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REVIEW 2 major objections 3 minor 88 references

Nucleon Tomography with 0-jettiness

T0 review · 2 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Imposing a 0-jettiness veto on W and Z production suppresses initial-state radiation and enhances the transverse single-spin asymmetry by up to 83 percent, making the Sivers sign-change test more definitive.

desk verdict The veto idea and the joint Sudakov are consistent—the alleged discrepancy with the supplemental is a misreading of the integration limits—but the enhancement numbers are leading-log estimates that still need the Sivers matching coefficient and uncertainty bands. read the letter →

arxiv 2506.15962 v1 pith:W4QQCKQH submitted 2025-06-19 hep-ph

Shen Fang , Shuo Lin , Ding Yu Shao , Jian Zhou This is my paper
classification hep-ph
keywords 0-jettinessbeamthrusttransversemomentumdependentdistributionsSiversfunctionsinglespinasymmetryjointresummationDrell-YanQiu-Sterman
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 proposes a new way to map the nucleon's intrinsic three-dimensional structure: apply a 0-jettiness veto (a cut on an event shape that penalizes central gluon radiation) to Drell-Yan-like processes, so that the measured transverse momentum is dominated by the partons' intrinsic motion rather than by perturbative initial-state radiation. The authors show that, for transverse single-spin asymmetries in $W^\pm$ and $Z^0$ production in polarized proton-proton collisions at 500 GeV, the veto substantially increases the asymmetry—for example, by 83 percent for $Z^0$ at $q_\perp = 5$ GeV—compared with the inclusive case. To make this prediction, they derive a joint-resummed Sudakov factor that simultaneously resums large logarithms of the veto scale $\tau_0$ and of the boson's transverse momentum, unifying three effective-theory regions with $\theta$-function transitions. If correct, the method converts the veto scale into a tunable handle that suppresses TMD-evolution dilution, giving a sharper experimental test of the predicted sign change of the Sivers function and extending naturally to spin-dependent SIDIS at a future electron-ion collider.

What carries the argument

The load-bearing object is the 0-jettiness variable $\tau = \frac{2}{Q^2}\sum_i \min\{p_a\cdot l_i, p_b\cdot l_i\}$, an event shape that assigns small weight to beam-collinear particles and large weight to central emissions; the veto $\tau<\tau_0$ suppresses central initial-state radiation. The argument is carried by the joint Sudakov factor in Eq. (10), which exponentiates both $\ln(1/\tau_0)$ and $\ln(Q^2/q_\perp^2)$ logarithms by splicing together three soft-collinear effective theory regimes (one for large impact parameter, one intermediate, one for small impact parameter) with $\theta$-function transitions. Because the light-cone divergence has the same structure for spin-dependent and spin-independent TMDs, the same factor is applied to the Sivers function, whose non-perturbative content is then isolated by the veto.

What would settle it

Calculate the extra veto-dependent correction to the Sivers function that the paper leaves for future work, and check whether it is numerically negligible at the veto values used; if it is not, the predicted 83 percent enhancement is not reliable. Alternatively, measure the $Z^0$ single-spin asymmetry ratio with and without the veto in the same $q_\perp$ bin and see whether it matches the predicted increase.

Watch

Extended reading notes

Core claim

The central discovery claim is that a 0-jettiness veto suppresses the central initial-state radiation whose recoil and evolution effects dilute TMD observables, so that transverse single-spin asymmetries in $W^\pm$ and $Z^0$ production grow as the veto scale $\tau_0$ is lowered. The paper derives the veto-modified Sudakov factor $S_P(b)$ for isolated Drell-Yan-type processes, Eq. (10), in which the standard TMD evolution is replaced by a piecewise combination of soft-collinear effective theory regions, and applies this same factor to the Sivers function. The predicted effect is large: for example, at $\tau_0 = 0.015$ the $Z^0$ asymmetry integrated over $q_\perp$ from 1.5 to 6 GeV increases by about 42 percent, and at $q_\perp = 5$ GeV the enhancement reaches 83 percent, even though the veto reduces the event count and raises the statistical error by about 27 percent. This makes the comparison between Drell-Yan and SIDIS a more sensitive test of the Sivers sign-change prediction.

Load-bearing premise

The spin predictions assume the veto changes the spin-dependent and spin-independent cross sections in exactly the same way; if an additional veto-dependent correction term specific to the Sivers function turns out to be large, the quoted enhancement numbers would shift.

Editorial extensions

If this is right

  • At fixed $q_\perp$, the predicted SSA magnitude grows as $\tau_0$ decreases; for $Z^0$ at $q_\perp = 5$ GeV the enhancement reaches 83 percent relative to no veto.
  • The veto costs events: at $\tau_0 = 0.015$ the normalized $Z^0$ yield in $q_\perp$ between 1.5 and 6 GeV is about 62 percent of the inclusive yield, so the statistical error grows by about 27 percent, but the asymmetry increases by about 42 percent, improving overall sensitivity.
  • A stronger SSA signal in $W^\pm$ and $Z^0$ production makes the comparison with SIDIS more sensitive to the predicted sign change of the Sivers function.
  • The same joint-resummed framework applies to SIDIS at a future electron-ion collider, where applying the veto enhances pion asymmetries at moderately large transverse momentum.
  • Tuning the veto scale provides a controllable lever for isolating intrinsic parton transverse momentum from perturbative radiation, with applicability beyond spin asymmetries.

Reading between the lines

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

  • Beyond the paper, the veto strategy should also sharpen other spin-dependent TMD observables, since it reduces the TMD-evolution dilution that grows with the hard scale; dijet and electron-jet measurements at a future electron-ion collider are natural places to test this.
  • Beyond the paper, the predicted enhancement numbers inherit the assumptions of the non-perturbative Sudakov and Sivers parametrizations used in the numerics; updated global extractions could change the magnitude of the 83 percent example without changing the qualitative effect.
  • Beyond the paper, the theta-function interpolation among the three effective-theory regimes could be tested against a full fixed-order calculation at moderate transverse momentum, where both logarithms are moderate.
  • Beyond the paper, a dedicated measurement at multiple veto values could turn the $\tau_0$ dependence of the SSA into a direct probe of the spin-dependent non-perturbative Sudakov factor, not just of the Sivers function.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. The paper proposes using a 0-jettiness veto to suppress initial-state radiation in transverse momentum-dependent (TMD) observables, with the aim of enhancing sensitivity to intrinsic parton motion. It presents a joint resummation framework that resums both veto logarithms and TMD transverse-momentum logarithms, and applies it to transverse single-spin asymmetries (SSAs) in W^± and Z^0 production at RHIC. The authors report a substantial enhancement of the SSA (e.g., 83% for Z^0 at q_perp = 5 GeV) and argue that this facilitates a more definitive test of the predicted Sivers sign change. The paper also sketches an extension to SIDIS at the EIC.

Significance. If the central claims are correct, this work offers a new experimental lever to disentangle intrinsic non-perturbative transverse-momentum structure from perturbative radiation, and it extends joint resummation to spin-dependent TMD observables for the first time. The idea of using a tunable veto scale to amplify SSAs is potentially important for RHIC, the LHC, and the EIC. The paper is commendably clear in its heuristic derivation and provides a formal SCET treatment in the Supplemental Material. However, the quantitative predictions—especially the headline 83% enhancement—are load-bearing and currently rest on an unresolved inconsistency between the main-text Sudakov factor and the SCET result, as well as on an explicitly acknowledged but uncomputed matching coefficient for the Sivers function.

major comments (2)
  1. [TMDs with 0-jettiness (Eq. (10)) and Supplemental Material (Eq. (S-25))] The main-text Sudakov factor in Eq. (10) is not consistent with the rigorous SCET result in Eq. (S-25), despite the statement at the end of the Supplemental Material that the two are consistent. The theta functions in Eq. (10) are θ(t−μ_b^2) and θ(τ0 t − μ_b^2), whereas Eq. (S-25) uses θ(μ_b^2 − τ0 Q^2) and θ(μ_b^2 − τ0^2 Q^2); these supports are opposite for the first term. Moreover, Eq. (10) contains a fourth term ∫_{τ0 t}^{t} dμ^2/μ^2 ln(μ^2/(τ0 t)) that has no counterpart in Eq. (S-25). In the SCET+ regime (τ0^2 Q^2 < μ_b^2 < τ0 Q^2), which is exactly the regime relevant for the benchmark point τ0=0.015, Q=91 GeV, μ_b^2=31 GeV^2 (q_perp≈5 GeV), this extra term contributes about (CF/π) α_s × (1/2) ln^2(1/τ0), while Eq. (S-25) contains no such term. Consequently, the numerical predictions, including the 83% enhancement quoted in the abstract, are not quantitatively supported until this discrepancy is resolved. The authors must either correct Eq. (10) to match the SCET derivation, or justify the fourth term within the heuristic derivation, and then recompute the phenomenological results.
  2. [Impact of 0-jettiness on spin asymmetries] The central quantitative claim relies on the assumption that the joint-resummed Sudakov factor for the Sivers function is identical to the unpolarized one under the 0-jettiness veto, with no additional veto-dependent one-loop matching coefficient. The authors explicitly state that 'a full computation of the one-loop matching coefficient for the Sivers function with a 0-jettiness veto in the collinear twist-3 formalism is left for future investigation.' Since Eq. (11) uses this Sudakov factor for the spin-dependent cross section and Eq. (12) forms the ratio, the quoted enhancement (e.g., 83% for Z^0 at q_perp=5 GeV) is a leading-log estimate with an unquantified uncertainty. If the missing matching coefficient is numerically significant, the enhancement could change. The paper should either compute or estimate this matching term, or explicitly qualify the enhancement as a model-dependent estimate subject to this uncertainty.
minor comments (3)
  1. [Introduction] The phrase 'epandeAcollisions' appears to be a typo for 'ep and eA collisions'.
  2. [Eq. (10)] The suppressed Heaviside theta functions in Eq. (10) should be written explicitly in the integral limits or included as factors. The current notation, in which a lower limit can exceed the upper limit in some kinematic regions, is confusing and contributes to the inconsistency with Eq. (S-25).
  3. [Abstract and Conclusions] The abstract and conclusions present the 83% enhancement without qualification. Given the omitted matching coefficient and the Sudakov inconsistency, this number should be presented as an illustrative estimate pending a complete calculation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the 0-jettiness Sudakov factor and the SSA enhancement are derived quantities, not fits or self-citations.

full rationale

The central prediction is the ratio of SSAs with and without a 0-jettiness veto. The veto dependence enters only through the perturbative Sudakov factor derived in Eq. (10) (and the SCET version S-25); the Sivers normalization N_q(x) cancels in the ratio, so no fitted parameter is renamed as a prediction. The unpolarized and Sivers nonperturbative Sudakov factors are taken from external global fits [49,69] and are not tuned to the RHIC W/Z SSA data the paper predicts. The extension of the unpolarized Sudakov to the Sivers function is an assumption, explicitly flagged: "a full computation of the one-loop matching coefficient for the Sivers function with a 0-jettiness veto in the collinear twist-3 formalism is left for future investigation." That is an acknowledged limitation, not a circular step. The cited prior work [37,43] supplies the SCET framework, but the combined formula (S-25)/(10) is the paper's own construction; even if it disagrees numerically with the SCET+ expression (S-19), that is a correctness issue, not circularity. Self-citations such as [67] and [79] support standard matching and evolution statements and are not load-bearing for the central claim. The prediction is therefore self-contained against external benchmarks, and no derivation step reduces to its inputs by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's predictions rest on standard TMD factorization and on fitted nonperturbative inputs from prior global analyses. The central veto-enhancement ratio is largely independent of the Sivers normalization, which lowers the circularity burden. No new particles or fields are introduced.

free parameters (4)
  • b_max = 1.5 GeV^-1
    Hand-chosen regulator for the b* prescription in Eq. (13). Standard in TMD analyses, but the central predictions depend mildly on it.
  • Nonperturbative Sudakov parameters for unpolarized TMDs = 0.42, 0.106, Q0 = sqrt(2.4) GeV
    Taken from Ref. [69], fitted to Drell-Yan data in prior global analyses. Used in Eq. (14) for the unpolarized Sudakov factor.
  • Nonperturbative Sudakov parameter for Sivers function = 0.18 b^2 coefficient
    Taken from Ref. [49], fitted to SIDIS data. Used in Eq. (16) for the Sivers Sudakov factor.
  • N_q(x) parameterization of Qiu-Sterman function = See Table 2 of Ref. [49]
    Parameterizes T_F,q(x,x) = N_q(x) f_q(x) in Eq. (15). Sets the absolute SSA magnitude; largely cancels in the tau0 enhancement ratio at fixed kinematics but affects the plotted A_N.
assumptions (5)
  • domain assumption Standard TMD factorization for Drell-Yan processes at NLL accuracy, as encoded in Eq. (2).
    The analysis starts from the CSS-style TMD resummation formula and assumes its validity for the unpolarized cross section.
  • domain assumption The scale evolution of polarization-dependent TMDs is governed by the same Collins-Soper equation as unpolarized TMDs.
    Invoked in the section 'Impact of 0-jettiness on spin asymmetries' to extend the unpolarized Sudakov factor directly to the Sivers function.
  • domain assumption The Qiu-Sterman function can be parameterized as T_F,q(x,x,mu) = N_q(x) f_q(x,mu).
    Eq. (15), following the 'most economical choice' from Refs. [70,71]. This is a model assumption rather than a derived relation.
  • domain assumption SCET factorization in the SCET I, SCET +, and SCET II regimes, with the canonical scale choices given in the supplemental material.
    The joint resummation result in Eq. (S-25) relies on the mode decomposition and factorization formulas in the three kinematic regimes.
  • domain assumption Nonperturbative Sudakov parameterizations from low-energy global fits extrapolate to RHIC and EIC energies.
    The numerical predictions use Eqs. (14) and (16) fitted to existing data, assuming their validity at the higher scales and with the veto imposed.

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Pith. "Pith review of Nucleon Tomography with 0-jettiness." pith.science (2026). https://pith.science/paper/W4QQCKQH

@misc{pith2026250615962,
  author       = {Pith},
  title        = {Pith review of: Nucleon Tomography with 0-jettiness},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W4QQCKQH}},
  note         = {Machine review of arXiv:2506.15962}
}
abstract

We propose a novel strategy to systematically isolate the nucleon's intrinsic non-perturbative three-dimensional structure by employing 0-jettiness to suppress initial-state radiation in transverse momentum-dependent (TMD) observables. Applying this method to transverse single spin asymmetries (SSAs) in W+/- and Z0 boson production at RHIC, we demonstrate a substantial enhancement of the asymmetry signal (e.g., by 83% for Z0 SSA at $q_\perp$=5 GeV), enabling a more definitive test of the predicted sign change of the Sivers function -- a key prediction of TMD factorization. We further explore its applicability to spin-dependent measurements at the Electron-Ion Collider. Our analysis is formulated within a joint resummation framework that systematically resums large logarithms associated with both the veto scale and the gauge boson's transverse momentum.

Figures

Figures reproduced from arXiv: 2506.15962 by the authors.

Figure 1
Figure 1. FIG. 1: Schematic illustration of the final state configuration [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The normalized [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2: SSAs for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: The SSAs for [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The kinematic modes in three regimes for SCET [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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