We report on the complete computation of the mixed QCD-electroweak corrections to the neutral-current Drell-Yan process. Our calculation holds in the entire range of dilepton invariant masses. We present phenomenological results for several kinematical distributions in the case of bare muons both in the resonant region and for high invariant masses. We also consider the forward-backward asymmetry, which is a key observable to measure the weak mixing angle. We finally extend our calculation to dressed leptons and compare our results in the massless limit to those available in the literature.

Belgium

Italy

Tommaso Armadillo

Roberto Bonciani

Switzerland

Luca Buonocore

Simone Devoto

Massimiliano Grazzini

Stefan Kallweit

India

Narayan Rana

Alessandro Vicini

Mixed QCD-EW corrections to the neutral-current Drell-Yan process

We present the first fully differential next-to-next-to-leading order (NNLO) QCD calculation for the production of a top-antitop quark pair in association with a Higgs boson $$ \left(t\overline{t}H\right) $$ at hadron colliders. The computation is exact, except for the finite part of the two-loop virtual contribution, which we estimate using two different methods that yield consistent results within their respective uncertainties. The first method relies on a soft-Higgs factorisation formula that we develop up to the three-loop order. The second is based on a high-energy expansion in the small top-mass limit. Combining the newly computed corrections with the complete set of next-to-leading order (NLO) QCD+EW results provides the most advanced perturbative prediction currently available at the LHC for both inclusive and differential $$ t\overline{t}H $$ cross sections. The uncertainties due to the missing exact two-loop contribution are conservatively estimated to be at the percent level, both for the total cross section and for most of the differential distributions, and therefore subleading compared to the residual perturbative uncertainties.

Javier Mazzitelli

Germany

Chiara Savoini

Precise predictions for

We present the two-loop mixed strong-electroweak virtual corrections to the charged current Drell-Yan process. The final-state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two different internal massive lines, has been worked out relying on semi-analytical techniques, using complex-valued masses. We can provide, at any arbitrary phase-space point, the solution as a power series in the W-boson mass, around a reference value. Starting from these expansions, we can prepare a numerical grid for any value of the W-boson mass within their radius of convergence in a negligible amount of time.

CERN

Two-loop mixed QCD-EW corrections to charged current Drell-Yan

The production of a top-antitop quark pair in association with a <math><mrow><mi>W</mi></mrow></math> boson (<math><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover><mi>W</mi></math>) is one of the heaviest signatures currently probed at the Large Hadron Collider. Since the first observation reported in 2015, the corresponding rates have been found to be consistently higher than the standard model predictions, which are based on next-to-leading order calculations in the QCD and electroweak interactions. We present the first next-to-next-to-leading order QCD computation of <math><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover><mi>W</mi></math> production at hadron colliders. The calculation is exact, except for the finite part of the two-loop virtual corrections, which is estimated using two different approaches that lead to consistent results within their uncertainties. We combine the newly computed next-to-next-to-leading order QCD corrections with the complete next-to-leading order QCD plus electroweak results, thus obtaining the most advanced perturbative prediction available to date for the <math><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover><mi>W</mi></math> inclusive cross section. The tension with the latest ATLAS and CMS results remains at the <math><mrow><mn>1</mn><mi>σ</mi><mtext>−</mtext><mn>2</mn><mi>σ</mi></mrow></math> level.

Luca Rottoli

Precise Predictions for the Associated Production of a <math><mi>W</mi></math> Boson with a Top-Antitop Quark Pair at the LHC

We consider extensions of the soft-gluon effective coupling that generalize the Catani-Marchesini-Webber (CMW) coupling in the context of soft-gluon resummation beyond the next-to-leading logarithmic accuracy. Starting from the probability density of correlated soft emission in d dimensions we introduce a class of soft couplings relevant for resummed QCD calculations of hard-scattering observables. We show that at the conformal point, where the d-dimensional QCD β function vanishes, all these effective couplings are equal and they are also equal to the cusp anomalous dimension. We present explicit results in d dimensions for the soft-emission probability density and the soft couplings at the second-order in the QCD coupling α S. In d = 4 dimensions we obtain the explicit relation between the soft couplings at   <math> <mi>O</mi> </math>  $$ \mathcal{O} $$ (  <math> <msubsup> <mi>α</mi> <mi>S</mi> <mn>3</mn> </msubsup> </math>  $$ {\alpha}_{\textrm{S}}^3 $$ ). Finally, we study the structure of the soft coupling in the large-n  F  limit and we present explicit expressions to all orders in perturbation theory. We also check that, at the conformal point, our large-n  F  results agree with the known result of the cusp anomalous dimension.

Stefano Catani

Argentina

Daniel Florian

Soft-gluon effective coupling: perturbative results and the large-n  F  limit to all orders

We consider QCD radiative corrections to the production of a heavy-quark pair in hadronic collisions. We present the computation of the soft-parton contributions at low transverse momentum of the heavy-quark pair up to second order in the QCD coupling α S. These results complete the evaluation at the next-to-next-to-leading order (NNLO) of the transverse-momentum resummation formula for this process. Moreover, they give all the ingredients that are needed for the NNLO implementation of the q  T  subtraction formalism for heavy-quark production. We discuss the details of the computation and we provide a code that can be used to obtain the relevant results in numerical form.

Soft-parton contributions to heavy-quark production at low transverse momentum

We present the first calculation for the hadroproduction of a <math><mi>W</mi></math> boson in association with a massive bottom (<math><mi>b</mi></math>) quark-antiquark pair at next-to-next-to-leading order (NNLO) in QCD perturbation theory. We exploit the hierarchy between the <math><mi>b</mi></math>-quark mass and the characteristic energy scale of the process to obtain a reliable analytic expression for the two-loop virtual amplitude with three massive legs, starting from the corresponding result available for massless <math><mi>b</mi></math> quarks. The use of massive <math><mi>b</mi></math> quarks avoids the ambiguities associated with the correct flavor assignment in massless calculations, paving the way to a more realistic comparison with experimental data. We present phenomenological results considering proton-proton collisions at center-of-mass energy <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>13.6</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math> for inclusive <math><mi>W</mi><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> production and within a fiducial region relevant for the associated production of a <math><mi>W</mi></math> boson and a Higgs boson decaying into a <math><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> pair, for which <math><mi>W</mi><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></math> production represents one of the most relevant backgrounds. We find that the NNLO corrections are substantial and that their inclusion is mandatory to obtain reliable predictions.

Associated production of a <math><mi>W</mi></math> boson and massive bottom quarks at next-to-next-to-leading order in QCD

The associated production of a Higgs boson with a top-antitop quark pair is a crucial process at the LHC since it allows for a direct measurement of the top-quark Yukawa coupling. We present the computation of the radiative corrections to this process at the next-to-next-to-leading order (NNLO) in QCD perturbation theory. This is the very first computation for a <math><mrow><mn>2</mn><mo>→</mo><mn>3</mn></mrow></math> process with massive colored particles at this perturbative order. We develop a soft Higgs boson approximation for loop amplitudes, which enables us to reliably quantify the impact of the yet unknown two-loop contribution. At the center-of-mass energy <math><mrow><msqrt><mrow><mi>s</mi></mrow></msqrt><mo>=</mo><mn>13</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></mrow></math>, the NNLO corrections increase the next-to-leading order result for the total cross section by about 4% and lead to a significant reduction of perturbative uncertainties.

Higgs Boson Production in Association with a Top-Antitop Quark Pair in Next-to-Next-to-Leading Order QCD

We present the two-loop mixed strong-electroweak virtual corrections to the neutral current Drell-Yan process and we provide, as supplementary material, the explicit formulae of the infrared-subtracted finite remainder. The final state collinear singularities are regularised by the lepton mass. The evaluation of all the relevant Feynman integrals, including those with up to two internal massive lines, has been worked out relying on analytical and semi-analytical techniques, in the case of complex-valued masses.

Two-loop mixed QCD-EW corrections to neutral current Drell-Yan

We report on the first fully differential calculation of the next-to-next-to-leading-order (NNLO) QCD radiative corrections to the production of bottom-quark pairs at hadron colliders. The calculation is performed by using the q  T  subtraction formalism to handle and cancel infrared singularities in real and virtual contributions. The computation is implemented in the Matrix framework, thereby allowing us to efficiently compute arbitrary infrared-safe observables in the four-flavour scheme. We present selected predictions for bottom-quark production at the Tevatron and at the LHC at different collider energies, and we perform some comparisons with available experimental results. We find that the NNLO corrections are sizeable, typically of the order of 25–35%, and they lead to a significant reduction of the perturbative uncertainties. Therefore, their inclusion is crucial for an accurate theoretical description of this process.