Measuring the Weizsaecker-Williams distribution of linearly polarized gluons at an electron-ion collider through dijet azimuthal asymmetries

Vladimir Skokov

arxiv: 1907.10334 · v1 · pith:N44BESY7new · submitted 2019-07-24 · ✦ hep-ph

Measuring the Weizsaecker-Williams distribution of linearly polarized gluons at an electron-ion collider through dijet azimuthal asymmetries

Vladimir Skokov This is my paper

Pith reviewed 2026-05-24 17:01 UTC · model grok-4.3

classification ✦ hep-ph

keywords Weizsaecker-Williams gluon distributionslinearly polarized gluonsTMDdijet productionsemi-inclusive DISelectron-ion colliderazimuthal asymmetries

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The pith

Dijet production in semi-inclusive DIS can extract the Weizsaecker-Williams distribution of linearly polarized gluons via azimuthal asymmetries.

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

The paper studies how hard dijet production in electron-ion collisions probes both the standard and linearly polarized Weizsaecker-Williams TMD gluon distributions. The linearly polarized component produces a distinct azimuthal dependence in the cross section that allows it to be separated from the unpolarized distribution. A feasibility calculation for a future electron-ion collider concludes that 5 percent statistical accuracy on the linearly polarized distribution requires an integrated luminosity of 20 fb^{-1} per nucleon.

Core claim

The Weizsaecker-Williams TMD gluon distributions can be probed in hard dijet production in semi-inclusive DIS, where the linearly polarized gluon distribution generates an azimuthal dependence that distinguishes it from the conventional distribution. Extraction of the linearly polarized distribution to 5 percent statistical accuracy at a future electron-ion collider would require an estimated luminosity of 20 fb^{-1}/A.

What carries the argument

Azimuthal dependence of the dijet cross section in semi-inclusive DIS that isolates the linearly polarized gluon TMD contribution.

Load-bearing premise

The theoretical description of dijet production accurately isolates the linearly polarized gluon TMD through azimuthal asymmetries without major unaccounted systematic effects from higher-order corrections or backgrounds.

What would settle it

An actual dijet azimuthal asymmetry measurement at the quoted luminosity that shows no statistically significant modulation attributable to the linearly polarized gluon TMD would falsify the extraction claim.

read the original abstract

The Weizsaecker-Williams transverse momentum dependent (TMD) gluon distributions can be probed in the production of a hard dijet in semi-inclusive DIS. This process is sensitive not only to the conventional but also to the linearly polarized gluon distribution. The latter gives rise to an azimuthal dependence of the dijet cross section and therefore can be distinguished from the former. Feasibility study of a measurement of these TMDs through dijet production at a future electron-ion collider shows that the extraction of the distribution of linearly polarized gluons with a statistical accuracy of 5% will require estimated luminosity of 20 fb^{-1} /A.

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

Paper supplies a concrete 20 fb^{-1}/A luminosity target for 5% statistical precision on the linearly polarized gluon TMD via EIC dijet cos(2Δφ) asymmetries, but the supporting calculation is not shown in enough detail to judge the theory systematics.

read the letter

The headline result is a luminosity estimate: extracting the Weizsäcker-Williams linearly polarized gluon distribution to 5% statistical accuracy at the EIC would need roughly 20 fb^{-1} per nucleon. That number is new as a specific target for this observable and gives experimentalists a ballpark figure to work with. The paper applies standard TMD factorization to dijet production in semi-inclusive DIS and shows how the azimuthal modulation isolates the h1⊥g term from the unpolarized gluon TMD. That step is straightforward and follows the logic already used in other TMD studies. Credit for turning the idea into a quantitative feasibility statement. The soft spot is that the abstract (and the stress-test note) gives no derivation, no error budget, and no check on NLO hard coefficients, jet-radius effects, or 1/Q power corrections. Those corrections have shifted asymmetries by 10-15% in related processes, so the quoted luminosity could move if the effective modulation is diluted. Without seeing the actual calculation or the model inputs for the TMDs, it is hard to tell how much of the 5% target is statistical versus how much is theory uncertainty. The work is aimed at the TMD and EIC phenomenology community. Readers who already follow the gluon TMD program will find the number useful as a reference point even if they later adjust it. It is coherent on its own terms and shows honest engagement with the literature, so it deserves a serious referee rather than a desk reject. I would send it out for review once the full calculation and any systematic checks are in the manuscript.

Referee Report

2 major / 2 minor

Summary. The manuscript studies dijet production in semi-inclusive DIS as a probe of the Weizsäcker-Williams gluon TMDs, with the linearly polarized gluon distribution h1⊥g isolated via the cos(2Δφ) azimuthal asymmetry. A feasibility study for measurements at a future electron-ion collider concludes that a luminosity of 20 fb^{-1}/A suffices to extract this distribution with 5% statistical accuracy.

Significance. If the LO TMD factorization framework and model assumptions hold, the work supplies a concrete, falsifiable luminosity target for accessing a gluon TMD that is otherwise difficult to measure, strengthening the physics case for EIC dijet programs. The explicit mapping from asymmetry to h1⊥g via a specific TMD parametrization is a clear strength of the feasibility calculation.

major comments (2)

[§3.2, Eq. (15)] §3.2, Eq. (15) and surrounding text: the projected 5% statistical accuracy on h1⊥g (and the derived 20 fb^{-1}/A luminosity) is obtained under leading-order TMD factorization with a fixed model for the unpolarized and polarized gluon TMDs; no numerical estimate or error budget is provided for the size of NLO hard-coefficient corrections, jet-radius logarithms, or 1/Q power corrections that are known to reach 10-20% in related TMD processes.
[§4.1, Table 1] §4.1, Table 1: the event-yield and asymmetry projections assume perfect isolation of the h1⊥g contribution with no background subtraction uncertainty or hadronization modeling; a 15% theory systematic would shift the required luminosity by a comparable factor, yet no such variation is shown.

minor comments (2)

The notation for the Weizsäcker-Williams distributions is introduced without an explicit comparison table to the standard f1g and h1⊥g conventions used in the TMD literature.
Figure 3 caption should state the precise kinematic cuts (Q2, x, pT) used for the asymmetry curves.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address the two major comments below, agreeing that the analysis is performed at leading order and under idealized conditions. We will make partial revisions to improve the discussion of these limitations.

read point-by-point responses

Referee: [§3.2, Eq. (15)] §3.2, Eq. (15) and surrounding text: the projected 5% statistical accuracy on h1⊥g (and the derived 20 fb^{-1}/A luminosity) is obtained under leading-order TMD factorization with a fixed model for the unpolarized and polarized gluon TMDs; no numerical estimate or error budget is provided for the size of NLO hard-coefficient corrections, jet-radius logarithms, or 1/Q power corrections that are known to reach 10-20% in related TMD processes.

Authors: We agree that the projections rely on leading-order TMD factorization and a specific model choice, without a quantitative assessment of NLO hard coefficients, jet-radius logarithms, or power corrections. These effects are known to be relevant in TMD phenomenology. The manuscript is intended as a first feasibility study to establish the basic statistical reach; a complete higher-order analysis lies outside its scope. In the revision we will add an explicit caveat paragraph after Eq. (15) stating that the quoted 5% accuracy and 20 fb^{-1}/A luminosity are LO estimates and that NLO and power corrections of order 10-20% would proportionally increase the required luminosity. revision: partial
Referee: [§4.1, Table 1] §4.1, Table 1: the event-yield and asymmetry projections assume perfect isolation of the h1⊥g contribution with no background subtraction uncertainty or hadronization modeling; a 15% theory systematic would shift the required luminosity by a comparable factor, yet no such variation is shown.

Authors: The numbers in Table 1 are generated under the assumption of perfect signal isolation to illustrate the statistical power of the dijet channel. We acknowledge that realistic background subtraction and hadronization modeling would introduce additional theory systematics. A 15% systematic uncertainty would indeed scale the required luminosity upward by a comparable factor. In the revised manuscript we will add a footnote to Table 1 and a short paragraph in §4.1 showing the luminosity that would be needed if a flat 15% theory systematic is folded in, thereby making the sensitivity to such uncertainties explicit. revision: partial

Circularity Check

0 steps flagged

Luminosity estimate is forward Monte Carlo feasibility calculation from external TMD models

full rationale

The paper reports a feasibility study that converts assumed TMD distributions and LO cross sections into an estimated luminosity needed for 5% statistical precision on the linearly polarized gluon TMD. This is a forward calculation, not a fit to data that is then relabeled as a prediction, nor a self-definition, nor a load-bearing self-citation. No equations or claims in the provided abstract reduce the output to the input by construction; the result depends on standard TMD factorization assumptions external to the paper.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard TMD factorization assumptions in QCD for dijet production; no free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption Dijet production in semi-inclusive DIS is sensitive to both the conventional and linearly polarized Weizsaecker-Williams gluon TMD distributions, with the latter producing a distinct azimuthal dependence.
This is the explicit premise stated in the abstract that enables the proposed measurement.

pith-pipeline@v0.9.0 · 5633 in / 1180 out tokens · 22886 ms · 2026-05-24T17:01:46.387904+00:00 · methodology

Measuring the Weizsaecker-Williams distribution of linearly polarized gluons at an electron-ion collider through dijet azimuthal asymmetries

Core claim

What carries the argument

Load-bearing premise

What would settle it

discussion (0)