Weak interactions in top-quark pair production at hadron colliders: An update

Weak corrections for top-quark pair production at hadron colliders are revisited. Predictions for collider energies of 8 TeV, adopted to the recent LHC run, and for 13 as well as 14 TeV, presumably relevant for the next round of LHC experiments, are presented. Kinematic regions with large momentum transfer are identified, where the corrections become large and may lead to strong distortions of differential distributions, thus mimicking anomalous top-quark couplings. As a complementary case we investigate the threshold region, corresponding to configurations with small relative velocity between top and antitop quarks, which is particularly sensitive to the top-quark Yukawa coupling. We demonstrate, that nontrivial upper limits on this coupling, complementary to those recently derived by the CMS and the ATLAS collaborations, are well within reach of ongoing experiments. We, furthermore, suggest a prescription that allows the implementation of these corrections in current Monte Carlo generators. Furthermore, the weak corrections have been included in the publicly available hathor library. The numerical results presented in this article use the same setup as the recently calculated next-to-next-to-leading-order QCD corrections. The results can thus be combined to give the most precise theoretical predictions.

Figure 1

Lowest-order QCD (a)–(d) and weak (e) amplitudes.

Figure 2

Sample diagrams for the virtual corrections to the quark-induced process.

Figure 3

Sample diagrams for the virtual corrections for the gluon-induced process. $\mathrm{\Gamma }$ stands for all contributions from the gauge boson, Goldstone boson and Higgs exchange.

Figure 4

Sample diagrams for the real corrections to the quark-induced process.

Figure 5

Sample diagrams for the proper combination of virtual and real corrections to the quark-induced process. The dotted lines show different cuts corresponding to virtual and real corrections.

Figure 6

Leading-order differential cross section for the LHC (8 TeV) as a function of $p_{\text{T}}$. The lower plot shows the fraction from gluon fusion (red, solid) and the fraction from quark-antiquark annihilation (blue, dashed).

Figure 7

Leading-order differential cross section for the LHC (8 TeV) as a function of $M_{t\overline{t}}$. The lower plot shows the fraction from gluon fusion (red, solid) and the fraction from quark-antiquark annihilation (blue, dashed).

Figure 8

Relative weak corrections at parton level for the quark- and gluon-induced reactions as functions of the squared parton energy $\widehat{s}$ for two characteristic masses of the Higgs boson.

Figure 9

Relative weak corrections for the quark- and gluon-induced reactions as functions of the scattering angle close to threshold ($\sqrt{\widehat{s}}=370\mathrm{GeV}$, solid line) and at high energies ($\sqrt{\widehat{s}}=3\mathrm{TeV}$, dotted line).

Figure 10

Relative weak corrections for the total cross section as functions of the total center-of-mass energy for two different masses of the Higgs boson and for a rescaled Yukawa coupling.

Figure 11

Weak corrections as function of the top-quark mass.

Figure 12

Relative weak corrections for the invariant $t\overline{t}$ mass (left) and transverse momentum (right) distributions for the LHC for Higgs masses of 126 GeV and 1 TeV.

Figure 13

Rapidity distributions with invariant mass cuts at leading order (left) and relative weak corrections (right).

Figure 14

Relative weak corrections for the mass distribution in the framework of the SM assuming $M_H=126\mathrm{GeV}$ (solid blue curve) and 1000 GeV (dashed red curve), and for the case of an enhanced Yukawa coupling $g_Y=2g_Y^{\mathrm{SM}}$ with $M_H=126\mathrm{GeV}$ (dotted black curve).

Figure 15

Same as Fig. 14 but for the Tevatron.

Figure 16

Same as Fig. 6 but for 13 TeV.

Figure 17

Same as Fig. 7 but for 13 TeV.

Figure 18

Same as Fig. 6 but for 14 TeV.

Figure 19

Same as Fig. 7 but for 14 TeV.

Figure 20

Same as Fig. 12 but for 13 TeV.

Figure 21

Same as Fig. 12 but for 14 TeV.

Figure 22

Same as Fig. 13 but for 13 TeV.

Figure 23

Same as Fig. 13 but for 14 TeV.

Figure 24

Same as Fig. 14 but for 13 TeV.

Figure 25

Same as Fig. 14 but for 14 TeV.