Electroweak production of top-quark pairs in $e^{+}{e}^{-}$ annihilation at NNLO in QCD: The vector current contributions

We report on a calculation of the vector current contributions to the electroweak production of top quark pairs in $e^{+}{e}^{-}$ annihilation at next-to-next-to-leading order in quantum chromodynamics. Our setup is fully differential and can be used to calculate any infrared-safe observable. The real emission contributions are handled by a next-to-next-to-leading order generalization of the phase-space slicing method. We demonstrate the power of our technique by considering its application to various inclusive and exclusive observables.

Figure 1

Dependence of separate contributions to ${\mathrm{\Delta }}^{(2),\gamma }$ with full colors on the cutoff for different collision energies.

Figure 2

Dependence of $\delta {\mathrm{\Delta }}^{(2),\gamma }$ with full colors on the cutoff and the fitted curves for different collision energies.

Figure 3

Comparison of ${\mathrm{\Delta }}^{(2),\gamma }$ with the threshold results ${\mathrm{\Delta }}_{th}^{(2),\gamma }$ and high-energy expansion results ${\mathrm{\Delta }}_{he}^{(2),\gamma }$ in terms of their absolute values and ratios.

Figure 4

Comparison of different color structures of $R^{(2)}$ with the high-energy expansion $R_{he}^{(2)}$ and Padé approximation $R_{PD}^{(2)}$ in the high-energy region.

Figure 5

Comparison of different color structures of $R^{(2)}$ with the threshold results $R_{\text{th}}^{(2)}$ and Padé approximation $R_{PD}^{(2)}$ in the threshold region.

Figure 6

Scale dependence of ${\mathrm{\Delta }}^{(1),\gamma }$ and ${\mathrm{\Delta }}^{(1),\gamma }+{\mathrm{\Delta }}^{(2),\gamma }$ for different collision energies.

Figure 7

$\mathcal{O}({\alpha }_s)$ and $\mathcal{O}({\alpha }_s^2)$ corrections in different $\cos {\theta }_t$ bins, ${\mathrm{\Delta }}_{\text{bin}}^{(1),\gamma }$ and ${\mathrm{\Delta }}_{\text{bin}}^{(2),\gamma }$ for different collision energies and different ${\delta }_E$ choices.

Figure 8

NLO and NNLO corrections in different $p_{T,t}$ bins, ${\mathrm{\Delta }}_{\text{bin}}^{(1),\gamma }$ and ${\mathrm{\Delta }}_{\text{bin}}^{(2),\gamma }$, for different collision energies and different ${\delta }_E$ choices.

Figure 9

Differential distribution, $d\sigma /d{m}_{t\overline{t}}$ on left, $d\sigma /d{\varphi }_{t\overline{t}}$ on right, at the LO, $\mathcal{O}({\alpha }_s)$ (multiplied by 4), and $\mathcal{O}({\alpha }_s^2)$ (multiplied by 10).