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REVIEW 2 major objections 5 minor 67 references

Dynamic multi-scale NLO and jet merging improve full off-shell ttW+ predictions at the LHC.

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T0 review · grok-4.5

2026-07-14 04:05 UTC pith:RPEI2ZEI

load-bearing objection Solid first MiNLO application to fully off-shell multi-lepton ttW+(j/jj) plus a new Helac-NLO implementation; claims hold up under the authors' own tests. the 2 major comments →

arxiv 2607.11652 v1 pith:RPEI2ZEI submitted 2026-07-13 hep-ph hep-ex

Multi-scale improved predictions for boldsymbol{pp to tbar{t}W^+ +X}

Nikolaos Dimitrakopoulos , Malgorzata Worek This is my paper
classification hep-ph hep-ex
keywords MiNLOttW+full off-shellNLO QCDscale settingjet mergingSudakov form factorsmulti-lepton
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows that assigning renormalization and factorization scales from the most probable jet branching history, together with Sudakov form factors that resum large logarithms, produces NLO QCD predictions for the full off-shell multi-lepton ttW+ process that agree with ordinary fixed-order results while systematically shrinking scale uncertainties once extra jets are present. The same multi-scale machinery is then used to merge 0-, 1- and 2-jet samples so that the inclusive multi-lepton signature is described more accurately, especially in regions where hard radiation is important. The comparison is performed at 13 TeV for both integrated fiducial rates and differential distributions, and the method is implemented inside a public multi-purpose NLO framework so that it can be reused for other processes. Readers who care about precision modeling of same-sign lepton backgrounds or about reducing theory error on a process that already shows mild tension with data will find the concrete numerical gains and the residual freedom in the core-scale choice directly relevant.

Core claim

For the full off-shell pp o e+ u e u¯ au+ u au bb¯(j) processes at 13 TeV, multi-scale improved NLO (MiNLO) predictions agree with standard fixed-order NLO within scale uncertainties for every central-scale choice examined, yet the MiNLO scale bands are systematically smaller once two extra jets are present or when a suboptimal fixed scale is used; merging the 0-, 1- and 2-jet samples with a merging cut further reduces those bands for most differential observables relative to pure NLO.

What carries the argument

The MiNLO algorithm: an inverse kT clustering that reconstructs ordered nodal scales qi for every additional jet, assigns heta s(qi) and Sudakov form factors to those scales, and expands the form factors to cancel double-counted NLO terms, leaving only an arbitrary core-process scale qcore free.

Load-bearing premise

The overall energy scale of the core process without extra jets is still chosen by hand; only the scales of the additional jets are fixed by the clustering algorithm.

What would settle it

Compute the same full off-shell multi-lepton distributions with an independent NLO generator that implements a different multi-scale prescription (or with a complete NNLO calculation once available) and check whether the central values and residual scale bands still agree within a few percent for the same fiducial cuts.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The manuscript implements the multi-scale improved NLO (MiNLO) method inside Helac-NLO and applies it to full off-shell pp → e+νe μ-ν̄μ τ+ντ bb(j/jj) production in the multi-lepton channel at √s = 13 TeV. It compares standard fixed-order (N)LO QCD predictions with Mi(N)LO results at the integrated and differential levels for several fixed and dynamical core-scale choices, documents the residual freedom in q_core and the clustering radius R, and constructs multi-jet merged predictions (up to two extra jets) intended to improve the description of the inclusive ttW+ process. The central numerical claim is that MiNLO and fixed-order NLO agree within scale uncertainties for all considered central scales, while MiNLO systematically reduces those uncertainties once two extra jets are present or when suboptimal fixed scales are used.

Significance. Full off-shell NLO QCD for ttW+ with additional jets is a high-complexity calculation of direct relevance to LHC multi-lepton measurements and SMEFT analyses. Extending MiNLO to this final state, implementing it in Helac-NLO, and validating against Sherpa for simpler processes constitute a genuine technical advance. The exhaustive scale-variation tables, alternative R/μ R/resolution-scale variants, and differential distributions with uncertainty bands make the comparison reproducible and useful for the community. The residual freedom in q_core is treated as an explicit systematic rather than hidden, which strengthens the paper.

major comments (2)
  1. Section 6 and Eqs. (6.1)–(6.2): the multi-jet merging is performed with an explicit pT,merging cut rather than the MiNLO-style merging without a merging scale that is standard in the literature (Hamilton et al., 2013; Hamilton et al., 2016). The authors correctly note that a full MiNLO merging for this process would require dedicated resummation matching that is not yet available, but the present construction therefore remains a conventional exclusive/inclusive sum. The claim that the merged sample “improves the description” of the underlying process should be qualified more carefully: for well-chosen dynamical scales the reduction in scale uncertainty is modest and still depends on the arbitrary pT,merging value (Fig. 6).
  2. Section 6 and Table 4 / Appendix A: the two-jet sample is retained only at LO. While this is openly stated as a limitation for future work, the merged predictions that include this sample (Eq. (6.2)) inherit large LO scale uncertainties that partially cancel the benefit of MiNLO on the lower-multiplicity samples. A quantitative estimate of how much the merged uncertainty bands would shrink once the NLO ttW+jj calculation becomes available would strengthen the central claim of Section 6.
minor comments (5)
  1. Section 2, Eq. (2.4): the rapidity/momentum-sign condition used to resolve the initial-state clustering ambiguity is sensible but not standard; a short sentence comparing it with the treatment in Sherpa or the original MiNLO papers would help the reader.
  2. Table 1 and Table 2: the K-factor columns are useful, but the last column (σMiNLO/σNLO) is almost always 0.97–1.00; stating this explicitly in the text would make the agreement more immediately visible.
  3. Figures 3–5 and 10–12: the bottom panels show scale-uncertainty bands normalized to the central value; adding a second ratio panel that directly overlays the absolute size of the MiNLO versus NLO uncertainty bands would make the claimed reduction easier to judge by eye.
  4. References: the recent NNLO QCD results for on-shell ttW (Becchetti et al., 2606.09503) are cited; a brief remark on how the present full-off-shell MiNLO study complements those calculations would be welcome.
  5. Typographical: “Mi(N)LOnoξ F” is used both as a label and as a subscript; a consistent notation (e.g. MiNLO|no ξ F) would improve readability.

Circularity Check

0 steps flagged

No significant circularity: standard MiNLO/CKKW construction applied to new full-off-shell calculations; comparisons and scale variations are independent numerical results.

full rationale

The paper's derivation chain is the standard multi-scale improved NLO (MiNLO) procedure of Hamilton et al. (cited as [3]) and Höche et al. ([4]), implemented inside the authors' Helac-NLO framework and applied to full off-shell pp o tt̄W^{+}(j/jj) multi-lepton final states. Nodal scales are extracted by inverse k_T clustering (Eqs. 2.1–2.5), Sudakov factors are the usual NLL form (Eq. 2.8), and the NLO subtraction of the O(α_s) expansion of those factors (Eq. 2.12) is the textbook double-counting removal. The core scale q_core remains an external free choice (explicitly stated in Sec. 2), and all results are obtained by varying it together with the usual 7-point (ξ_R,ξ_F) envelope; no parameter is fitted to data and then re-presented as a prediction. Self-citations ([6,29,40,43,55–63]) supply only the pre-existing Helac-NLO infrastructure and earlier fixed-order baselines for the same process; they are not used to justify uniqueness, force an ansatz, or close a logical loop. Validation against an independent code (Sherpa) further confirms that the numerical outputs are not self-referential. The multi-jet merging (Sec. 6) is a conventional exclusive/inclusive sum with an explicit p_T,merging cut; it does not redefine any observable in terms of itself. Consequently the central claim—that MiNLO and fixed-order NLO agree within uncertainties while MiNLO reduces scale dependence for higher jet multiplicity or suboptimal scales—is a genuine computational comparison, not a tautology.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 0 invented entities

The calculation rests on standard QCD factorization, the CKKW/MiNLO construction, and conventional SM/PDF inputs. Free parameters are the usual scale-variation factors plus the clustering radius R and the arbitrary core-scale definition. No new dynamical entities are postulated.

free parameters (3)
  • clustering radius R = 0.4 (default)
    Input to the inverse kT algorithm; default R=0.4, varied to 1.0 as a systematic (Section 2 and Table 2).
  • core scale q_core
    Remains an external choice (HT/2, ET/2, mt+mW/2, au); only the nodal scales of extra jets are fixed by MiNLO (Section 2).
  • merging scale pT,merging = 60 GeV (default for differentials)
    Arbitrary cut used to combine jet multiplicities; results shown for a range 25–100 GeV (Section 6).
axioms (3)
  • domain assumption QCD factorization and the validity of the NLO fixed-order expansion for the core process
    Standard assumption underlying all NLO calculations in the paper (Introduction and Section 3).
  • domain assumption The CKKW/MiNLO prescription for assigning nodal scales and Sudakov form factors correctly resums the large logarithms associated with ordered emissions
    Taken from Hamilton et al. (2012) and subsequent literature; used without re-derivation (Section 2).
  • domain assumption NNPDF3.1 PDFs and the listed SM input parameters (mt, mW, au, etc.) are adequate
    Standard external inputs (Section 3).

pith-pipeline@v1.1.0-grok45 · 35316 in / 2425 out tokens · 21253 ms · 2026-07-14T04:05:17.558243+00:00 · methodology

0 comments
read the original abstract

We compare standard fixed-order NLO QCD predictions for the full off-shell $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} \, (j) + X$ processes in the multi-lepton decay channel with the results obtained using the MiNLO approach. The MiNLO method, now also implemented in the Helac-NLO framework, provides a dynamic determination of the renormalization and factorization scale settings by identifying the most likely branching histories of the additional jets through an inverse $k_T$-clustering algorithm. The inclusion of Sudakov form factors accounts for the large logarithms that arise in the presence of widely separated scales. We perform a dedicated comparison of the two approaches at both the integrated and differential (fiducial) cross-section levels for the LHC Run II energy of $\sqrt{s}=13$ TeV. Finally, we present the merging of the full off-shell predictions for $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} \, + X$, $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} \, j +X$ and $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} \, jj$, with the aim of improving the description of the underlying $pp \to e^+\nu_e\, \mu^-\bar{\nu}_\mu\, \tau^+\nu_\tau\, b\bar{b} + X$ process.

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