Two-loop integrals for $t \bar{t} +$jet production at hadron colliders in the leading colour approximation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911859332874240 |
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| author | Badger, Simon Becchetti, Matteo Giraudo, Nicolò Zoia, Simone |
| author_facet | Badger, Simon Becchetti, Matteo Giraudo, Nicolò Zoia, Simone |
| contents | We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for $pp \rightarrow t\bar{t}j$. We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical '${\rm d} \log$' form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically on $ε$ and contains non-logarithmic one-forms in addition to the canonical ${\rm d} \log$'s. We solve the systems of differential equations numerically using generalised series expansions with the boundary terms obtained using the auxiliary mass flow method. A summary of all one-loop and two-loop planar topologies is presented including the list of alphabet letters for the '${\rm d} \log$' form systems and high-precision boundary values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12325 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-loop integrals for $t \bar{t} +$jet production at hadron colliders in the leading colour approximation Badger, Simon Becchetti, Matteo Giraudo, Nicolò Zoia, Simone High Energy Physics - Phenomenology High Energy Physics - Theory We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for $pp \rightarrow t\bar{t}j$. We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical '${\rm d} \log$' form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically on $ε$ and contains non-logarithmic one-forms in addition to the canonical ${\rm d} \log$'s. We solve the systems of differential equations numerically using generalised series expansions with the boundary terms obtained using the auxiliary mass flow method. A summary of all one-loop and two-loop planar topologies is presented including the list of alphabet letters for the '${\rm d} \log$' form systems and high-precision boundary values. |
| title | Two-loop integrals for $t \bar{t} +$jet production at hadron colliders in the leading colour approximation |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.12325 |