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 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.