Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Soft background fields at next-to-leading power in transverse momentum dependent SIDIS with jets

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper derives a next-to-leading-power factorization for e + h → e + jet + X at small transverse momentum, using the background field method with explicit soft modes and defining physical twist-3 TMDs free of rapidity and endpoint…

desk verdict A careful, technically sophisticated NLP TMD factorization paper whose main soft spot is an all-order claim about endpoint divergences that is verified only at LO. read the letter →

arxiv 2507.03072 v1 pith:FKCYL4UF submitted 2025-07-03 hep-ph nucl-th

Max Jaarsma , Oscar del Rio , Ignazio Scimemi , Wouter Waalewijn This is my paper
classification hep-phnucl-th
keywords next-to-leadingpowerfactorizationtransversemomentumdependentdistributionsbackgroundfieldmethodsemi-inclusivedeep-inelasticscatteringtwist-3partonendpointdivergencessoftmodesazimuthalasymmetries
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper derives a factorization formula for the process electron + hadron → electron + jet + anything, valid at small transverse momentum and accurate through next-to-leading power (NLP) in the ratio of transverse momentum to hard scale. The derivation adds explicit soft background fields to the background field method, placing it between two earlier approaches that had seemed to disagree, and the paper shows how that disagreement is resolved at the computed order. The concrete payoff is a set of physical twist-3 transverse-momentum-dependent parton distributions that are free of both rapidity divergences and endpoint divergences, together with a factorized cross section covering all lepton and target polarizations. One azimuthal asymmetry, the $\sin\phi_J$ term for a longitudinally polarized target, receives at leading-logarithmic accuracy contributions from only a twist-3 hadronic distribution and a twist-2 jet function, which makes it a direct probe of higher-twist structure for the Electron-Ion Collider.

What carries the argument

The load-bearing device is the background field method extended by a soft background field, combined with an overlap-subtraction scheme. Collinear fields are split into pure-collinear and soft-overlap parts, a decoupling transformation $\psi \to S_n \psi$ removes the leading-power soft-collinear interactions, and inverting the factorized matrix elements subtracts the double-counted region. Rapidity divergences are regulated with the $\delta$-regulator, and the subtraction terms are engineered so that the endpoint divergence appearing when the extra collinear gluon of a twist-3 operator becomes soft cancels against the overlap contribution. This construction is what makes the physical twist-3 TMDs well-defined and what turns the transverse derivatives in the kinematic power corrections into manifestly rapidity-finite combinations involving the Collins-Soper kernel.

What would settle it

Compute the difference between the naive and overlap-subtracted twist-3 distributions, $F^{\rm naive}_{21} - F^{\rm o.s.}_{21}$ from Eqs. (4.58) and (4.61), at next-to-leading order in $\alpha_s$: if $\lim_{\xi\to 0}\xi\,(F^{\rm naive}_{21} - F^{\rm o.s.}_{21})$ no longer vanishes, the physical twist-3 TMDs retain endpoint divergences and the factorization breaks down. A second, independent check is to compute the hard-collinear matching coefficient $K$ in Eq. (4.87) at one loop and test whether $H_2 = H_1 + H_2 \otimes K$ holds; if it does not, the effective-current disagreement with the SCET approach of ref. [6] becomes a genuine higher-order discrepancy.

Watch

Extended reading notes

Core claim

The central claim is a next-to-leading-power factorization of the SIDIS-with-jets hadronic tensor, written as convolutions of hard functions, overlap-subtracted twist-2 and twist-3 TMD parton distributions, and twist-2 and twist-3 jet functions. The derivation builds an effective current operator from background fields for collinear, anti-collinear, and soft modes; after matching onto gauge-invariant SCET operators and imposing current conservation, reparameterization invariance, and discrete symmetries, five independent Wilson coefficients remain. The load-bearing step is the overlap subtraction: a background field is introduced for the region where soft and collinear modes double-count, and inverting the resulting decoupling transformation defines physical twist-3 TMDs, Eqs. (4.77)–(4.84), in which the endpoint divergences of the naive distributions are cancelled. On this basis the paper presents the factorized cross section for $e + h \to e + \text{jet} + X$ with its complete set of angular form factors for arbitrary initial-state polarization, and shows that the $\sin\phi_J$ asymmetry at leading-logarithmic order depends only on the twist-3 distribution $g^\perp_{2L}$ and the twist-2 jet function $J_{11}$. The hadronic tensor agrees with both prior approaches at the perturbative order computed, with Eq. (4.87) identified as the condition for agreement to survive at higher orders.

Load-bearing premise

The all-order claim rests on the assumption that the overlap subtraction removes the endpoint divergence at every order in the coupling, a property verified only at leading order in Eq. (4.63) and argued from the identification of the subtraction term with the limit in which the collinear gluon becomes soft; if that identification fails beyond leading order, the twist-3 distributions defined in Eqs. (4.77)–(4.84) still carry endpoint divergences and the manifestly finite cross section presented in Sec. 5 is not established.

Editorial extensions

If this is right

  • The $\sin\phi_J$ asymmetry for a longitudinally polarized target is at leading-logarithmic order a pure twist-3 observable, depending only on $g^\perp_{2L}$ and $J_{11}$, so Electron-Ion Collider data on it would directly constrain a poorly known higher-twist distribution.
  • The operator-level definitions in Eqs. (4.77)–(4.84) give explicit matrix elements for the subtraction terms used in earlier twist-3 TMD treatments, making the twist-3 distributions renormalizable, evolvable objects that can be extracted from data.
  • The complete form-factor list for $e + h \to e + \text{jet} + X$ at NLP covers all lepton and target polarizations with perturbatively calculable jet functions, so the same framework extends to additional azimuthal and spin asymmetries.
  • Most sub-leading soft matrix elements vanish by boost invariance, leaving a single soft gluon matrix element, and the resulting hadronic tensor matches both prior approaches at the computed order with Eq. (4.87) governing all-order agreement.
  • Model-based predictions for the asymmetry, built from Boer-Mulders and Sivers-inspired models of $g^\perp_{2L}$, differ mainly at small $x$ and agree within current parameter uncertainties, showing the observable is sensitive to the modeling of its twist-3 input.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same soft-background-field plus overlap-subtraction machinery should carry over to Drell-Yan and $e^+e^-$ annihilation at NLP; the soft functions $F$, $G$, $H$ vanish here only because the measurement is boost-invariant, so in observables that break boost invariance the analogous matrix elements would be physical rather than regulator artifacts.
  • If Eq. (4.87) fails at higher loops, the disagreement between the position-space background-field and label-formalism SCET results is real, and a one-loop determination of $K$ would settle which basis is missing terms; conversely, if it holds, the apparent disagreement is a low-order coincidence that resolves itself.
  • At next-to-leading-logarithmic order the imaginary part of the hard function activates the twist-3 jet function $J_{21}$ and the helicity TMD $g_1$, so the clean LL probe identified here acquires additional perturbatively computable contributions that a precision extraction of $g^\perp_{2L}$ would have to include.
  • The fact that the naive-minus-subtracted combination is finite at leading order because the subtraction matches the soft-gluon limit suggests a general principle: endpoint divergences at NLP are overlap divergences in disguise, so systematic overlap subtraction may remove them in other sub-leading-power observables wherever the same soft limit applies.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper derives a next-to-leading-power (NLP) TMD factorization for e + h -> e + jet + X in the small-transverse-momentum limit, using the background field method with an additional soft background field. The authors construct the NLP effective current, build the overlap-subtracted hadronic tensor in terms of twist-2 and twist-3 TMD PDFs and jet functions, compare their result with the frameworks of refs. [5,6], and give a full set of cross-section form factors. They also present a leading-logarithmic phenomenological prediction for the sin(phi_J) asymmetry, which they find depends only on a twist-3 hadronic distribution and a twist-2 jet function. The paper is careful to label open items, notably the condition in Eq. (4.87) for agreement with ref. [6] at higher orders.

Significance. If the factorization is fully established, this would be a valuable methodological step: it provides operator-level definitions of physical twist-3 TMDs with explicit overlap subtraction, a systematic derivation of NLP jet functions, and an observable whose leading-logarithmic contribution isolates a twist-3 hadronic distribution. The paper has genuine strengths: the tree-level cross-check against full QCD in Eq. (3.45), the systematic four-step overlap-subtraction construction in Sec. 4.2, the explicit comparison with previous frameworks culminating in Eq. (4.87), and the careful mapping to the parametrizations of refs. [54,59] in Appendix A. The phenomenological section is clearly presented as model-dependent, with the Boer-Mulders and Sivers models properly identified as toy inputs. The remaining gaps are all-order assertions that are load-bearing for the finiteness and completeness claims, so the result is not yet fully established as stated.

major comments (3)
  1. [4.2.4, Eq. (4.63)] The cancellation of endpoint divergences between the naive twist-3 TMD in Eq. (4.58) and the overlap-subtraction term in Eq. (4.61) is verified only at leading order for an external quark state. The passage from Eq. (4.63) to the finiteness statement in Eq. (4.64) relies on the assertion that the relation holds to all orders because the subtraction corresponds to the limit where the collinear gluon becomes soft. This is an extrapolation: beyond tree level, the soft Wilson-line matrix element with A_{T,n} in Eq. (4.61) is a different object from the xi->0 limit of the naive distribution, and the two could differ by endpoint-singular terms. Since the finiteness of the physical TMDs in Eqs. (4.77)-(4.84) and the manifestly finite cross section in Sec. 5.2 depend on this cancellation, the central claim is established only conditionally. I recommend proving the all-order statement or providing at least a one-loop verification under the same delta-regulator, or reformulating the factorization as conditional on this property.
  2. [4.1, Eqs. (4.24)-(4.27)] The vanishing of the soft matrix elements S_F, S_G, and S_H is argued from boost invariance and checked only at leading order; the text then states that this conclusion holds to all orders in perturbation theory. These terms are dropped from the NLP hadronic tensor, so the completeness of Eqs. (4.76) and (4.86) rests on that all-order statement. The power-mixing discussion in Sec. 4.2.3 further shows that overlap subtractions of higher-power operators can be lifted in power counting, so the all-order vanishing is not automatic. A one-loop check with the delta-regulator, or a formal proof that the regulated operators including inverse derivatives transform trivially under the relevant boost, would remove this gap. Without such a check, the completeness claim remains an extrapolation of the same type as the endpoint-divergence claim.
  3. [3.5 and 4.4, Eq. (4.87)] The reconciliation with ref. [6] rests on the relation H2(xi,Q^2) = H1(Q^2) + (H2 x K)(xi,Q^2) + O(xi), which the paper explicitly leaves unproven. This relation is not a detail: it is the decisive condition for absorbing the soft-gluon contribution into the collinear and anti-collinear distributions, and hence for the claimed agreement with ref. [6] beyond the lowest perturbative order. The manuscript should either prove this relation at the first order where it matters, or state more prominently that the agreement with ref. [6] is conjectural beyond the order explicitly checked. The current wording is honest, but the strength of the agreement claim in the abstract and introduction should match the conditional status of Eq. (4.87).
minor comments (5)
  1. [3 (heading)] The section heading contains a typo: 'at to next-to-leading power' should read 'at next-to-leading power'.
  2. [4.2, Eq. (4.29)] Eq. (4.29) writes the Wilson-line integral for W with dy^+ while the argument y^- n suggests it should be dy^-; compare Eq. (3.9).
  3. [5.3.2, Eq. (5.73)] Eq. (5.73) contains a duplicated 'was was derived'.
  4. [4.4, Eq. (4.87)] The convolution notation (H2 x K)(xi,Q^2) is introduced only verbally; defining the convolution explicitly would improve reproducibility.
  5. [5.3.1, Eq. (5.63)] The toy model in Eq. (5.63) uses a Gaussian damping e^{-xi^2/2} without specifying the width of the Gaussian; stating whether the width is fixed or fitted would improve the reproducibility of the phenomenological curves.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the NLP factorization is derived from full QCD matching and independent-framework comparisons; the all-order endpoint-divergence expectation is a rigor gap, not a circular reduction.

full rationale

The central NLP factorization is not constructed by fitting the target cross section. The effective current (Sec. 3) is obtained from the full-QCD current by integrating out hard modes (Eqs. (2.15), (3.2)), matching to gauge-invariant SCET building blocks, and constraining Wilson coefficients by current conservation and RPI; no target hadronic tensor is inserted as an input. The hadronic tensor (Sec. 4.3) is a direct product of current insertions, and the overlap-subtracted twist-3 TMDs in Eqs. (4.77)-(4.84) are operator definitions with subtractions that follow from the soft-collinear overlap analysis of Sec. 4.2, not from demanding finiteness of a pre-chosen cross section. Agreement with refs. [5,6] is a cross-check against external published frameworks; Sec. 4.4 even leaves Eq. (4.87) as an unproven condition for higher-order agreement, which is the opposite of importing a uniqueness theorem. The main caveat is not circular: in Sec. 4.2.4 the LO verification Eq. (4.63) is extended by 'We expect that this relation holds to all orders in the coupling and on a non-perturbative level as well', and the manifestly finite convolution Eq. (4.64) is concluded from that expectation. If the all-order identification fails, the physical twist-3 distributions still have endpoint divergences and the Sec. 5 cross section is not established. This is an omitted-proof/assumption gap, not a reduction of the result to its inputs. Self-citations ([5,44,60]) supply method, evolution, and J21 ingredients, but these are published independent derivations and do not assume the present factorization formula. The phenomenological section uses external Boer-Mulders/Sivers parameterizations and is explicitly a model illustration, not a prediction forced by a fit.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central factorization theorem introduces no new particles, forces, or conserved quantities. The soft background field is a bookkeeping device that already exists in the effective-theory literature. The only fitted quantities appear in the phenomenological section: parameters of the Boer-Mulders and Sivers models, plus an ad hoc Gaussian damping in the twist-3 model. The listed axioms are the load-bearing background assumptions the derivation inherits, several of which are explicitly flagged by the authors as unproven at all orders.

free parameters (3)
  • Boer-Mulders model parameters = N_q=0.854(+0.378,-1.076), N_antiq=-0.0854(+0.1076,-0.0378), alpha=9.4(+5.4,-0.9), lambda=0.2 GeV (Eq. 5.69)
    Inputs from ref. [58] fit to Drell-Yan angular data; used only for the phenomenological LL prediction of the sin phi_J asymmetry, not for the factorization theorem.
  • Sivers model parameters = A_f, N_f, beta_f, eps_f in Table 1; r0=0.54(+0.60,-0.53), r1=5.22(+1.18,-3.43), r2=203(+71,-133) GeV^2 (Eq. 5.71)
    Inputs from ref. [104] fit to Sivers asymmetry data; used as an alternative model for g_perp_2L in Figs. 3 and 4.
  • Ad hoc Gaussian damping in the twist-3 TMD model = e^{-xi^2/2}, no fitted value
    Eq. (5.63) introduces a Gaussian damping in xi with unit variance by hand. It shapes the LL phenomenological prediction and has no derivation from QCD.
assumptions (6)
  • domain assumption Glauber gluon exchanges can be neglected at NLP because their leading-power contributions cancel in TMD cross sections.
    Sec. 2 states 'we neglect Glauber modes altogether' citing refs. [15,69] for leading power; no NLP proof is given. If Glauber modes contribute at next-to-leading power, the mode factorization is incomplete.
  • domain assumption The overlap subtraction can be implemented with the displayed soft-Wilson-line and additive terms, dropping higher-order overlap interaction terms.
    Sec. 4.2.2, LP contribution paragraph: 'In principle, one also needs to consider higher-order overlap interaction terms, but we omit those in the present analysis.' The resulting physical TMDs inherit this truncation.
  • domain assumption Endpoint-divergence cancellation by overlap subtraction holds to all orders.
    Eq. (4.63) is a leading-order check; the all-order claim is an expectation based on identifying the subtraction with the soft-gluon limit. This underpins Eqs. (4.77)-(4.84) and the finite cross section in Sec. 5.
  • domain assumption The soft matrix elements F, G, and H vanish by boost invariance to all orders.
    Sec. 4.1 argues that an imbalance of inverse derivatives, combined with the trivial boost action on the vacuum and the TMD measurement, forces these matrix elements to vanish; this is checked at LO with regulators. The argument is used to discard many NLP soft operators.
  • standard math The multipole expansion identity and inverse-derivative definitions from ref. [5] apply at NLP with process-dependent boundaries.
    Eqs. (3.3)-(3.6) import the all-order multipole expansion from ref. [5]; the boundary convention encodes whether the state is initial or final. The paper relies on this to simplify the effective current.
  • domain assumption Current conservation and RPI constrain Wilson coefficients pointwise, in particular C_bar-q-g-q = delta(z+) C1 in Eq. (3.42).
    Sec. 3.3 sets aside convolutions in the conservation analysis. Ref. [6] obtains an additional hard-collinear term; the paper itself flags the unresolved disagreement and proposes condition Eq. (4.87).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Soft background fields at next-to-leading power in transverse momentum dependent SIDIS with jets." pith.science (2026). https://pith.science/paper/FKCYL4UF

@misc{pith2026250703072,
  author       = {Pith},
  title        = {Pith review of: Soft background fields at next-to-leading power in transverse momentum dependent SIDIS with jets},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FKCYL4UF}},
  note         = {Machine review of arXiv:2507.03072}
}
abstract

We present a factorization formula for the $e + h \rightarrow e + \text{jet} + X$ cross section at small transverse momenta up to next-to-leading power (NLP), derived using the background field method (BFM) with explicit inclusion of soft modes. We discuss the relation between soft modes and overlap subtractions at NLP, showing that the inclusion of soft modes enables a definition of twist-3 operators with properly subtracted rapidity and endpoint divergences. We also derive the effective current operator at NLP and identify additional structures compared to previous approaches based on soft-collinear effective theory and the BFM without soft modes. Nevertheless, for the hadronic tensor, we find agreement at the perturbative order that we are working at, and identify a condition that needs to be satisfied for this agreement to extend to higher orders. Furthermore, we construct the most general form factors for this process, taking into account the polarization of the initial states. These involve perturbatively-calculable jet functions, opening a path to precise determinations of twist-3 hadronic distributions. Finally, our formalism is illustrated with phenomenological results for a specific azimuthal asymmetry, whose leading-logarithmic contribution depends solely on a twist-3 hadronic distribution and a twist-2 jet function.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Next-to-next-to-leading power corrections to unpolarized Semi-Inclusive Deep Inelastic Scattering

    hep-ph 2026-01 conditional novelty 6.0 of 10

    Analytic 1/Q² corrections to the four unpolarized SIDIS structure functions are derived from the rapidity-factorization 'gauge-completion' approach, giving f1⊗D1 and h1^⊥⊗H1^⊥ convolutions with numerical estimates for...

Reference graph

Works this paper leans on

108 extracted references · 13 canonical work pages · cited by 1 Pith paper

  1. [6]

    Ebert, A

    M.A. Ebert, A. Gao and I.W. Stewart, Factorization for azimuthal asymmetries in SIDIS at next-to-leading power, JHEP 06 (2022) 007 [ 2112.07680]

    arXiv 2022

  2. [1]

    Collins, Foundations of Perturbative QCD , vol

    J. Collins, Foundations of Perturbative QCD , vol. 32, Cambridge University Press (2011), 10.1017/9781009401845

    doi:10.1017/9781009401845 2011

  3. [2]

    Becher and M

    T. Becher and M. Neubert, Drell-Yan Production at Small qT , Transverse Parton Distributions and the Collinear Anomaly , Eur. Phys. J. C 71 (2011) 1665 [ 1007.4005]

    arXiv 2011

  4. [3]

    Echevarria, A

    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 [1111.4996]

    arXiv 2012

  5. [4]

    J.-Y. Chiu, A. Jain, D. Neill and I.Z. Rothstein, A Formalism for the Systematic Treatment of Rapidity Logarithms in Quantum Field Theory , JHEP 05 (2012) 084 [ 1202.0814]

    arXiv 2012

  6. [5]

    Vladimirov, V

    A. Vladimirov, V. Moos and I. Scimemi, Transverse momentum dependent operator expansion at next-to-leading power , JHEP 01 (2022) 110 [ 2109.09771]

    arXiv 2022

  7. [7]

    Moult and H.X

    I. Moult and H.X. Zhu, Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation , JHEP 08 (2018) 160 [ 1801.02627]

    arXiv 2018

  8. [8]

    H.T. Li, Y. Makris and I. Vitev, Energy-energy correlators in Deep Inelastic Scattering , Phys. Rev. D 103 (2021) 094005 [ 2102.05669]

    arXiv 2021

Show all 108 references
  1. [9]

    Z.-B. Kang, K. Lee, D.Y. Shao and F. Zhao, Probing transverse momentum dependent structures with azimuthal dependence of energy correlators , JHEP 03 (2024) 153 [2310.15159]

    2024 arXiv

  2. [10]

    Z.-B. Kang, S. Lee, J. Penttala, F. Zhao and Y. Zhou, Transverse Energy-Energy Correlator for Vector Boson-Tagged Hadron Production in pp and pA collisions, 2410.02747

    arXiv

  3. [11]

    Bris Cuerpo, I

    A. Bris Cuerpo, I. Scimemi and A. Vladimirov, In preparation,

  4. [12]

    Altarelli, G

    G. Altarelli, G. Parisi and R. Petronzio, Transverse Momentum in Drell-Yan Processes, Phys. Lett. B 76 (1978) 351

    1978

  5. [13]

    Dokshitzer, D

    Y.L. Dokshitzer, D. Diakonov and S.I. Troian, Hard Processes in Quantum Chromodynamics, Phys. Rept. 58 (1980) 269

    1980

  6. [14]

    Collins and D.E

    J.C. Collins and D.E. Soper, Back-To-Back Jets in QCD , Nucl. Phys. B 193 (1981) 381

    1981

  7. [15]

    Collins, D.E

    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. B 250 (1985) 199

    1985

  8. [16]

    Boer and W

    D. Boer and W. Vogelsang, Asymmetric jet correlations in p p uparrow scattering , Phys. Rev. D 69 (2004) 094025 [ hep-ph/0312320]

    2004 arXiv

  9. [17]

    Bacchetta, C.J

    A. Bacchetta, C.J. Bomhof, P.J. Mulders and F. Pijlman, Single spin asymmetries in hadron-hadron collisions, Phys. Rev. D 72 (2005) 034030 [ hep-ph/0505268]

    2005 arXiv

  10. [18]

    Bacchetta, C

    A. Bacchetta, C. Bomhof, U. D’Alesio, P.J. Mulders and F. Murgia, The Sivers single-spin asymmetry in photon-jet production , Phys. Rev. Lett. 99 (2007) 212002 [ hep-ph/0703153]. – 62 –

    2007 arXiv

  11. [19]

    Gutierrez-Reyes, I

    D. Gutierrez-Reyes, I. Scimemi, W.J. Waalewijn and L. Zoppi, Transverse momentum dependent distributions with jets , Phys. Rev. Lett. 121 (2018) 162001 [ 1807.07573]

    2018 arXiv

  12. [20]

    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 , JHEP 10 (2019) 031 [ 1904.04259]

    2019 arXiv

  13. [21]

    Gutierrez-Reyes, Y

    D. Gutierrez-Reyes, Y. Makris, V. Vaidya, I. Scimemi and L. Zoppi, Probing Transverse-Momentum Distributions With Groomed Jets , JHEP 08 (2019) 161 [1907.05896]

    2019 arXiv

  14. [22]

    Chien, R

    Y.-T. Chien, R. Rahn, S. Schrijnder van Velzen, D.Y. Shao, W.J. Waalewijn and B. Wu, Recoil-free azimuthal angle for precision boson-jet correlation , Phys. Lett. B 815 (2021) 136124 [2005.12279]

    2021 arXiv

  15. [23]

    W.K. Lai, X. Liu, M. Wang and H. Xing, Unveiling Nucleon 3D Chiral-Odd Structure with Jet Axes , 2205.04570

    arXiv

  16. [24]

    Chien, R

    Y.-T. Chien, R. Rahn, D.Y. Shao, W.J. Waalewijn and B. Wu, Precision boson-jet azimuthal decorrelation at hadron colliders , JHEP 02 (2023) 256 [ 2205.05104]

    2023 arXiv

  17. [25]

    D’Alesio, F

    U. D’Alesio, F. Murgia and C. Pisano, Azimuthal asymmetries for hadron distributions inside a jet in hadronic collisions , Phys. Rev. D 83 (2011) 034021 [ 1011.2692]

    2011 arXiv

  18. [26]

    D’Alesio, L

    U. D’Alesio, L. Gamberg, Z.-B. Kang, F. Murgia and C. Pisano, Testing the process dependence of the Sivers function via hadron distributions inside a jet , Phys. Lett. B 704 (2011) 637 [ 1108.0827]

    2011 arXiv

  19. [27]

    R. Bain, Y. Makris and T. Mehen, Transverse Momentum Dependent Fragmenting Jet Functions with Applications to Quarkonium Production , JHEP 11 (2016) 144 [1610.06508]

    2016 arXiv

  20. [28]

    Neill, I

    D. Neill, I. Scimemi and W.J. Waalewijn, Jet axes and universal transverse-momentum-dependent fragmentation, JHEP 04 (2017) 020 [ 1612.04817]

    2017 arXiv

  21. [29]

    Z.-B. Kang, X. Liu, F. Ringer and H. Xing, The transverse momentum distribution of hadrons within jets , JHEP 11 (2017) 068 [ 1705.08443]

    2017 arXiv

  22. [30]

    Makris and V

    Y. Makris and V. Vaidya, Transverse Momentum Spectra at Threshold for Groomed Heavy Quark Jets , JHEP 10 (2018) 019 [ 1807.09805]

    2018 arXiv

  23. [31]

    Neill, A

    D. Neill, A. Papaefstathiou, W.J. Waalewijn and L. Zoppi, Phenomenology with a recoil-free jet axis: TMD fragmentation and the jet shape , JHEP 01 (2019) 067 [ 1810.12915]

    2019 arXiv

  24. [32]

    Z.-B. Kang, K. Lee, J. Terry and H. Xing, Jet fragmentation functions for Z-tagged jets, Phys. Lett. B 798 (2019) 134978 [ 1906.07187]

    2019 arXiv

  25. [33]

    Z.-B. Kang, K. Lee and F. Zhao, Polarized jet fragmentation functions , Phys. Lett. B 809 (2020) 135756 [ 2005.02398]

    2020 arXiv

  26. [34]

    D’Alesio, C

    U. D’Alesio, C. Flore and M. Zaccheddu, Collins function for pion-in-jet production in polarized pp collisions: a test of universality and factorization , 2506.21959

  27. [35]

    Arratia, Y

    M. Arratia, Y. Song, F. Ringer and B.V. Jacak, Jets as precision probes in electron-nucleus collisions at the future Electron-Ion Collider , Phys. Rev. C 101 (2020) 065204 [1912.05931]

    2020 arXiv

  28. [36]

    Arratia, Y

    M. Arratia, Y. Furletova, T.J. Hobbs, F. Olness and S.J. Sekula, Charm jets as a probe for strangeness at the future Electron-Ion Collider , Phys. Rev. D 103 (2021) 074023 [2006.12520]. – 63 –

    2021 arXiv

  29. [37]

    Arratia, Z.-B

    M. Arratia, Z.-B. Kang, A. Prokudin and F. Ringer, Jet-based measurements of Sivers and Collins asymmetries at the future electron-ion collider , Phys. Rev. D 102 (2020) 074015 [2007.07281]

    2020 arXiv

  30. [38]

    Arratia, Y

    M. Arratia, Y. Makris, D. Neill, F. Ringer and N. Sato, Asymmetric jet clustering in deep-inelastic scattering, Phys. Rev. D 104 (2021) 034005 [ 2006.10751]

    2021 arXiv

  31. [39]

    X. Liu, F. Ringer, W. Vogelsang and F. Yuan, Lepton-jet Correlation in Deep Inelastic Scattering, Phys. Rev. D 102 (2020) 094022 [ 2007.12866]

    2020 arXiv

  32. [40]

    Z.-B. Kang, K. Lee, D.Y. Shao and F. Zhao, Spin asymmetries in electron-jet production at the future electron ion collider , JHEP 11 (2021) 005 [ 2106.15624]

    2021 arXiv

  33. [41]

    Yang and X

    W. Yang and X. Yang, Intrinsic asymmetries in semi-inclusive deeply inelastic scattering at the Electron-Ion Collider , Phys. Rev. D 106 (2022) 093003 [ 2209.01629]

    2022 arXiv

  34. [42]

    Caucal, E

    P. Caucal, E. Iancu, A.H. Mueller and F. Yuan, Jet Definition and Transverse-Momentum–Dependent Factorization in Semi-inclusive Deep-Inelastic Scattering, Phys. Rev. Lett. 134 (2025) 061903 [ 2408.03129]

    2025 arXiv

  35. [43]

    Billis, F.J

    G. Billis, F.J. Tackmann and J. Talbert, Higher-Order Sudakov Resummation in Coupled Gauge Theories, JHEP 03 (2020) 182 [ 1907.02971]

    2020 arXiv

  36. [44]

    Scimemi and A

    I. Scimemi and A. Vladimirov, Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum , JHEP 06 (2020) 137 [1912.06532]

    2020 arXiv

  37. [45]

    MAP (Multi-dimensional Analyses of Partonic distributions)collaboration, Unpolarized transverse momentum distributions from a global fit of Drell-Yan and semi-inclusive deep-inelastic scattering data , JHEP 10 (2022) 127 [ 2206.07598]

    2022 arXiv

  38. [46]

    V. Moos, I. Scimemi, A. Vladimirov and P. Zurita, Extraction of unpolarized transverse momentum distributions from the fit of Drell-Yan data at N 4LL, JHEP 05 (2024) 036 [2305.07473]

    2024 arXiv

  39. [47]

    Camarda, L

    S. Camarda, L. Cieri and G. Ferrera, Drell–Yan lepton-pair production: qT resummation at N4LL accuracy, Phys. Lett. B 845 (2023) 138125 [ 2303.12781]

    2023 arXiv

  40. [48]

    MAP (Multi-dimensional Analyses of Partonic distributions)collaboration, Flavor dependence of unpolarized quark transverse momentum distributions from a global fit, JHEP 08 (2024) 232 [ 2405.13833]

    2024 arXiv

  41. [49]

    Billis, J.K.L

    G. Billis, J.K.L. Michel and F.J. Tackmann, Drell-Yan transverse-momentum spectra at N3LL′ and approximate N 4LL with SCETlib , JHEP 02 (2025) 170 [ 2411.16004]

    2025 arXiv

  42. [50]

    MAP (Multi-dimensional Analyses of Partonic distributions)collaboration, A Neural-Network Extraction of Unpolarised Transverse-Momentum-Dependent Distributions , 2502.04166

    arXiv

  43. [51]

    V. Moos, I. Scimemi, A. Vladimirov and P. Zurita, Determination of unpolarized TMD distributions from the fit of Drell-Yan and SIDIS data at N 4LL, 2503.11201

  44. [52]

    Ebert, I

    M.A. Ebert, I. Moult, I.W. Stewart, F.J. Tackmann, G. Vita and H.X. Zhu, Subleading power rapidity divergences and power corrections for q T , JHEP 04 (2019) 123 [1812.08189]

    2019 arXiv

  45. [53]

    Gamberg, Z.-B

    L. Gamberg, Z.-B. Kang, D.Y. Shao, J. Terry and F. Zhao, Transverse-momentum-dependent factorization at next-to-leading power , 2211.13209. – 64 –

    arXiv

  46. [54]

    Rodini and A

    S. Rodini and A. Vladimirov, Definition and evolution of transverse momentum dependent distribution of twist-three , JHEP 08 (2022) 031 [ 2204.03856]

    2022 arXiv

  47. [55]

    Ferrera, W.-L

    G. Ferrera, W.-L. Ju and M. Sch¨ onherr,Zero-bin subtraction and the q T spectrum beyond leading power, JHEP 04 (2024) 005 [ 2312.14911]

    2024 arXiv

  48. [56]

    Balitsky, 1 /Q2 power corrections to TMD factorization for Drell-Yan hadronic tensor , Nucl

    I. Balitsky, 1 /Q2 power corrections to TMD factorization for Drell-Yan hadronic tensor , Nucl. Phys. B 1006 (2024) 116658 [ 2404.15116]

    2024 arXiv

  49. [57]

    Liu, P.-A

    X.-T. Liu, P.-A. Liu, Y.-L. Liu and A.-P. Chen, Evolution of unpolarized transverse momentum dependent parton distributions of twist-3 , Phys. Rev. D 111 (2025) 114025 [2409.09667]

    2025 arXiv

  50. [58]

    Piloneta and A

    S. Piloneta and A. Vladimirov, Angular distributions of Drell-Yan leptons in the TMD factorization approach, JHEP 12 (2024) 059 [ 2407.06277]

    2024 arXiv

  51. [59]

    Rodini and A

    S. Rodini and A. Vladimirov, Transverse momentum dependent factorization for SIDIS at next-to-leading power, Phys. Rev. D 110 (2024) 034009 [ 2306.09495]

    2024 arXiv

  52. [60]

    del Castillo, M

    R.F. del Castillo, M. Jaarsma, I. Scimemi and W. Waalewijn, Transverse momentum measurements with jets at next-to-leading power , JHEP 02 (2024) 074 [ 2307.13025]

    2024 arXiv

  53. [61]

    Bauer and I.W

    C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory , Phys. Lett. B 516 (2001) 134 [ hep-ph/0107001]

    2001 arXiv

  54. [62]

    Bauer, D

    C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory , Phys. Rev. D 65 (2002) 054022 [ hep-ph/0109045]

    2002 arXiv

  55. [63]

    Bauer, S

    C.W. Bauer, S. Fleming, D. Pirjol, I.Z. Rothstein and I.W. Stewart, Hard scattering factorization from effective field theory , Phys. Rev. D 66 (2002) 014017 [ hep-ph/0202088]

    2002 arXiv

  56. [64]

    Beneke, A.P

    M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power , Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152]

    2002 arXiv

  57. [65]

    Becher, A

    T. Becher, A. Broggio and A. Ferroglia, Introduction to Soft-Collinear Effective Theory , vol. 896, Springer (2015), 10.1007/978-3-319-14848-9, [ 1410.1892]

    2015 arXiv

  58. [66]

    Rodini, A.C

    S. Rodini, A.C. Alvaro and B. Pasquini, Collinear matching for next-to-leading power transverse-momentum distributions, Phys. Lett. B 845 (2023) 138163 [ 2306.15052]

    2023 arXiv

  59. [67]

    Vladimirov, Kinematic power corrections in TMD factorization theorem , JHEP 12 (2023) 008 [ 2307.13054]

    A. Vladimirov, Kinematic power corrections in TMD factorization theorem , JHEP 12 (2023) 008 [ 2307.13054]

    2023 arXiv

  60. [68]

    Rothstein and I.W

    I.Z. Rothstein and I.W. Stewart, An Effective Field Theory for Forward Scattering and Factorization Violation, JHEP 08 (2016) 025 [ 1601.04695]

    2016 arXiv

  61. [69]

    Collins, D.E

    J.C. Collins, D.E. Soper and G.F. Sterman, Soft Gluons and Factorization , Nucl. Phys. B 308 (1988) 833

    1988

  62. [70]

    Manohar, T

    A.V. Manohar, T. Mehen, D. Pirjol and I.W. Stewart, Reparameterization invariance for collinear operators, Phys. Lett. B 539 (2002) 59 [ hep-ph/0204229]

    2002 arXiv

  63. [71]

    Marcantonini and I.W

    C. Marcantonini and I.W. Stewart, Reparameterization Invariant Collinear Operators, Phys. Rev. D 79 (2009) 065028 [ 0809.1093]

    2009 arXiv

  64. [72]

    Beneke, A

    M. Beneke, A. Broggio, M. Garny, S. Jaskiewicz, R. Szafron, L. Vernazza et al., Leading-logarithmic threshold resummation of the Drell-Yan process at next-to-leading power, JHEP 03 (2019) 043 [ 1809.10631]. – 65 –

    2019 arXiv

  65. [73]

    Manohar and I.W

    A.V. Manohar and I.W. Stewart, The Zero-Bin and Mode Factorization in Quantum Field Theory, Phys. Rev. D 76 (2007) 074002 [ hep-ph/0605001]

    2007 arXiv

  66. [74]

    Lee and G.F

    C. Lee and G.F. Sterman, Universality of nonperturbative effects in event shapes , eConf C0601121 (2006) A001 [ hep-ph/0603066]

    2006 arXiv

  67. [75]

    Idilbi and T

    A. Idilbi and T. Mehen, On the equivalence of soft and zero-bin subtractions , Phys. Rev. D 75 (2007) 114017 [ hep-ph/0702022]

    2007 arXiv

  68. [76]

    Echevarr ´ ıa, A

    M.G. Echevarr ´ ıa, A. Idilbi and I. Scimemi,Soft and Collinear Factorization and Transverse Momentum Dependent Parton Distribution Functions , Phys. Lett. B 726 (2013) 795 [1211.1947]

    2013 arXiv

  69. [77]

    Echevarria, I

    M.G. Echevarria, I. Scimemi and A. Vladimirov, Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order, JHEP 09 (2016) 004 [ 1604.07869]

    2016 arXiv

  70. [78]

    Vladimirov, Structure of rapidity divergences in multi-parton scattering soft factors , JHEP 04 (2018) 045 [ 1707.07606]

    A. Vladimirov, Structure of rapidity divergences in multi-parton scattering soft factors , JHEP 04 (2018) 045 [ 1707.07606]

    2018 arXiv

  71. [79]

    Echevarria, I

    M.G. Echevarria, I. Scimemi and A. Vladimirov, Universal transverse momentum dependent soft function at NNLO , Phys. Rev. D 93 (2016) 054004 [ 1511.05590]

    2016 arXiv

  72. [80]

    Liu and M

    Z.L. Liu and M. Neubert, Factorization at subleading power and endpoint-divergent convolutions in h → γγ decay, JHEP 04 (2020) 033 [ 1912.08818]

    2020 arXiv

  73. [81]

    Z.L. Liu, B. Mecaj, M. Neubert and X. Wang, Factorization at subleading power, Sudakov resummation, and endpoint divergences in soft-collinear effective theory , Phys. Rev. D 104 (2021) 014004 [ 2009.04456]

    2021 arXiv

  74. [82]

    Beneke, M

    M. Beneke, M. Garny, S. Jaskiewicz, J. Strohm, R. Szafron, L. Vernazza et al., Endpoint factorization and next-to-leading power resummation of gluon thrust , PoS LL2022 (2022) 068 [2207.14199]

    2022 arXiv

  75. [83]

    Gao, Transverse Momentum Distributions at Subleading Power and Quark-Gluon-Quark Correlators, Presented at REF workshop 2022

    A. Gao, Transverse Momentum Distributions at Subleading Power and Quark-Gluon-Quark Correlators, Presented at REF workshop 2022

    2022

  76. [84]

    Gao, Renormalization for NLP TMD Quark-Gluon-Quark Correlators , Presented at SCET workshop 2023

    A. Gao, Renormalization for NLP TMD Quark-Gluon-Quark Correlators , Presented at SCET workshop 2023

    2023

  77. [85]

    Quantum Field Theory at the Frontiers of the Strong Interaction

    J. Michel, Subleading-Power Soft Subtleties in SIDIS , Presented at the ESI workshop “Quantum Field Theory at the Frontiers of the Strong Interaction” in 2023

    2023

  78. [86]

    Balitsky and A

    I. Balitsky and A. Tarasov, Power corrections to TMD factorization for Z-boson production , JHEP 05 (2018) 150 [ 1712.09389]

    2018 arXiv

  79. [87]

    Beneke, M

    M. Beneke, M. Garny, R. Szafron and J. Wang, Anomalous dimension of subleading-power N-jet operators, JHEP 03 (2018) 001 [ 1712.04416]

    2018 arXiv

  80. [88]

    Abdul Khalek et al., Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report , Nucl

    R. Abdul Khalek et al., Science Requirements and Detector Concepts for the Electron-Ion Collider: EIC Yellow Report , Nucl. Phys. A 1026 (2022) 122447 [ 2103.05419]

    2022 arXiv

  81. [89]

    Z.-B. Kang, F. Ringer and I. Vitev, Jet substructure using semi-inclusive jet functions in SCET, JHEP 11 (2016) 155 [ 1606.07063]

    2016 arXiv

  82. [90]

    Bertolini, T

    D. Bertolini, T. Chan and J. Thaler, Jet Observables Without Jet Algorithms , JHEP 04 (2014) 013 [ 1310.7584]. – 66 –

    2014 arXiv

  83. [91]

    HERMES collaboration, Quark helicity distributions in the nucleon for up, down, and strange quarks from semi-inclusive deep-inelastic scattering , Phys. Rev. D 71 (2005) 012003 [hep-ex/0407032]

    2005 arXiv

  84. [92]

    Boer and P.J

    D. Boer and P.J. Mulders, Time-reversal odd distribution functions in leptoproduction , Physical Review D 57 (1998) 5780–5786

    1998

  85. [93]

    D. Boer, P. Mulders and F. Pijlman, Universality of t-odd effects in single spin and azimuthal asymmetries , Nuclear Physics B 667 (2003) 201–241

    2003

  86. [94]

    Ralston and D.E

    J.P. Ralston and D.E. Soper, Production of Dimuons from High-Energy Polarized Proton Proton Collisions , Nucl. Phys. B 152 (1979) 109

    1979

  87. [95]

    Tangerman and P.J

    R.D. Tangerman and P.J. Mulders, Intrinsic transverse momentum and the polarized Drell-Yan process, Phys. Rev. D 51 (1995) 3357 [ hep-ph/9403227]

    1995 arXiv

  88. [96]

    Mulders and R.D

    P.J. Mulders and R.D. Tangerman, The Complete tree level result up to order 1/Q for polarized deep inelastic leptoproduction, Nucl. Phys. B 461 (1996) 197 [ hep-ph/9510301]

    1996 arXiv

  89. [97]

    Bacchetta, M

    A. Bacchetta, M. Diehl, K. Goeke, A. Metz, P.J. Mulders and M. Schlegel, Semi-inclusive deep inelastic scattering at small transverse momentum , JHEP 02 (2007) 093 [hep-ph/0611265]

    2007 arXiv

  90. [98]

    D. Boer, L. Gamberg, B. Musch and A. Prokudin, Bessel-Weighted Asymmetries in Semi Inclusive Deep Inelastic Scattering , JHEP 10 (2011) 021 [ 1107.5294]

    2011 arXiv

  91. [99]

    Deur, S.J

    A. Deur, S.J. Brodsky and G.F. de T´ eramond, The qcd running coupling , Progress in Particle and Nuclear Physics 90 (2016) 1–74

    2016

  92. [100]

    Barone, S

    V. Barone, S. Melis and A. Prokudin, The Boer-Mulders effect in unpolarized SIDIS: An Analysis of the COMPASS and HERMES data on the cos 2 phi asymmetry , Phys. Rev. D 81 (2010) 114026 [ 0912.5194]

    2010 arXiv

  93. [101]

    Barone, S

    V. Barone, S. Melis and A. Prokudin, Azimuthal asymmetries in unpolarized drell-yan processes and the boer-mulders distributions of antiquarks , Physical Review D 82 (2010)

    2010

  94. [102]

    Barone, M

    V. Barone, M. Boglione, J. Gonzalez Hernandez and S. Melis, Phenomenological analysis of azimuthal asymmetries in unpolarized semi-inclusive deep inelastic scattering , Physical Review D 91 (2015)

    2015

  95. [103]

    Bastami, H

    S. Bastami, H. Avakian, A.V. Efremov, A. Kotzinian, B.U. Musch, B. Parsamyan et al., Semi-inclusive deep-inelastic scattering in wandzura-wilczek-type approximation , Journal of High Energy Physics 2019 (2019)

    2019

  96. [104]

    M. Bury, A. Prokudin and A. Vladimirov, Extraction of the Sivers function from SIDIS, Drell-Yan, and W ±/Z boson production data with TMD evolution , JHEP 05 (2021) 151 [2103.03270]

    2021 arXiv

  97. [105]

    K. Yang, T. Liu, P. Sun, Y. Zhao and B.-Q. Ma, Extraction of trans-helicity worm-gear distributions and opportunities at the electron-ion collider in china , 2024

    2024

  98. [106]

    Bacchetta, A

    A. Bacchetta, A. Bongallino, M. Cerutti, M. Radici and L. Rossi, Exploring the three-dimensional momentum distribution of longitudinally polarized quarks in the proton , 2409.18078

    arXiv

  99. [107]

    Beneke, Y

    M. Beneke, Y. Ji and X. Wang, Renormalization of the next-to-leading-power γγ → h and gg → h soft quark functions , JHEP 05 (2024) 246 [ 2403.17738]. – 67 –

    2024 arXiv

  100. [108]

    Beneke, Y

    M. Beneke, Y. Ji, E. S¨ underhauf and X. Wang,Renormalization of the next-to-leading-power soft function for the Drell-Yan off-diagonal channel , JHEP 05 (2025) 067 [ 2502.01973]. – 68 –

    2025 arXiv

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.