Top Quark Pair Production beyond NNLO

TL;DR

This work develops an approximate $N^3$LO prediction for heavy-quark pair production in hadron collisions by leveraging the Mellin-space analytic structure of the cross section and combining soft-gluon (large-$N$) with high-energy (small-$N$) resummations. The method extends an approach previously used for Higgs production, addressing the more complex color and kinematic structure of heavy-quark production and validating against known NNLO results. The resulting $N^3$LO approximation increases the LHC top-pair cross section by about 4% relative to NNLO and reduces scale uncertainties, providing a practical, high-precision tool for phenomenology and PDF fits. The study carefully treats unphysical momentum-space singularities, Coulomb effects, and momentum-conservation constraints, delivering both parton- and hadron-level predictions with quantified uncertainties.

Abstract

We construct an approximate expression for the total cross section for the production of a heavy quark-antiquark pair in hadronic collisions at next-to-next-to-next-to-leading order (N$^3$LO) in $α_s$. We use a technique which exploits the analyticity of the Mellin space cross section, and the information on its singularity structure coming from large N (soft gluon, Sudakov) and small N (high energy, BFKL) all order resummations, previously introduced and used in the case of Higgs production. We validate our method by comparing to available exact results up to NNLO. We find that N$^3$LO corrections increase the predicted top pair cross section at the LHC by about 4% over the NNLO.

Figures (9)

• Figure 1: The contributions to $C(N)$ from soft gluon emission $\exp\left[G_{\mathbf{I}}(N,\alpha_s)\right]$ (Sudakov terms) and Coulomb terms $J_{\mathbf{I}}(N,\alpha_s)$ (Coulomb terms), at NLO (left) and NNLO (right). The combined effect Eq. \ref{['eq:finalfact0']} is also shown (Complete soft approximation).
• Figure 2: Same as Fig. \ref{['fig:confrontoCoulombSoft1']} but at N$^3$LO. The two different Coulomb curves differ by the inclusion of the pNRQCD estimate of $J_{\mathbf{I}}^{$3$}$ (see text).
• Figure 3: Position of the saddle point as a function of $\sqrt{s}$ for fixed top quark mass.
• Figure 4: Comparison between exact results and our approximation at NLO (left) and NNLO (right) for the Mellin-space coefficient function $C(N)$; the large-$N$ contribution (A-soft) Eq.(\ref{['eq:softapp']}), the small-$N$ contribution (high-energy) Eq.(\ref{['eq:HE']}), and the combined approximation of Eq. \ref{['eq:approx']} (approx) are shown. The bottom plots show the ratio of the approximate to the exact result.
• Figure 5: Same as Fig. \ref{['fig:NLONNLO']}, but at N$^3$LO.