Two-loop integrals for tt̅γ production at hadron colliders in the leading-colour approximation
Abstract
We complete the calculation of the two-loop Feynman integrals required for the next-to-next-to-leading order QCD corrections to on-shell top--antitop production in association with a photon at hadron colliders, in the leading-colour approximation. The same integrals also enter the subleading-colour corrections to top--antitop production in association with a jet. We construct integral bases that satisfy algebraic differential equations. These are largely in canonical form; the exceptions are a few entries, associated with elliptic curves or nested square roots, that depend at most quadratically on the dimensional regulator ε. We solve the differential equations in terms of a tailored set of special functions, which will enable the analytic extraction of the two-loop finite remainder. We evaluate these functions by numerically solving the differential equations they satisfy, and show that the resulting routine is fast and stable enough in the physical region for phenomenological applications.
Related
- Two-loop amplitude for the associated production of a top-anti-top pair and a W boson at hadron colliders
- Analytic two-loop corrections to top-quark pair production at hadron colliders
- Antenna subtraction at NNLO for heavy quark pair production at hadron colliders: the non-diagonal channels
- Two-loop QCD amplitudes for tt̅W production at the LHC in the leading-colour approximation
- Probing the proton structure with minimum bias and low-pt dimuon events at hadron colliders
BibTeX
@misc{bera2026twoloop,
title = {{Two-loop integrals for $t\bartγ$ production at hadron colliders in the leading-colour approximation}},
author = {Souvik Bera and Colomba Brancaccio and Dhimiter Canko and Federico Ripani and Simone Zoia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42062},
eprint = {2610.42062},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42062},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Two-loop integrals for tt̅γ production at hadron colliders in the leading-colour approximation
AU - Souvik Bera
AU - Colomba Brancaccio
AU - Dhimiter Canko
AU - Federico Ripani
AU - Simone Zoia
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42062
UR - https://arxiv.org/abs/2610.42062
AB - We complete the calculation of the two-loop Feynman integrals required for the next-to-next-to-leading order QCD corrections to on-shell top--antitop production in association with a photon at hadron colliders, in the leading-colour approximation. The same integrals also enter the subleading-colour corrections to top--antitop production in association with a jet. We construct integral bases that satisfy algebraic differential equations. These are largely in canonical form; the exceptions are a few entries, associated with elliptic curves or nested square roots, that depend at most quadratically on the dimensional regulator ε. We solve the differential equations in terms of a tailored set of special functions, which will enable the analytic extraction of the two-loop finite remainder. We evaluate these functions by numerically solving the differential equations they satisfy, and show that the resulting routine is fast and stable enough in the physical region for phenomenological applications.
ER -