Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist

The Les Houches Standard Model (SM) Precision Wishlist is an exhaustive yet compact document reporting the current state of the art in theoretical predictions
for key reactions at high-energy colliders and the associated challenges. More importantly, it outlines the path forward for future improvements that the theory
community should address in order to advance the precision programme carried out at the LHC.
The paper is therefore not intended to provide details on specific methods, but rather to serve as an overview.
As such, it is certainly a useful document for experts in the high-energy physics phenomenology and SM precision communities, both theorists and experimentalists.
The paper is well written and conveys its content effectively.
Another very useful aspect is that it collects an exhaustive list of references to which the interested reader can readily refer.

I believe the document meets the SciPost Physics Acceptance Criteria and is suitable for publication, provided the authors address the comments below.

A disclaimer before proceeding with my comments: all that follows respects the knowledge cut-off set by the authors, namely 31 December 2024.
Significant progress has occurred in 2025, and some of the key challenges discussed in the paper have been partially addressed.
I will refrain from reporting on such developments here.

General comments:

• In Sec. 2.1 the authors write: “It is encouraged to use NLO QCD (or even NNLO QCD) PDFs where possible, even for computation of lower perturbative accuracy.” I would not go so far as to claim that there is universal consensus within the theory community on this prescription. Assuming that the current minimum standard for theory simulations is the use of at least NLO-QCD accurate generators, one could question whether adopting NNLO-QCD PDF sets is formally consistent. To mention just two points:
  a) NNLO PDF sets are fitted using NNLO-accurate predictions;
  b) one should not expect a compensation of factorisation evolution logarithms between different perturbative orders.
  Since this sentence reads as a relatively strong recommendation, I feel the authors should elaborate further and explain why this approach is to be preferred.

• In Sec. 2.3, when presenting progress on the computation of subleading power corrections to slicing methods, the authors refer - in the context of N-jettiness - to LL and NLL corrections computed either in SCET or in direct QCD. I believe this should instead read: LL → LP (leading power) and NLL → NLP (next-to-leading power).

• In Sec. 3, “On-shell and off-shell descriptions”, when presenting the pole approximation, the authors write: “this approximation includes resonant diagrams as well as non-factorisable contributions that arise from soft gauge-boson exchange.” I would suggest being more precise and writing “soft photon or soft gluon exchange”, as otherwise this statement could be misinterpreted as referring to the exchange of virtual soft Z or W bosons.

• Still in Sec. 3 (“On-shell and off-shell descriptions”), the second paragraph starts with “In order to describe non-resonant effects of a process, a full off-shell calculation is required” and proceeds to discuss the challenges associated with fully decayed particles. The authors then describe the state of the art as 2→8 at NLO and 2→3 at NNLO QCD. While 2→8 at NLO is indeed representative of the current state-of-the-art, I believe the reference to NNLO QCD is misleading. As of December 2024, all 2→3 processes computed at NNLO QCD involve either massless final-state particles (photons or jets) or unstable particles treated as stable, e.g. ttH [Catani et al., 2210.07846] or ttW [Buonocore et al., 2306.16311]. As for NNLO-QCD, progress towards fully off-shell top–antitop production has only been presented in 2025 [Buonocore et al., 2507.11410].

• Sections 3.1 to 3.4 contain rather dense material that requires careful reading. I would suggest slightly improving the layout of the individual subsections to enhance readability. At present, only “LH21 status” is explicitly highlighted in italics. I would find it useful to also highlight the progress — perhaps with a label such as “Progress:” — as well as the experimental status and projections, which often appear in the final paragraph of each subsection. In this regard, I also find it somewhat inconsistent that for some processes a clear description of the experimental status is provided, while for others it is not. Having this information systematically for all processes would be extremely useful, in particular to assess whether improved theoretical input is required or whether the bottleneck lies on the experimental side. While I appreciate that providing an exhaustive description is a big challenge in itself, I would at least encourage the authors to be more explicit or to justify cases where experimental projections are not included.

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Comments on the bibliography

• In Sec. 2.3, when presenting N-jettiness slicing, the authors write: “Explicitly worked out at NNLO QCD for hadron-collider processes with up to one jet.”. In [Bell et al., 2312.11626] and [Agarwal et al., 2403.03078], the NNLO N-jettiness soft function is computed for arbitrarily many jets. Although no LHC processes with two or more resolved jets have yet been described at NNLO QCD using the N-jettiness slicing method, I believe it is fair to state that the method has been extended beyond the one-jet case. The two references mentioned above appear later in the text in connection with progress towards N³LO QCD.

• In Sec. 2.3, when discussing the Projection-to-Born method, the authors write: “Applied at NNLO QCD to VBF [308], Higgs-pair production [309], …” I would suggest making it explicit that Ref. [309] refers to Higgs-pair production in VBF. A non-expert reader might otherwise interpret this as including gluon fusion.

• In Sec. 3.1.11, immediately before citing Ref. [680], the sentence “The master amplitudes for the leading-colour two-loop amplitudes have been computed in Ref. [680]” should read “The master integrals … have been computed” (instead of master amplitudes).

• In Sec. 3.3.2, the fifth paragraph begins with a discussion of Z + b \bar{b} matched to parton showers in the MiNNLO framework. I believe this material would be more appropriately placed in Sec. 3.3.4, which is explicitly dedicated to V + b \bar{b}.

• In Sec. 3.3.5 (VV′), the authors should consider including Ref. [Canko et al., 2412.06972], which appeared in December 2024 and presents the first results for three-loop master integrals for vector-boson pair production (the complete set relevant for the amplitude in the large-Nc limit appeared in December 2025).

• In Sec. 3.3.6 (VV′ + j), the authors should consider citing Ref. [Abreu et al., 2408.05201], which appeared in August 2024 and presents planar master integrals relevant for vector-boson pair production in association with a jet at the two-loop level.

• In Sec. 3.4.1, when discussing the status of top–antitop production, the authors refer to Refs. [946] and [947] (L.-B. Chen et al.), presenting them as analytic calculations of N3LO QCD corrections. However, these papers concern QCD corrections to the (semi-leptonic [946]) decay of the top quark, rather than to top-pair production itself. I therefore do not see a clear motivation for discussing them in this context. If the authors find it necessary to include them, I would suggest stating explicitly from the outset that the discussion concerns the decay stage, in order to avoid confusion (as opposed to the current presentation, where this is clarified only after Ref. [947]).

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Typos

• At the end of Sec. 2.2, immediately after Ref. [133], capitalise “we”.

• Immediately after Eq. (3): “whose matching coefficients known up to” → “whose matching coefficients are known up to”.

• Last paragraph on p. 13: “[…] to reduce the sensitivity to log-enhanced terms (” — an opening parenthesis is not closed.

• First paragraph on p. 20: “[…] momentum above 450 GeV is 115 fb with an uncertainty of 128 fb) [556]” — a closing parenthesis appears without a corresponding opening one.

Ask for minor revision

The paper provides a thorough review of the state-of-the-art theory calculations for LHC applications and lists the key developments needed to match the ever increasing experimental precision. It will serve as a very useful reference for the HEP community and an indicator of the next key directions. I find that the paper fully meets the SciPost Physics Community Reports Acceptance Criteria and recommend it to be published after a minor revision.

General comments:

1) The review claims to point out areas where progress is needed in order to match the experimental precision, "... we indicate processes and missing higher-order corrections that are required to reach the theoretical accuracy that matches the anticipated experimental precision.". For most processes in Section 3, the anticipated experimental precision (current and HL-LHC) is clearly laid out, and where experimental precision surpasses the theory precision, the case is compelling. However, for a handful of channels the rationale for targeting additional higher-order corrections is not spelled out. To help readers appreciate the theoretical challenges in the "desired" precision, it would be useful to briefly discuss, for each of the following, why existing calculations fall short of projected experimental uncertainties: - HH+2j - tH - bbH - V+bb - VV+j - yy, yy+>=1j, yyy - ttj - tt+>=2j - tt+bb - tZj

2) 2.1 Parton distribution functions "It is encouraged to use NLO QCD (or even NNLO QCD) PDFs where possible, even for computation of lower perturbative accuracy" -> Naively it seems that using a consistent setup might be better (e.g. NLO PDFs with NLO calculations). Do comparisons with data show that taking the NNLO PDFs is always better than NLO? I suggest clarifying this point or provide additional information for the readers.

3) 2.1 Parton distribution functions, 2nd paragraph -> References for PDF sets are not provided (CT18, MSHT20, NNPDF3.1/4.0). Perhaps that's fine because you cite PDF4LHC21. However, in that case consider citing PDF4LHC15 for consistency or provide a reference for each PDF set. Preferably, everything would be properly cited.

4) Page 13, Jet algorithms, identified final states, and fragmentation -> The section discusses several cases of mismatch between theory and experiment (or fixed-order vs ME + PS). Another issue, not mentioned here, is the mismatch between the "particle-level" observables and "parton-level" observables, which are particularly important for measurements with jets (e.g. discussed briefly in 2506.13449, Figure 1). I suggest mentioning this as another source of uncertainty, which must be addressed when we compare e.g. V+HF measurements to fixed-order calculations or for their inclusion in global PDF fits.

5) Section 3.1 Higgs boson associated processes -> In this section you often refer to ATLAS analyses for the state-of-the-art experimental precision. However, CMS results with similar precision are sometimes not mentioned. I think it would be better to cite results from both collaborations where appropriate. For example, ATLAS references without a matching CMS reference are [511], [536], [555], [556], [608], and possibly others.

6) Page 19, last paragraph "If the remaining systematic errors (dominated for the diphoton analysis by the spurious signal systematic error) remain the same, the resultant systematic error would be of the order of 9%, leading to a total error of approximately 9.5%." -> Experiments will likely find a way to deal with the spurious signal systematic uncertainty and reduce it such that it will be more comparable to the statistical uncertainty. Would that change any of the conclusions on what calculations are needed? Please explain in the text if it's relevant.

1) Address the general comments from the Report

2) Page 4, 1st paragraph -> Capitalize "ploughshare"

3) Page 4, last paragraph "... as for example in the Higgs Cross Section Working Group. (See the discussion on approximate N3LO PDFs below.)" -> Should this rather be formatted as "... as for example in the Higgs Cross Section Working Group (see the discussion on approximate N3LO PDFs below)."?

4) Page 6, 3rd paragraph "There are sizeable differences in the gg PDF luminosity not observed in the qq PDF luminosity." -> Suggest clarifying what differences exactly you mean. In both cases the blue and green curves do not agree within the uncertainty bands shown at around 100 - 200 GeV.

5) Page 6, 3rd paragraph "... and then to take the ratio of the two ratios, as shown in Figure 2." -> Figure 2 does not seem to show a double-ratio as specified in the text. It just shows the ratio of aN3LO to NNLO PDFs. Please correct appropriately.

6) Figure 1 right -> There are spikes in the error bands, most notably in the green curve at 500 GeV. Are these just numerical issues that could be fixed?

7) Page 12, Electroweak corrections, 1st paragraph "run III of the LHC" -> The official name of the 3rd run is "Run 3", not "run III". Please change appropriately throughout the text (e.g. also on page 32, possibly others).

8) Page 12, Electroweak corrections, 2nd and 3rd paragraph -> Repetitive use of the word "plethora", consider rephrasing one of the sentences.

9) Section 3.1 Higgs boson associated processes -> It might be better to drop the reference to Table 2 in this section and include it only in Section 3.1.2 Production. This would also solve the ordering issue where Table 2 is referenced before Table 1.

10) Section 3.1.1 Higgs Decays -> Suggest stating whether the current precision in partial width calculations is sufficient or if higher-order calculations are needed (e.g. for HL-LHC). This would be similar to the "known" / "desired" format in the following.

11) Page 20, first paragraph, last sentence -> Capitalize "standard model" here and elsewhere

12) Page 23, last paragraph -> Suggest stating whether the "known" and "desired" theory calculations will be precise enough for this data.

Ask for minor revision