-gluon final states in   <math> <mi>q</mi> <mover> <mi>q</mi> <mo>¯</mo> </mover> </math>  $$ q\overline{q} $$  annihilation

The production of Higgs bosons in weak boson fusion has the second largest cross section among Higgs-production processes at the Large Hadron Collider. As such, this process plays an important role in detailed studies of Higgs interactions with vector bosons. In this paper we extend the available description of Higgs boson production in weak boson fusion by considering anomalous weak interactions of the Higgs boson and next-to-next-to-leading order (NNLO) QCD radiative corrections at the same time. We find that, while leading order QCD predictions are too uncertain to allow for detailed studies of the anomalous couplings, next-to-leading order (NLO) QCD results are sufficiently precise, most of the time. The NNLO QCD corrections alter the NLO QCD predictions only marginally, but their availability enhances the credibility of conclusions based on NLO QCD computations.

Fabrizio Caola

Anomalous Higgs boson couplings in weak boson fusion production at NNLO in QCD

We compute mixed QCD-electroweak corrections to the neutral-current Drell-Yan production of a pair of massless leptons in the high invariant mass region. Our computation is fully differential with respect to the final state particles. At relatively low values of the dilepton invariant mass, m  ℓℓ  ∼ 200 GeV, we find unexpectedly large mixed QCD-electroweak corrections at the level of −1%. At higher invariant masses, m  ℓℓ  ∼ 1 TeV, we observe that these corrections can be well approximated by the product of QCD and electroweak corrections. Hence, thanks to the well-known Sudakov enhancement of the latter, they increase at large invariant mass and reach e.g. −3% at m  ℓℓ  = 3 TeV. Finally, we note that the inclusion of mixed corrections reduces the theoretical uncertainty related to the choice of electroweak input parameters to below the percent level.

Federico Buccioni

Herschel Chawdhry

Matthias Heller

Andreas Manteuffel

Mixed QCD-electroweak corrections to dilepton production at the LHC in the high invariant mass region

We compute the next-to-next-to-leading order QCD corrections to Higgs boson production in weak boson fusion followed by its decay to a b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$  pair or to a pair of leptonically-decaying W bosons. Our calculation allows us to compute realistic fiducial cross sections and assess the impact of fiducial cuts applied to the Higgs boson decay products on the magnitude of QCD radiative corrections in weak boson fusion.

NNLO QCD corrections to weak boson fusion Higgs boson production in the H → b   <math> <mover> <mi>b</mi> <mo>¯</mo> </mover> </math>  $$ \overline{b} $$  and H → WW * → 4l decay channels

We combine the NNLO QCD description of Higgs boson production in association with an electroweak vector boson <math><mrow><mi>V</mi><mo>=</mo><mi>W</mi></mrow></math> or <math><mi>Z</mi></math> with a similarly precise description of Higgs boson decays into a pair of massive <math><mi>b</mi></math> quarks and with the anomalous couplings that modify interactions of the Higgs and electroweak vector bosons. The resulting numerical code provides the most advanced theoretical tool to investigate such anomalous couplings in the associated Higgs boson production process. We study the impact of anomalous couplings on fiducial cross sections and differential distributions and argue that, with increased QCD precision, smaller anomalous couplings become accessible in kinematic regions where the effects of higher-dimensional operators in the Standard Model effective field theory remain small and the effective field theory expansion is under control.

Wojciech Bizoń

Anomalous couplings in associated <math><mi>V</mi><mi>H</mi></math> production with Higgs boson decay to massive <math><mi>b</mi></math> quarks at NNLO in QCD

We present a calculation of the next-to-leading order (NLO) QCD corrections to gluon-induced electroweak gauge boson pair production,  $$gg \rightarrow ZZ$$  <math> <mrow> <mi>g</mi> <mi>g</mi> <mo>→</mo> <mi>Z</mi> <mi>Z</mi> </mrow> </math>   and  $$gg \rightarrow W^+W^-$$  <math> <mrow> <mi>g</mi> <mi>g</mi> <mo>→</mo> <msup> <mi>W</mi> <mo>+</mo> </msup> <msup> <mi>W</mi> <mo>-</mo> </msup> </mrow> </math>  , matched to the PYTHIA 8 parton shower in the POWHEG approach. The calculation consistently incorporates the continuum background, the Higgs-mediated  $$gg\rightarrow H^* \rightarrow VV$$  <math> <mrow> <mi>g</mi> <mi>g</mi> <mo>→</mo> <msup> <mi>H</mi> <mo>∗</mo> </msup> <mo>→</mo> <mi>V</mi> <mi>V</mi> </mrow> </math>   process, and their interference. We consider leptonic decay modes of the vector bosons and retain offshell and non-resonant contributions. The processes considered are loop-induced at leading order and thus contain two-loop virtual contributions as well as loop-squared real contributions. Parton-shower effects are found to be marginal in inclusive observables and quite sizeable in observables that are exclusive in additional jet radiation. The Monte Carlo generator presented here allows for realistic experimental effects to be incorporated in state-of-the-art precision analyses of diboson production and of the Higgs boson in the offshell regime.