Analytic two-loop corrections to top-quark pair production at hadron colliders
Abstract
We present the complete two-loop QCD amplitudes for the production of a top-quark pair in the quark--antiquark annihilation and gluon-fusion channels in analytic form up to order 𝒪(ε2). Our analysis maintains full dependence on the top-quark mass and on the number of colours. The amplitudes are expressed in terms of 417 master integrals, which we compute by means of differential equations in ε-factorised form. Their calculation involves several elliptic curves and a hyperelliptic curve of genus two, which makes top-quark pair production an ideal arena for recent methods to construct canonical bases beyond polylogarithms. To the best of our knowledge, this is the first scattering amplitude in which iterated integrals related to a genus-two surface survive in the finite remainder in four space-time dimensions. We provide high-precision series expansions at the threshold and combine them with the numerical solution of the differential equations in a code that evaluates the UV-renormalised infrared-finite remainders at arbitrary points of the physical phase space.
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BibTeX
@misc{buccioni2026analytic,
title = {{Analytic two-loop corrections to top-quark pair production at hadron colliders}},
author = {Federico Buccioni and Christoph Nega and Benjamin Sauer and Lorenzo Tancredi and Fabian J. Wagner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32543},
eprint = {2610.32543},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32543},
}
RIS
TY - UNPB
TI - Analytic two-loop corrections to top-quark pair production at hadron colliders
AU - Federico Buccioni
AU - Christoph Nega
AU - Benjamin Sauer
AU - Lorenzo Tancredi
AU - Fabian J. Wagner
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32543
UR - https://arxiv.org/abs/2610.32543
AB - We present the complete two-loop QCD amplitudes for the production of a top-quark pair in the quark--antiquark annihilation and gluon-fusion channels in analytic form up to order 𝒪(ε^2). Our analysis maintains full dependence on the top-quark mass and on the number of colours. The amplitudes are expressed in terms of 417 master integrals, which we compute by means of differential equations in ε-factorised form. Their calculation involves several elliptic curves and a hyperelliptic curve of genus two, which makes top-quark pair production an ideal arena for recent methods to construct canonical bases beyond polylogarithms. To the best of our knowledge, this is the first scattering amplitude in which iterated integrals related to a genus-two surface survive in the finite remainder in four space-time dimensions. We provide high-precision series expansions at the threshold and combine them with the numerical solution of the differential equations in a code that evaluates the UV-renormalised infrared-finite remainders at arbitrary points of the physical phase space.
ER -