SciPost Submission Page
Advances in Local Analytic Sector Subtraction: massive NLO and elements of NNLO automation
by Gloria Bertolotti, Giovanni Limatola, Paolo Torrielli, and Sandro Uccirati
Submission summary
| Authors (as registered SciPost users): | Gloria Bertolotti |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202511_00066v1 (pdf) |
| Date submitted: | Nov. 25, 2025, 7:39 p.m. |
| Submitted by: | Gloria Bertolotti |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
In this article we present a number of developments within the scheme of Local Analytic Sector Subtraction for infrared divergences in QCD. First, we extend the scheme to deal with next-to-leading-order (NLO) singularities related to massive QCD particles in the final state. Then, we document a new implementation of the NLO subtraction scheme in the MadNkLO automated numerical framework, which is constructed to host higher-order subtraction algorithms. In particular, we discuss improvements in its performances with respect to the original implementation. Finally we describe the MadNkLO implementation of the first elements relevant to Local Analytic Sector Subtraction at next-to-next-to-leading order (NNLO), in the case of massless QCD partons in the final state.
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:
Awaiting resubmission
Reports on this Submission
Report
The manuscript “Advances in Local Analytic Sector Subtraction: massive NLO and elements of
NNLO automation” by G. Bertolotti, G. Limatola, P. Torrielli, and S. Uccirati presents a number of
developments of the Local Analytic Sector Subtraction (LASS) scheme, one of the more recent
approaches for handling infrared divergences in higher-order perturbative calculations in quantum
field theory.
The paper is generally well written and clearly presented, and the results discussed are technically
sound and uncontroversial. However, in its current form the manuscript exhibits several conceptual
and structural weaknesses that, in my view, prevent it from meeting the standards required for
publication. I therefore recommend major revision prior to further consideration. Below I outline
these issues in more detail, together with suggestions that I believe could substantially strengthen
the paper.
As it stands, the manuscript reads as a collection of relatively small and largely independent
advances, which are not sufficiently integrated into a coherent narrative. Individually, the presented
results do not appear strong enough to warrant publication, and their combination in the present
form does not sufficiently enhance their overall impact.
More specifically, the paper is divided into two main parts: Section 2, which discusses the extension
of the LASS scheme at NLO to processes involving massive particles, and Section 3, which focuses
on progress towards automating LASS within the MadNkLO numerical framework.
The first part of the paper addresses the treatment of infrared divergences at NLO in the presence
of massive and massless emitters. This problem has been well understood for at least two decades,
and established solutions already exist in the literature. While extending LASS to the massive case
is a necessary and important step, the material presented here appears largely incremental.
Subsections 2.2 and 2.3 mainly review momentum mappings that are already well known at NLO.
Subsection 2.4, which discusses the analytic integration of the massive eikonal current, is the most
original contribution of this section. Nevertheless, given the current state of the art, this calculation
remains relatively straightforward in isolation.
Section 3 shifts focus to technical aspects of the numerical implementation of LASS within the
MadNkLO framework. While such developments are important, this section appears somewhat
disconnected from the earlier parts of the paper. The NNLO results are limited to the simplest
partonic channel of the simplest process, and only the scaling behaviour of infrared limits is shown.
While this is a necessary validation step, it does not yet constitute a novel physical result.
I suggest reorganizing the paper by perturbative order, with a first part devoted to NLO and a
second part to NNLO. The NLO section should integrate the massive extension with the numerical
implementation and include more quantitative comparisons of numerical performance. The NNLO
section should be expanded to include either differential distributions or more complex partonic
channels, or clearly state current limitations. See the "requested changes" part for a more detailed explanation.
With revisions along these lines, the manuscript could reach the standard required for publication in
SciPost. I therefore recommend resubmission after major revision.
NNLO automation” by G. Bertolotti, G. Limatola, P. Torrielli, and S. Uccirati presents a number of
developments of the Local Analytic Sector Subtraction (LASS) scheme, one of the more recent
approaches for handling infrared divergences in higher-order perturbative calculations in quantum
field theory.
The paper is generally well written and clearly presented, and the results discussed are technically
sound and uncontroversial. However, in its current form the manuscript exhibits several conceptual
and structural weaknesses that, in my view, prevent it from meeting the standards required for
publication. I therefore recommend major revision prior to further consideration. Below I outline
these issues in more detail, together with suggestions that I believe could substantially strengthen
the paper.
As it stands, the manuscript reads as a collection of relatively small and largely independent
advances, which are not sufficiently integrated into a coherent narrative. Individually, the presented
results do not appear strong enough to warrant publication, and their combination in the present
form does not sufficiently enhance their overall impact.
More specifically, the paper is divided into two main parts: Section 2, which discusses the extension
of the LASS scheme at NLO to processes involving massive particles, and Section 3, which focuses
on progress towards automating LASS within the MadNkLO numerical framework.
The first part of the paper addresses the treatment of infrared divergences at NLO in the presence
of massive and massless emitters. This problem has been well understood for at least two decades,
and established solutions already exist in the literature. While extending LASS to the massive case
is a necessary and important step, the material presented here appears largely incremental.
Subsections 2.2 and 2.3 mainly review momentum mappings that are already well known at NLO.
Subsection 2.4, which discusses the analytic integration of the massive eikonal current, is the most
original contribution of this section. Nevertheless, given the current state of the art, this calculation
remains relatively straightforward in isolation.
Section 3 shifts focus to technical aspects of the numerical implementation of LASS within the
MadNkLO framework. While such developments are important, this section appears somewhat
disconnected from the earlier parts of the paper. The NNLO results are limited to the simplest
partonic channel of the simplest process, and only the scaling behaviour of infrared limits is shown.
While this is a necessary validation step, it does not yet constitute a novel physical result.
I suggest reorganizing the paper by perturbative order, with a first part devoted to NLO and a
second part to NNLO. The NLO section should integrate the massive extension with the numerical
implementation and include more quantitative comparisons of numerical performance. The NNLO
section should be expanded to include either differential distributions or more complex partonic
channels, or clearly state current limitations. See the "requested changes" part for a more detailed explanation.
With revisions along these lines, the manuscript could reach the standard required for publication in
SciPost. I therefore recommend resubmission after major revision.
Requested changes
I believe that with some modifications and rearrangement the paper can still meet the threshold for publication. I suggest some changes below:
- The weakest part of the paper is the lack of a coherent narrative, since the first part deals with more theoretical developments on the NLO massive side, and the second part gives details on the numerical implementation and focuses more on the massless NNLO case. My suggestion is, instead of organizing the paper into massive NLO + massless NNLO, to have a first part on NLO and a second part on NNLO. The first part would include a recap of the LASS scheme at NLO together with the extension to the massive case and together with the numerical implementation which is currently reported in Section 3.1 (the comparison with standard FKS). In this respect, I also suggest to further investigate how the updated numerical implementation compares at NLO to the other well-established subtraction method, I.e. Catani-Seymour. Since LASS is a sort of hybrid between FKS and CS, the comparison with both could be even more instructive. Moreover, at the end of section 3.1 the authors say that MadNkLO turns out to be more stable than aMC@NLO and that Figs 2,3 were obtained using only a fraction of PS points yielding therefore a shorter runtime. I suggest to be more specific here since the numerical performance is a big chunk of this paper. Can you be more quantitative? e.g. exactly how many PS points compared to Madgraph and exact comparison of runtime? When discussing the extension of the NLO part to the massive case and in particular when discussing pole cancellation, I think it would be good to show explicit final formulas, even at the cost of repeating formulas already given in previous papers. The fact that LASS is fully analytic and chooses smart counterterms is a strength of this scheme and should be emphasised wherever possible.
2.Having dealt with the NLO part, the second part of the paper can then focus on the NNLO refinements. I believe here the main formulas from previous papers can be reported briefly before presenting numerical results. I believe that the numerical part for the NNLO case should be extended. In particular, I would suggest to complete the study for the e+e- -> qqb q’ qb’ to show not only the scaling of the limits but also some distributions at least for the double real channels. Even if that is still not a physical results, it shows that the method is in principle capable of producing such results. Alternatively, I would show at least the present study for another (perhaps more intricate) partonic channels (e.g. the full gluonic one). If none of the suggested extensions is possible at the moment, I suggest to clearly state in the text what the limitations are in the technology and what still needs to be overcome in order to produce final results for this process.
Recommendation
Ask for major revision
Report
The paper presents developments related to the treatment of implicit infrared divergences arising in the computation of differential observables calculated beyond leading order in fixed order perturbative QCD. The issues are addressed in the context of the subtraction scheme called : Local analytic Sector subtraction.
It is the third paper of this kind, following Refs.[52,53] with partly the same list of authors, and with the results derived in this paper building up on the ingredients presented in those previous publications.
To set the context, in Ref. [52], this subtraction framework was presented with the scope of handling infrared divergences arising at NLO level from the presence of massless initial or final state partons while in [53], a set of expressions needed at NNLO for generic coloured massless final states were constructed within this framework, with the claim that those could be implemented in any numerical code computing differential
cross sections measured at high energy particle colliders.
The main outcomes of this paper are :
a) As described in section 2, the extension of the formalism to treat the infrared behaviour of cross sections computed at NLO due to the presence of massive final states, the implementation in the existing (from Ref. [52]) MAdNLO framework and code and the validation of the latter code using results obtained with the MADGRAPH_5_aMC_NLO package, Refs [64,65], for 2-jet and heavy-quark pair production , with QCD radiation arising from final state particles only.
b) As described in section 3, the implementation of elements required at NNLO in QCD in the MAdNLO code for one specific double real channel related to di-jet production in electron-positron annihilation.
As stated by the authors themselves in the introduction, NLO is a solved problem since the 90’s and predictions computed at NNLO level are becoming the standard: 2 -> 2 at NNLO has been computed for a variety of processes involving more and more complex final states. These differential predictions are obtained implementing well-established NNLO methods with ingredients based on known factorisation properties of QCD amplitudes in soft or collinear limits, and using parton-level event generators, allowing a direct comparison with data. The latter lead in the past decades to more and more precise determinations of fundamental parameters of the Standard Model theory, like the strong coupling or a better understanding of the parton content of the proton. For a recent review on the state-of the art precision attained in perturbative QCD predictions nowadays, and a presentation of well-established methods allowing the computation of NNLO-type differential predictions, for lepton and hadron collider observables, see for example, the Les Houches Report 2023, [arXiv:2504.06689].
Compared to the current knowledge of radiative corrections included in computations as reported in the mentioned report, and leading to increasingly precise theoretical predictions, in this paper, only partial results with limited phenomenological impact are presented:
The authors claim that the submitted manuscript meet the expectation (2):
Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work.
The relevance at NNLO level of these results is however very limited and the potential of the developments as basis for multi-pronged follow-up work is not enough convincingly demonstrated: Only the construction at double-real level is probed (cf. outcome b) as above).
To satisfy the expectation (2) the other classes of contributions present at real-virtual and double-virtual levels and constructed by the authors themselves in Ref. [53], need to be implemented in the MAdNLO code too, in order to compute physical observables for specific processes and comparing those with existing results in the literature employing other well-established NNLO methods.
Furthermore, following the general acceptance criterium, the paper should provide citations to the relevant literature in a way that is as representative and as complete as possible:
This required acceptance criterium is not satisfied here, specially not for the relevant literature dealing with the current state of the art for predictions related to heavy quark pair production.
At NLO, the formalism was elaborated more than twenty years ago as an extension of the massless dipole formalism and mentioned here as Refs. [61,62]. There here is no mentioning in this paper of developments nor of existing computations of observables at NNLO level, which is however the current knowledge in this research area as also reported in the Les Houches Report2023, mentioned above.
As an example, the pionneering computation for the total top-pair production cross section has been computed more than ten years ago using the residue subtraction method implemented in the numerical code (STRIPPER) [arXiv:1005.0274] as described in [arXiv:1303.6254] , is not mentioned. Since then, and in the last decade, differential observables related to heavy quark pair production have been computed using various NNLO methods (slicing or subtraction) for lepton or hadron colliders. Publications presenting those precise predictions are not mentioned here either.
For all the reasons mentioned above, I do not recommend the publication of this manuscript in SciiPost in its present form.
It is the third paper of this kind, following Refs.[52,53] with partly the same list of authors, and with the results derived in this paper building up on the ingredients presented in those previous publications.
To set the context, in Ref. [52], this subtraction framework was presented with the scope of handling infrared divergences arising at NLO level from the presence of massless initial or final state partons while in [53], a set of expressions needed at NNLO for generic coloured massless final states were constructed within this framework, with the claim that those could be implemented in any numerical code computing differential
cross sections measured at high energy particle colliders.
The main outcomes of this paper are :
a) As described in section 2, the extension of the formalism to treat the infrared behaviour of cross sections computed at NLO due to the presence of massive final states, the implementation in the existing (from Ref. [52]) MAdNLO framework and code and the validation of the latter code using results obtained with the MADGRAPH_5_aMC_NLO package, Refs [64,65], for 2-jet and heavy-quark pair production , with QCD radiation arising from final state particles only.
b) As described in section 3, the implementation of elements required at NNLO in QCD in the MAdNLO code for one specific double real channel related to di-jet production in electron-positron annihilation.
As stated by the authors themselves in the introduction, NLO is a solved problem since the 90’s and predictions computed at NNLO level are becoming the standard: 2 -> 2 at NNLO has been computed for a variety of processes involving more and more complex final states. These differential predictions are obtained implementing well-established NNLO methods with ingredients based on known factorisation properties of QCD amplitudes in soft or collinear limits, and using parton-level event generators, allowing a direct comparison with data. The latter lead in the past decades to more and more precise determinations of fundamental parameters of the Standard Model theory, like the strong coupling or a better understanding of the parton content of the proton. For a recent review on the state-of the art precision attained in perturbative QCD predictions nowadays, and a presentation of well-established methods allowing the computation of NNLO-type differential predictions, for lepton and hadron collider observables, see for example, the Les Houches Report 2023, [arXiv:2504.06689].
Compared to the current knowledge of radiative corrections included in computations as reported in the mentioned report, and leading to increasingly precise theoretical predictions, in this paper, only partial results with limited phenomenological impact are presented:
The authors claim that the submitted manuscript meet the expectation (2):
Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work.
The relevance at NNLO level of these results is however very limited and the potential of the developments as basis for multi-pronged follow-up work is not enough convincingly demonstrated: Only the construction at double-real level is probed (cf. outcome b) as above).
To satisfy the expectation (2) the other classes of contributions present at real-virtual and double-virtual levels and constructed by the authors themselves in Ref. [53], need to be implemented in the MAdNLO code too, in order to compute physical observables for specific processes and comparing those with existing results in the literature employing other well-established NNLO methods.
Furthermore, following the general acceptance criterium, the paper should provide citations to the relevant literature in a way that is as representative and as complete as possible:
This required acceptance criterium is not satisfied here, specially not for the relevant literature dealing with the current state of the art for predictions related to heavy quark pair production.
At NLO, the formalism was elaborated more than twenty years ago as an extension of the massless dipole formalism and mentioned here as Refs. [61,62]. There here is no mentioning in this paper of developments nor of existing computations of observables at NNLO level, which is however the current knowledge in this research area as also reported in the Les Houches Report2023, mentioned above.
As an example, the pionneering computation for the total top-pair production cross section has been computed more than ten years ago using the residue subtraction method implemented in the numerical code (STRIPPER) [arXiv:1005.0274] as described in [arXiv:1303.6254] , is not mentioned. Since then, and in the last decade, differential observables related to heavy quark pair production have been computed using various NNLO methods (slicing or subtraction) for lepton or hadron colliders. Publications presenting those precise predictions are not mentioned here either.
For all the reasons mentioned above, I do not recommend the publication of this manuscript in SciiPost in its present form.
Recommendation
Reject