Electroweak prodution of top-quark pairs in e+e- annihilation at NNLO in QCD: the vector contributions

TL;DR

This work delivers a fully differential NNLO QCD calculation for the vector-current component of e+e- -> ttbar, using a generalized phase-space slicing approach that separates the cross section into soft-virtual and hard parts. The soft-virtual piece is factorized into a hard function derived from the heavy-quark vector form factor and a soft function built from Wilson lines within HQET, enabling a differential radiation-energy distribution. The hard part is computed with NLO subtraction techniques and automated one-loop tools, yielding an IR-finite, fully differential result that agrees with known threshold and high-energy limit predictions. The numerical study demonstrates reduced scale uncertainties at NNLO and provides inclusive and differential distributions (cosθ_t, p_T,t, etc.), establishing a practical framework for precise predictions of top-quark production at future e+e- colliders and setting the stage for incorporating Z-exchange and broader NNLO applications.

Abstract

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.

Figures (10)

• Figure 1: Dependence of separate contributions to $\Delta^{(2),\gamma}$ with full colors on the cut-off for different collision energies.
• Figure 2: Dependence of $\delta \Delta^{(2),\gamma}$ with full colors on the cut-off and the fitted curves for different collision energies.
• Figure 3: Comparison of $\Delta^{(2),\gamma}$ with the threshold results $\Delta^{(2),\gamma}_{th}$ and high-energy expansion results $\Delta^{(2),\gamma}_{he}$ in the threshold, transition, and high-energy region.
• Figure 4: Comparison of different color contributions of $R^{(2)}$ with the threshold results $R^{(2)}_{th}$ and high-energy expansion results $R^{(2)}_{he}$ in the threshold region.
• Figure 5: Comparison of different color contributions of $R^{(2)}$ with the threshold results $R^{(2)}_{th}$ and high-energy expansion results $R^{(2)}_{he}$ in the high-energy region.