One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}γ$ productions at the LHC through $\mathcal{O}(ε^2)$
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| Format: | Preprint |
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2025
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| _version_ | 1866914566101794816 |
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| author | Bera, Souvik Brancaccio, Colomba Canko, Dhimiter Hartanto, Heribertus Bayu |
| author_facet | Bera, Souvik Brancaccio, Colomba Canko, Dhimiter Hartanto, Heribertus Bayu |
| contents | We present analytic expressions for the one-loop QCD helicity amplitudes contributing to top-quark pair production in association with a photon or a jet at the Large Hadron Collider (LHC), evaluated through $\mathcal{O}(ε^2)$ in the dimensional regularisation parameter, $ε$. These amplitudes are required to construct the two-loop hard functions that enter the NNLO QCD computation. The helicity amplitudes are expressed as linear combinations of algebraically independent components of the $ε$-expanded master integrals--known as pentagon function--with the corresponding rational coefficients written in terms of momentum-twistor variables. We derive differential equations for the pentagon functions and solve them numerically using the generalised power series expansion method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}γ$ productions at the LHC through $\mathcal{O}(ε^2)$ Bera, Souvik Brancaccio, Colomba Canko, Dhimiter Hartanto, Heribertus Bayu High Energy Physics - Phenomenology We present analytic expressions for the one-loop QCD helicity amplitudes contributing to top-quark pair production in association with a photon or a jet at the Large Hadron Collider (LHC), evaluated through $\mathcal{O}(ε^2)$ in the dimensional regularisation parameter, $ε$. These amplitudes are required to construct the two-loop hard functions that enter the NNLO QCD computation. The helicity amplitudes are expressed as linear combinations of algebraically independent components of the $ε$-expanded master integrals--known as pentagon function--with the corresponding rational coefficients written in terms of momentum-twistor variables. We derive differential equations for the pentagon functions and solve them numerically using the generalised power series expansion method. |
| title | One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}γ$ productions at the LHC through $\mathcal{O}(ε^2)$ |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2505.10406 |