We calculate higher-order soft-gluon corrections for the associated production of a top-antitop quark pair and a Z boson (<math><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>Z</mi></math> production) in proton-proton collisions. We find that these corrections are numerically dominant and large. We present approximate NNLO (aNNLO) and approximate N$^{3}$LO (aN$^{3}$LO) cross sections that add, respectively, second-order and third-order soft-gluon corrections to the exact NLO QCD result. We also add electroweak (EW) corrections through NLO. We estimate uncertainties that arise from scale dependence, which are smaller at higher orders, and from parton distribution functions. We compare our aN$^{3}$LO QCD + NLO EW theoretical results to measurements of <math><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>Z</mi></math> cross sections from the LHC and find good agreement. We also calculate single-particle-inclusive differential distributions in top-quark transverse momentum and rapidity.

United States

Nikolaos Kidonakis

Chris Foster

Higher-order soft-gluon corrections for Cross Sections

We calculate the complete soft-gluon corrections for the production of colorless final states through N3LO in single-particle-inclusive kinematics. We present explicit analytical results and use them to study higher-order QCD corrections for the production of a heavy charged Higgs pair (H + H  − ) via quark-antiquark annihilation in the Two-Higgs-Doublet Model at LHC energies. We calculate the NNLO soft-gluon and virtual QCD corrections as well as the N3LO soft-gluon corrections to the total cross section and the charged-Higgs rapidity distribution. This is the first calculation of complete N3LO soft-gluon corrections for a process in single-particle-inclusive kinematics, and the results can be applied to other processes with colorless final states.

Alberto Tonero

N3LO soft-gluon corrections in single-particle-inclusive kinematics and H + H  −  production

We study higher-order QCD corrections for the production of a top–antitop quark pair ( $$t{{\bar{t}}}$$  <math> <mrow> <mi>t</mi> <mover> <mrow> <mi>t</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   production) at the Large Hadron Collider in the Standard Model Effective Field Theory. We consider effects of new physics parametrized by the top-quark chromomagnetic dipole operator. We calculate new physics contributions to the total cross section at approximate NNLO, with second-order soft-gluon corrections added to the complete NLO result, including uncertainties from scale dependence and from parton distributions. We also calculate new physics contributions at approximate NNLO for differential distributions in top-quark transverse momentum.

SMEFT chromomagnetic dipole operator contributions to  $$t{{\bar{t}}}$$  <math> <mrow> <mi>t</mi> <mover> <mrow> <mi>t</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math>   production at approximate NNLO in QCD

We study higher-order QCD corrections for the associated production of a top-antitop quark pair and a W boson (<math><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>W</mi></math> production) in proton-proton collisions. We calculate approximate NNLO (aNNLO) and approximate N$^{3}$LO (aN$^{3}$LO) cross sections, with second-order and third-order soft-gluon corrections added to the exact NLO QCD result, and we also include electroweak (EW) corrections through NLO. We calculate uncertainties from scale dependence, which are reduced at higher orders, and from parton distributions, and we also provide separate results for <math><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mi>W</mi></mrow><mrow><mo>+</mo></mrow></msup></math> and <math><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><msup><mrow><mi>W</mi></mrow><mrow><mo>−</mo></mrow></msup></math> production. We compare our results to recent measurements from the LHC, and we find that the aN$^{3}$LO QCD + NLO EW predictions provide improved agreement with the data. We also calculate differential distributions in top-quark transverse momentum and rapidity and find significant enhancements from the higher-order corrections. This is the first calculation of soft-gluon corrections in single-particle-inclusive kinematics for a <math><mn>2</mn><mo>→</mo><mn>3</mn></math> process where all final-state particles are massive.

Soft-gluon corrections in Production

We present theoretical predictions for top-quark total cross sections and for differential distributions in top-quark transverse momentum and rapidity. Third-order soft gluon corrections are added to the complete NNLO quantities to provide approximate <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math> (<math><mrow><mi>a</mi><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></mrow></math>) results, and electroweak corrections at NLO are also included. We calculate the theoretical uncertainties from scale dependence and from parton distribution functions in the proton, and estimate their impact on the total and differential cross sections. The higher-order corrections are large, and they reduce the scale uncertainties. The results presented in this work include the best current theoretical input and are in good agreement with recent data from the LHC.

Marco Guzzi

Top-quark cross sections and distributions at approximate <math><mrow><msup><mrow><mi>N</mi></mrow><mrow><mn>3</mn></mrow></msup><mi>LO</mi></mrow></math>

We study soft-gluon corrections for the associated production of a single top quark and a Z boson (tqZ production) at hadron colliders. We find that the radiative corrections are dominated by soft-gluon emission. We derive an approximate NNLO (aNNLO) cross section by adding second-order soft-gluon corrections to the exact NLO result. We calculate the aNNLO cross section at LHC energies, including uncertainties from scale dependence and from parton distributions. We also calculate differential distributions in top-quark rapidity. We show that the aNNLO corrections are significant and they enhance the NLO cross section while decreasing theoretical uncertainties.

Japan

Nodoka Yamanaka

Soft-gluon corrections for Production

I present a general method for determining the massive cusp anomalous dimension in QCD to a very high degree of accuracy using its asymptotic behavior at small and large quark velocities. I show that the method works exceedingly well at two and three loops where exact results are already known. I then present a calculation of the massive cusp anomalous dimension using its asymptotics at four loops, and I provide a detailed study of the results for different values of the number of flavors and for separate color structures. The method can be further extended and applied to higher numbers of loops.

Four-loop massive cusp anomalous dimension in QCD: A calculation from asymptotics

We study higher-order QCD corrections for the associated production of a top-antitop quark pair and a photon (<math><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover><mi>γ</mi></math> production) in proton-proton collisions. We calculate the approximate next-to-next-to-leading order cross section, with second-order soft-gluon corrections added to the complete next-to-leading order result, including uncertainties from scale dependence and from parton distributions. We compare our results to recent measurements from the LHC, and find that the soft-gluon corrections provide improved agreement with the data. We also calculate differential distributions in top-quark transverse momentum and rapidity.

Higher-order corrections in <math><mi>t</mi><mover><mi>t</mi><mo>¯</mo></mover><mi>γ</mi></math> cross sections

We study QCD corrections for the associated production of a single top quark and a photon ( $$tq\gamma $$  <math> <mrow> <mi>t</mi> <mi>q</mi> <mi>γ</mi> </mrow> </math>   production) at hadron colliders. We calculate the NLO cross section at LHC and future collider energies for a variety of kinematical cuts, and we estimate uncertainties from scale dependence and from parton distributions. We also calculate differential distributions in top-quark transverse-momentum and rapidity as well as photon energy. Finally, we study higher-order corrections from soft-gluon emission for this process, and we provide approximate NNLO (aNNLO) results for the cross section and top-quark differential distributions. We also compare our calculations with recent measurements from CMS and ATLAS at the LHC and find that the aNNLO corrections improve the comparison between the data and the Standard Model predictions.

QCD corrections in  $$tq\gamma $$  <math> <mrow> <mi>t</mi> <mi>q</mi> <mi>γ</mi> </mrow> </math>   production at hadron colliders

We discuss soft-gluon resummation for the associated production of a single top quark and a Higgs boson (<math><mi>t</mi><mi>q</mi><mi>H</mi></math> production) in single-particle-inclusive kinematics. We present analytical results for the higher-order corrections and numerical results for the cross sections at LHC energies. We calculate approximate next-to-next-to-leading-order total rates, including scale dependence and uncertainties from parton distributions, as well as top-quark transverse-momentum and rapidity distributions. In all cases we find that the soft-gluon corrections are dominant and provide important contributions to the total and differential cross sections.