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One-loop amplitudes for $\ttj$ and $\ttgamma$ productions at the LHC through $\mathcal{O}(\epsilon^2)$
by Souvik Bera, Colomba Brancaccio, Dhimiter Canko, Heribertus Bayu Hartanto
Submission summary
| Authors (as registered SciPost users): | Dhimiter Canko |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00039v1 (pdf) |
| Code repository: | https://zenodo.org/records/15398292 |
| Data repository: | https://zenodo.org/records/15398292 |
| Date submitted: | Sept. 22, 2025, 12:03 p.m. |
| Submitted by: | Canko, Dhimiter |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
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 $\mathcal{O}(\epsilon^2)$ in the dimensional regularisation parameter, $\epsilon$. 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 $\epsilon$-expanded master integrals, with the corresponding rational coefficients written in terms of momentum-twistor variables. We derive differential equations for the pentagon functions, which enable efficient numerical evaluation via generalised power series expansion method.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
The paper fulfils the necessary criteria to permit a publication in SciPost. Before
recommending the publication, however, I would like the authors to
address my comments below.
Requested changes
On page 14 the authors write that in order to determine the numerical boundary values of the MIs, they evaluate them at an arbitrary point of the physical phase space using AMFLOW with 70-digit precision.
Could the authors explain why such precision is needed? Wouldn't 34-digits precision, for example, be sufficient? What is the final precision the authors are aiming for here?
Small typos I found: - page 3 after citations [72–76] of a calculation --> for a calculation - Eq (54) a full stop at the end of a sentence is missing - Eq (55) should be a full stop instead of a comma - Eq (57) should be a comma instead of a full stop
I would suggest that you check all punctuation marks in the paper.
Recommendation
Ask for minor revision
Strengths
2-Timeliness.
Weaknesses
2-Lack of relevant details.
Report
One-loop amplitudes for these processes are already implemented in automated tools such as OpenLoops, and NLO predictions have been available for some time. However, the purpose of this article is not to provide new phenomenologically usable one-loop results, but rather to probe the complexity and prepare the ground for the challenging two-loop computation. For this reason, the Laurent expansion around $\epsilon = 0$, where $\epsilon$ is the dimensional regulator, is truncated at order $\epsilon^2$ to supply the terms needed for the subtraction of poles at two loops. Similar studies have been published for $t\bar{t}$ production in association with a Higgs and a $W$ boson.
Owing to the phenomenological relevance of these processes, the growing attention they are receiving, and the complexity of the two-loop computations, I believe this article would satisfy SciPost’s acceptance criteria, provided that the authors address the points of criticism listed in the attachment.
Requested changes
The list of requested changes is rather lengthy, hence I give it in the attachment for better formatting.
Recommendation
Ask for minor revision