SciPost Submission Page
Structure of non-global logarithms with Cambridge/Aachen clustering
by Kamel Khelifa-Kerfa
Submission summary
| Authors (as registered SciPost users): | Kamel Khelifa-Kerfa |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202511_00053v1 (pdf) |
| Date submitted: | Nov. 22, 2025, 12:33 p.m. |
| Submitted by: | Kamel Khelifa-Kerfa |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Computational, Phenomenological |
The author(s) disclose that the following generative AI tools have been used in the preparation of this submission:
Help in writing the python code
Proofreading the manuscript
Abstract
We determine the structure of both Abelian and non-Abelian non-global logarithms up to four loops for e+e− processes in perturbative QCD, where final-state jets are defined using the Cambridge-Aachen (C/A) clustering algorithm. The calculations are performed within the soft (eikonal) approximation using strong-energy ordering of the final-state partons. The resulting expressions include full colour and complete jet-radius dependence. Compared to the anti-kt and kt clustering algorithms, the C/A distribution minimises the impact of these non-global logarithms, making it the preferred choice among the three algorithms.
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
Strengths
1- The paper provides a systematic account of the single logarithmic structure of the e+e- di-jet squared invariant mass spectrum up to 4-loops, where the jets are clustered using C/A clustering.
2- The results are discussed carefully and put into the context of prior work on both the kt and anti-kt clustered variants of the observable. It is demonstrated that, within the computation of the C/A clustered observable, both the kt and anti-kt clustered variants can also be found.
3- Presently, this is the only result of its kind: a full colour calculation of C/A clustering and its non-global logarithms at fourth order. It is likely that this result will be useful for the benchmarking of future event generators, both traditional parton showers and the full-colour event generators currently under development.
4- Building on the similarities to the kt and anti-kt clustered variants of the observable, the all-orders structure is postulated.
Weaknesses
1- The paper largely builds on the work in reference [31]. Whilst this is the first time the approach has been applied to C/A clustering, there is not much additional insight to be found beyond what is already in [31]. Indeed, the observation that the computation of the C/A clustered observable contains both the kt and anti-kt variants directly mirrors the results of [31], wherein it was already noted that the kt variant similarly contains the anti-kt variant. The scope, novelty, and appeal of this paper are therefore quite narrow.
Report
I believe this work is meets the threshold for publication. It does motivate a path towards more reliable predictions for non-global and clustering logarithms by studying the C/A clustering. Additionally, the results of this work will be suitable benchmarks for future studies of these logarithms. However, these studies will likely not be follow-up work arising directly from this paper, but rather independent research programs. From the conclusions of this paper: "Developing an integro-differential equation similar to that of Banfi, Marchesini, and Smye, or a computational code analogous to that of Dasgupta and Salam that incorporates C/A clustering, would constitute a major step toward a deeper and more insightful understanding of how complex jet algorithms reshape the impact of non-global logarithms." I agree with this statement. However, this work does not directly lead in that direction; rather, it would provide a cross-check of the final result.
I recommend this work for publication with some small edits.
Requested changes
1- I think it is important to discuss in the abstract the observable for which these logarithms are computed, particularly the di-jet invariant mass. It is not clear to me that the results in this paper would be relevant to other jet observables computed with the C/A clustering.
2- The author seems to overlook recent developments in the full colour resummation of observables using numerical codes for amplitude evolution. I think the work in this paper could provide a valuable cross-check of these developments. Similarly, I think the full resummation of these logarithms will be most readily achieved within these existing frameworks. Of most relevance are citations 2505.13183 and 2502.12133; however, cross-checking the Deductor framework 0706.0017, 1705.08093 would also be interesting.
3- The lNc curve in the bottom right of Fig. 9 should closely approximate the result from a LC NLL accurate dipole shower, such as those by Panscales with CF=CA/2. The author might wish to include a reference to this.
4- The colour schemes and line choices in the final figures are difficult to read. Particularly awkward is Fig. 9, where it is odd that the 2-loop and 4-loop curves are dashed but the 3-loop curve is solid. Fig. 8 also changes colour for the 2-loop, 3-loop, and 4-loop curves only in the bottom-left panel. I would request that the author consider a more consistent and clear colour scheme between panels and figures.
Recommendation
Ask for minor revision
Strengths
- It provides a fixed-order calculation of both non-global (NGLs) and clustering logarithms (CLs) up to 4 loops for the single-jet mass in the Cambridge/Aachen (C/A) algorithm.
- A comparison with existing results for the kt and anti-kt algorithm is diligently carried out. This shows that both NGLs and CLs are reduced for the C/A algorithm.
Weaknesses
The main weakness is that this is a fixed-order calculation. In the large-Nc limit 1. The all-order resummation of these effects could have been obtained with a simple modification of the GNOLE program, publicly available at https://github.com/non-global/gnole 2. Similarly, GNOLE could have given access to the fixed-order coefficients computed here, at least in the large-Nc limit.
Report
Requested changes
I suggest two minor changes: 1. In eq. (11), Um is a product of individual sources, and not a sum 2. In eq. (23), there are four kinds of contributions, labelled a, b, c, d. In the proximity of the equation, there is no mention of the meaning of these labels. Their definition should also be recalled in Fig. 6.
Recommendation
Ask for minor revision
Author: Kamel Khelifa-Kerfa on 2026-01-08 [id 6217]
(in reply to Report 1 on 2026-01-05)We thank the referee for the insightful comments and valuable suggestions. Below we list our responses and the changes made to the manuscript:
1/ Equation (11) has been corrected. 2/ A sentence clarifying the four terms appearing in Equation (23) has been added immediately below that equation. 3/ Regarding Gnole, we plan to investigate implementing both the k_t and C/A algorithms. If successful (even if only in the large-Nc limit), this will constitute an important addition to the non-global community: it would enable automated resummation of non-global logarithms up to NL–NGLs for various jet algorithms, a capability not currently available in the literature.