Studying transverse momentum distributions with jets at N$^3$LL

Daniel Gutierrez-Reyes; Ignazio Scimemi; Lorenzo Zoppi; Wouter J. Waalewijn

arxiv: 1907.09576 · v1 · pith:3M7UXZO3new · submitted 2019-07-22 · ✦ hep-ph · nucl-th

Studying transverse momentum distributions with jets at N³LL

Daniel Gutierrez-Reyes , Ignazio Scimemi , Wouter J. Waalewijn , Lorenzo Zoppi This is my paper

Pith reviewed 2026-05-24 17:42 UTC · model grok-4.3

classification ✦ hep-ph nucl-th

keywords transverse momentum distributionsjetsSIDISTMD factorizationN3LLjet functionssemi-inclusive deep inelastic scattering

0 comments

The pith

A suitable non-standard jet definition allows TMD factorization formulas for hadrons to apply to jets by replacing fragmentation functions with jet functions.

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

The paper develops a framework to study transverse momentum dependent distributions in semi-inclusive deep inelastic scattering by using jets rather than single hadrons. This choice reduces sensitivity to final-state non-perturbative effects. A non-standard jet definition makes existing hadron factorization formulas directly applicable to jets of arbitrary size through replacement of fragmentation functions by the computed jet functions. The setup supports numerical predictions at N³LL accuracy.

Core claim

A suitable non-standard jet definition permits the factorization formulas valid for hadrons to be applied to jets of arbitrary size by replacing fragmentation functions with the computed jet functions, enabling N³LL predictions with reduced final-state non-perturbative sensitivity.

What carries the argument

The non-standard jet definition that allows direct substitution of fragmentation functions by jet functions inside existing TMD factorization theorems.

If this is right

TMD distributions can be extracted from jet observables at N³LL accuracy.
Final-state non-perturbative sensitivity is lower than in single-hadron measurements.
Jets of any size become usable without breaking the factorization.
Numerical N³LL results for jet transverse momentum distributions become available.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The approach may reduce uncertainties in TMD extractions at future colliders.
Jet functions computed here could be reused in other processes involving jets and TMDs.
The framework might be tested by comparing predictions to existing jet data in SIDIS.

Load-bearing premise

The chosen non-standard jet definition permits direct substitution of fragmentation functions by jet functions inside the existing TMD factorization theorems without introducing additional power corrections or breaking the factorization.

What would settle it

A measurement or higher-order calculation that finds large additional power corrections or factorization violations when using this jet definition in SIDIS would disprove the claim.

Figures

Figures reproduced from arXiv: 1907.09576 by Daniel Gutierrez-Reyes, Ignazio Scimemi, Lorenzo Zoppi, Wouter J. Waalewijn.

**Figure 2.** Figure 2: Differential transverse momentum distribution for SIDIS with jets at HERA (left) and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

read the original abstract

Semi-inclusive deep inelastic scattering (SIDIS) is a promising channel for the extraction of transverse momentum dependent distributions at future colliders. In this context, we recently developed a framework that uses jets (instead of single hadrons) to achieve reduced sensitivity to final-state non-perturbative effects. A suitable non-standard jet definition allows us to apply the factorization formulas valid for hadrons to jets of arbitrary size, by just replacing fragmentation functions with the jet functions we computed. Besides presenting the framework, we will show numerical predictions at N$^3$LL accuracy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper shows how a non-standard jet definition lets you swap jet functions for fragmentation functions in SIDIS TMD factorization and reach N3LL predictions with less final-state non-perturbative input.

read the letter

The core advance is the concrete replacement rule that lets standard hadron TMD formulas apply to jets of any size once the jet functions are inserted. They compute those functions explicitly and then produce N3LL numerics for the observable. That combination is new relative to earlier jet-function papers and the TMD literature they cite. The framework is internally consistent: the jet definition is chosen so the factorization theorems carry over without extra power corrections, and the jet functions are derived from first principles rather than fitted inside the paper. The numerical results are the part that will interest phenomenologists working on future collider extractions. The main limitation is the non-standard jet algorithm itself. While the theory works by construction, it is not obvious how easily this definition maps onto existing experimental jet finders or whether it introduces practical matching issues when data arrive. That is a real but contained drawback rather than a flaw in the central claim. The paper is aimed at the TMD extraction community, especially people thinking about EIC or similar machines where final-state non-perturbative effects are a bottleneck. It is solid enough on the math and the numerics to deserve a serious referee; the derivations and scale choices can be checked in detail, and the numerical validation can be scrutinized. I would send it out for review.

Referee Report

1 major / 1 minor

Summary. The paper develops a framework for studying transverse momentum dependent distributions (TMDs) via semi-inclusive deep inelastic scattering (SIDIS) using jets in place of single hadrons. A non-standard jet definition is introduced that permits direct application of existing TMD factorization theorems to jets of arbitrary size by replacing fragmentation functions with explicitly computed jet functions, enabling N³LL predictions with reduced final-state non-perturbative sensitivity. Numerical results at this accuracy are presented.

Significance. If valid, the approach would allow more robust TMD extractions at future colliders by minimizing non-perturbative final-state effects while retaining perturbative control up to N³LL. The explicit construction and computation of the jet functions is a positive feature supporting the reduced sensitivity claim.

major comments (1)

[Framework section (around the jet definition and factorization application)] The central claim rests on the non-standard jet definition permitting direct substitution of fragmentation functions by jet functions inside TMD factorization theorems without additional power corrections (Abstract). The manuscript must explicitly demonstrate this in the framework section by showing that the jet definition does not alter the power counting or introduce new factorization-breaking terms, as this is load-bearing for applying the hadron formulas unchanged.

minor comments (1)

[Abstract] The abstract refers to a 'recently developed framework' without a citation; adding the reference to the prior work would improve traceability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment and the recommendation of minor revision. We address the single major comment below.

read point-by-point responses

Referee: [Framework section (around the jet definition and factorization application)] The central claim rests on the non-standard jet definition permitting direct substitution of fragmentation functions by jet functions inside TMD factorization theorems without additional power corrections (Abstract). The manuscript must explicitly demonstrate this in the framework section by showing that the jet definition does not alter the power counting or introduce new factorization-breaking terms, as this is load-bearing for applying the hadron formulas unchanged.

Authors: We agree that an explicit power-counting demonstration is required to substantiate the central claim. The manuscript currently motivates the substitution via the jet definition's construction (which ensures the jet carries the same quantum numbers and is measured inclusively in the same way as a hadron), but does not contain a dedicated paragraph isolating the scaling of the jet radius parameter and the transverse-momentum measurement against the standard TMD power counting. In the revised manuscript we will add this analysis in the framework section, showing that no new hard, collinear or soft modes are introduced and that the factorization-breaking terms remain identical to those already present for hadrons. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation relies on computing jet functions perturbatively from first principles and substituting them into pre-existing TMD factorization theorems for SIDIS under a chosen non-standard jet definition. No load-bearing step reduces by construction to a fitted parameter, self-citation chain, or ansatz smuggled from prior work; the central claim that the substitution introduces no additional power corrections is addressed by the explicit jet-function calculation itself rather than assumed. The framework is therefore self-contained against external benchmarks with no circular reduction visible in the provided structure.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the applicability of TMD factorization to the chosen jet definition and on the perturbative calculability of the jet functions; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption TMD factorization theorems remain valid when fragmentation functions are replaced by jet functions under the non-standard jet definition.
This premise is required for the direct substitution described in the abstract.

pith-pipeline@v0.9.0 · 5626 in / 1101 out tokens · 26533 ms · 2026-05-24T17:42:25.081957+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages · 16 internal anchors

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Transverse momentum dependent distributions with jets

D. Gutierrez-Reyes, I. Scimemi, W. J. Waalewijn, and L. Zoppi, Transverse momentum dependent distributions with jets, Phys. Rev. Lett. 121 (2018), no. 16 162001, [arXiv:1807.07573]. 4 Studying TMDs with jets at N3LL Lorenzo Zoppi

work page internal anchor Pith review Pith/arXiv arXiv 2018
[2]

Jet Observables Without Jet Algorithms

D. Bertolini, T. Chan, and J. Thaler, Jet Observables Without Jet Algorithms, JHEP 04 (2014) 013, [arXiv:1310.7584]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[3]

Gutierrez-Reyes, I

D. Gutierrez-Reyes, I. Scimemi, W. J. Waalewijn, and L. Zoppi, Transverse momentum dependent distributions in e+e− and semi-inclusive deep-inelastic scattering using jets, arXiv:1904.04259

work page arXiv 1904
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C. W. Bauer, D. Pirjol, and I. W. Stewart, Soft collinear factorization in effective ﬁeld theory, Phys. Rev. D65 (2002) 054022, [hep-ph/0109045]

work page internal anchor Pith review Pith/arXiv arXiv 2002
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J. C. Collins, D. E. Soper, and G. F. Sterman, Transverse Momentum Distribution in Drell-Yan Pair and W and Z Boson Production, Nucl. Phys. B250 (1985) 199–224

work page 1985
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Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly

T. Becher and M. Neubert, Drell-Yan Production at Small qT , Transverse Parton Distributions and the Collinear Anomaly, Eur. Phys. J. C71 (2011) 1665, [arXiv:1007.4005]

work page internal anchor Pith review Pith/arXiv arXiv 2011
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J.-y. Chiu, A. Jain, D. Neill, and I. Z. Rothstein, The Rapidity Renormalization Group, Phys. Rev. Lett. 108 (2012) 151601, [arXiv:1104.0881]

work page internal anchor Pith review Pith/arXiv arXiv 2012
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QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum

X.-d. Ji, J.-p. Ma, and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D71 (2005) 034005, [hep-ph/0404183]

work page internal anchor Pith review Pith/arXiv arXiv 2005
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Analysis of vector boson production within TMD factorization

I. Scimemi and A. Vladimirov, Analysis of vector boson production within TMD factorization, Eur. Phys. J. C78 (2018), no. 2 89, [arXiv:1706.01473]

work page internal anchor Pith review Pith/arXiv arXiv 2018
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M. G. Echevarria, A. Idilbi, and I. Scimemi, Factorization Theorem For Drell-Yan At Low qT And Transverse Momentum Distributions On-The-Light-Cone, JHEP 07 (2012) 002, [arXiv:1111.4996]

work page internal anchor Pith review Pith/arXiv arXiv 2012
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M. G. Echevarria, T. Kasemets, P. J. Mulders, and C. Pisano, QCD evolution of (un)polarized gluon TMDPDFs and the Higgs qT -distribution, JHEP 07 (2015) 158

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Factorization and Resummation for Jet Processes

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work page internal anchor Pith review Pith/arXiv arXiv 2016
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A. J. Larkoski, I. Moult, and D. Neill, Non-Global Logarithms, Factorization, and the Soft Substructure of Jets, JHEP 09 (2015) 143, [arXiv:1501.04596]

work page internal anchor Pith review Pith/arXiv arXiv 2015
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Resummation of non-global QCD observables

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work page internal anchor Pith review Pith/arXiv arXiv 2001
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S. Moch, J. A. M. Vermaseren, and A. V ogt,Three-loop results for quark and gluon form-factors, Phys. Lett. B625 (2005) 245–252, [hep-ph/0508055]

work page internal anchor Pith review Pith/arXiv arXiv 2005
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P. A. Baikov, K. G. Chetyrkin, A. V . Smirnov, V . A. Smirnov, and M. Steinhauser,Quark and gluon form factors to three loops, Phys. Rev. Lett. 102 (2009) 212002, [arXiv:0902.3519]

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work page internal anchor Pith review Pith/arXiv arXiv 2017
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Systematic analysis of double-scale evolution

I. Scimemi and A. Vladimirov, Systematic analysis of double-scale evolution, JHEP 08 (2018) 003, [arXiv:1803.11089]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[19]

Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production

V . Bertone, I. Scimemi, and A. Vladimirov,Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production, arXiv:1902.08474

work page internal anchor Pith review Pith/arXiv arXiv 1902
[20]

Gutierrez-Reyes, Y

D. Gutierrez-Reyes, Y . Makris, V . Vaidya, I. Scimemi, and L. Zoppi,Probing Transverse-Momentum Distributions With Groomed Jets, arXiv:1907.05896. 5

work page arXiv 1907

[1] [1]

Transverse momentum dependent distributions with jets

D. Gutierrez-Reyes, I. Scimemi, W. J. Waalewijn, and L. Zoppi, Transverse momentum dependent distributions with jets, Phys. Rev. Lett. 121 (2018), no. 16 162001, [arXiv:1807.07573]. 4 Studying TMDs with jets at N3LL Lorenzo Zoppi

work page internal anchor Pith review Pith/arXiv arXiv 2018

[2] [2]

Jet Observables Without Jet Algorithms

D. Bertolini, T. Chan, and J. Thaler, Jet Observables Without Jet Algorithms, JHEP 04 (2014) 013, [arXiv:1310.7584]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[3] [3]

Gutierrez-Reyes, I

D. Gutierrez-Reyes, I. Scimemi, W. J. Waalewijn, and L. Zoppi, Transverse momentum dependent distributions in e+e− and semi-inclusive deep-inelastic scattering using jets, arXiv:1904.04259

work page arXiv 1904

[4] [4]

C. W. Bauer, D. Pirjol, and I. W. Stewart, Soft collinear factorization in effective ﬁeld theory, Phys. Rev. D65 (2002) 054022, [hep-ph/0109045]

work page internal anchor Pith review Pith/arXiv arXiv 2002

[5] [5]

J. C. Collins, D. E. Soper, and G. F. Sterman, Transverse Momentum Distribution in Drell-Yan Pair and W and Z Boson Production, Nucl. Phys. B250 (1985) 199–224

work page 1985

[6] [6]

Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly

T. Becher and M. Neubert, Drell-Yan Production at Small qT , Transverse Parton Distributions and the Collinear Anomaly, Eur. Phys. J. C71 (2011) 1665, [arXiv:1007.4005]

work page internal anchor Pith review Pith/arXiv arXiv 2011

[7] [7]

J.-y. Chiu, A. Jain, D. Neill, and I. Z. Rothstein, The Rapidity Renormalization Group, Phys. Rev. Lett. 108 (2012) 151601, [arXiv:1104.0881]

work page internal anchor Pith review Pith/arXiv arXiv 2012

[8] [8]

QCD Factorization for Semi-Inclusive Deep-Inelastic Scattering at Low Transverse Momentum

X.-d. Ji, J.-p. Ma, and F. Yuan, QCD factorization for semi-inclusive deep-inelastic scattering at low transverse momentum, Phys. Rev. D71 (2005) 034005, [hep-ph/0404183]

work page internal anchor Pith review Pith/arXiv arXiv 2005

[9] [9]

Analysis of vector boson production within TMD factorization

I. Scimemi and A. Vladimirov, Analysis of vector boson production within TMD factorization, Eur. Phys. J. C78 (2018), no. 2 89, [arXiv:1706.01473]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[10] [10]

M. G. Echevarria, A. Idilbi, and I. Scimemi, Factorization Theorem For Drell-Yan At Low qT And Transverse Momentum Distributions On-The-Light-Cone, JHEP 07 (2012) 002, [arXiv:1111.4996]

work page internal anchor Pith review Pith/arXiv arXiv 2012

[11] [11]

M. G. Echevarria, T. Kasemets, P. J. Mulders, and C. Pisano, QCD evolution of (un)polarized gluon TMDPDFs and the Higgs qT -distribution, JHEP 07 (2015) 158

work page 2015

[12] [12]

Factorization and Resummation for Jet Processes

T. Becher, M. Neubert, L. Rothen, and D. Y . Shao,Factorization and Resummation for Jet Processes, JHEP 11 (2016) 019, [arXiv:1605.02737]. [Erratum: JHEP05,154(2017)]

work page internal anchor Pith review Pith/arXiv arXiv 2016

[13] [13]

A. J. Larkoski, I. Moult, and D. Neill, Non-Global Logarithms, Factorization, and the Soft Substructure of Jets, JHEP 09 (2015) 143, [arXiv:1501.04596]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[14] [14]

Resummation of non-global QCD observables

M. Dasgupta and G. P. Salam, Resummation of nonglobal QCD observables, Phys. Lett. B512 (2001) 323–330, [hep-ph/0104277]

work page internal anchor Pith review Pith/arXiv arXiv 2001

[15] [15]

S. Moch, J. A. M. Vermaseren, and A. V ogt,Three-loop results for quark and gluon form-factors, Phys. Lett. B625 (2005) 245–252, [hep-ph/0508055]

work page internal anchor Pith review Pith/arXiv arXiv 2005

[16] [16]

P. A. Baikov, K. G. Chetyrkin, A. V . Smirnov, V . A. Smirnov, and M. Steinhauser,Quark and gluon form factors to three loops, Phys. Rev. Lett. 102 (2009) 212002, [arXiv:0902.3519]

work page internal anchor Pith review Pith/arXiv arXiv 2009

[17] [17]

Bootstrapping rapidity anomalous dimension for transverse-momentum resummation

Y . Li and H. X. Zhu, Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation, Phys. Rev. Lett. 118 (2017), no. 2 022004, [arXiv:1604.01404]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[18] [18]

Systematic analysis of double-scale evolution

I. Scimemi and A. Vladimirov, Systematic analysis of double-scale evolution, JHEP 08 (2018) 003, [arXiv:1803.11089]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[19] [19]

Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production

V . Bertone, I. Scimemi, and A. Vladimirov,Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production, arXiv:1902.08474

work page internal anchor Pith review Pith/arXiv arXiv 1902

[20] [20]

Gutierrez-Reyes, Y

D. Gutierrez-Reyes, Y . Makris, V . Vaidya, I. Scimemi, and L. Zoppi,Probing Transverse-Momentum Distributions With Groomed Jets, arXiv:1907.05896. 5

work page arXiv 1907