Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
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arXiv
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| Format: | Preprint |
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2025
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| author | Becchetti, Matteo Canko, Dhimiter Chestnov, Vsevolod Peraro, Tiziano Pozzoli, Mattia Zoia, Simone |
| author_facet | Becchetti, Matteo Canko, Dhimiter Chestnov, Vsevolod Peraro, Tiziano Pozzoli, Mattia Zoia, Simone |
| contents | We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a $W$ boson at hadron colliders in the leading colour approximation. These Feynman integrals also contribute to Higgs or $Z$-boson production in association with a top pair. We employ the method of differential equations (DEs), facilitated by the use of finite field methods to handle the algebraic complexity stemming from the seven-scale kinematics. The presence of the top quark in the virtual propagators, in addition to the mass of the external $W$ boson, gives rise to nested square roots and three elliptic curves. We obtain DEs that depend at most quadratically on the dimensional regulator $ε$ for sectors where these analytic structures appear, and are $ε$-factorised otherwise. We express the DEs in terms of a minimal set of differential one-forms, separating the logarithmic ones. We solve the DEs numerically in the physical kinematic region, with the method of generalised power series expansions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13011 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders Becchetti, Matteo Canko, Dhimiter Chestnov, Vsevolod Peraro, Tiziano Pozzoli, Mattia Zoia, Simone High Energy Physics - Phenomenology High Energy Physics - Theory We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a $W$ boson at hadron colliders in the leading colour approximation. These Feynman integrals also contribute to Higgs or $Z$-boson production in association with a top pair. We employ the method of differential equations (DEs), facilitated by the use of finite field methods to handle the algebraic complexity stemming from the seven-scale kinematics. The presence of the top quark in the virtual propagators, in addition to the mass of the external $W$ boson, gives rise to nested square roots and three elliptic curves. We obtain DEs that depend at most quadratically on the dimensional regulator $ε$ for sectors where these analytic structures appear, and are $ε$-factorised otherwise. We express the DEs in terms of a minimal set of differential one-forms, separating the logarithmic ones. We solve the DEs numerically in the physical kinematic region, with the method of generalised power series expansions. |
| title | Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2504.13011 |