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arxiv: 1907.11165 · v1 · pith:I5WUPBOInew · submitted 2019-07-25 · ✦ hep-ph

Applications of the WW-type approximation to SIDIS

S. Bastami , H. Avakian , A. V. Efremov , A. Kotzinian , B. U. Musch , B. Parsamyan , A. Prokudin , M. Schlegel
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G. Schnell P. Schweitzer K. Tezgin
This is my paper

Pith reviewed 2026-05-24 16:07 UTC · model grok-4.3

classification ✦ hep-ph
keywords SIDISTMDWW approximationfragmentation functionsparton distribution functionssemi-inclusive DISazimuthal asymmetries
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The pith

WW-type approximation relates TMDs and FFs to simplify SIDIS cross-sections up to 1/Q².

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

The paper investigates the complete SIDIS cross-section for unpolarized hadrons including O(1/Q²) corrections. It uses the WW-type approximation by assuming quark-gluon-quark correlators are negligible compared to quark-quark ones. This assumption generates relations that reduce the number of independent transverse-momentum-dependent parton distribution and fragmentation functions needed. The resulting simplified expression for the cross-section is then compared to available experimental data to gauge its validity.

Core claim

In the Wandzura-Wilczek-type approximation, where bar q g q-correlators are taken to be much smaller than bar q q-correlators, relations among TMD parton distribution functions and fragmentation functions arise. These relations allow the SIDIS cross-section to be expressed in terms of a smaller subset of these functions, valid through order 1/Q².

What carries the argument

The WW-type approximation, which neglects bar q g q-correlators relative to bar q q-correlators, thereby inducing relations between TMDs and FFs.

If this is right

  • The SIDIS cross-section depends on fewer independent functions.
  • Power-suppressed terms can be included without introducing new unknown correlators.
  • Data on unpolarized hadron production can test the approximation's range of validity.
  • Azimuthal modulations in the cross-section become linked through the relations.

Where Pith is reading between the lines

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

  • If the approximation holds, global fits of TMDs could use fewer parameters and achieve better constraints from SIDIS data.
  • The same logic may apply to other processes like Drell-Yan lepton pair production where similar correlators appear.
  • High-precision measurements at future facilities could further validate or refute the size of neglected terms.

Load-bearing premise

Quark-gluon-quark correlators remain much smaller than quark-quark correlators in the relevant kinematic regime of SIDIS.

What would settle it

A clear violation of one of the derived relations between TMDs or FFs in experimental data on unpolarized SIDIS would indicate the approximation does not hold.

Figures

Figures reproduced from arXiv: 1907.11165 by A. Kotzinian, A. Prokudin, A. V. Efremov, B. Parsamyan, B. U. Musch, G. Schnell, H. Avakian, K. Tezgin, M. Schlegel, P. Schweitzer, S. Bastami.

Figure 1
Figure 1. Figure 1: Preliminary COMPASS data on A cos(φh−φS) LT [21] compared with several model predictions [22–24] (a,b), and our calculation for COMPASS kinematics (c). those measurable in SIDIS and the Drell-Yan process. Nevertheless, these lattice studies indi￾cate that certain WW-type approximations are satisfied for the lowest Mellin moments as discussed in [11]. Besides, the lattice results also support the Gaussian A… view at source ↗
Figure 2
Figure 2. Figure 2: Preliminary COMPASS data on A cos(φS) LT [21] compared with a model prediction [23] (a,b), and our calculation for COMPASS kinematics (c). our calculations of the asymmetry in the relevant kinematics of the experiment. The results show a good compatibility within the range of uncertainties. 4. Examples of subleading-twist asymmetries in WW-type approximation The subleading-twist structure functions are mor… view at source ↗
Figure 3
Figure 3. Figure 3: A sinφh UL for proton target vs x from WW-type approximation in comparison to data. Left: π ± from HERMES [26]. Right: π 0 from HERMES [27] and JLab [28]. Eq. 2.1b. Parametrizations from [25] are used for transversity and Collins function. In [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

We explore the complete cross-section for the production of unpolarized hadrons in semi-inclusive deep-inelastic scattering up to power-suppressed $\mathcal{O}(1/Q^2)$ terms in the Wandzura-Wilczek-type (WW-type) approximation, which consists in systematically assuming that $\bar{q}gq$-correlators are much smaller than $\bar{q}q$-correlators. Under the applicability of WW-type approximations, certain relations among transverse momentum dependent parton distribution functions (TMDs) and fragmentation functions (FFs) occur which are used to approximate SIDIS cross-section in terms of a smaller subset of TMDs and FFs. We discuss the applicability of the WW-type approximations on the basis of available data.

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.

Referee Report

0 major / 3 minor

Summary. The manuscript explores the complete cross-section for unpolarized hadron production in semi-inclusive deep-inelastic scattering (SIDIS) up to O(1/Q²) under the Wandzura-Wilczek-type (WW-type) approximation. This approximation is defined by systematically taking bar q g q-correlators to be much smaller than bar q q-correlators. The resulting relations among TMD parton distribution functions and fragmentation functions are used to express the SIDIS cross-section in terms of a reduced subset of these functions. Applicability of the approximation is examined against available experimental data.

Significance. If the WW-type relations hold under the stated assumption, the work supplies a concrete reduction of the independent TMDs and FFs needed for SIDIS phenomenology up to twist-3, which can simplify global fits and data comparisons. The explicit check against data is a positive feature that grounds the approximation in observables rather than leaving it purely formal.

minor comments (3)
  1. [Abstract] The abstract states that relations 'occur which are used to approximate' the cross-section, but the manuscript should add a short explicit list (perhaps in §2 or §3) of which TMDs/FFs are eliminated by the WW-type assumption and which survive, to make the reduction transparent.
  2. [Data discussion] In the data-comparison section, the criteria for selecting the datasets used to test applicability should be stated more clearly (kinematic cuts, Q² range, etc.) so that readers can reproduce the assessment.
  3. [Introduction] Notation for the various correlators and the precise definition of the WW-type suppression (e.g., relative to which scale) should be collected in one place early in the text for easy reference.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and the recommendation for minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper explicitly defines the WW-type approximation as the input assumption that bar q g q-correlators are much smaller than bar q q-correlators, then explores the resulting relations among TMDs/FFs and the approximated SIDIS cross section up to O(1/Q^2). This structure is presented as an application of the stated assumption rather than a derivation from first principles or data fits; applicability is checked externally against available data. No load-bearing step reduces a prediction to a fitted parameter by construction, invokes a self-citation chain as the sole justification for a uniqueness claim, or renames an input as an output. The derivation chain remains self-contained under the declared approximation.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on one domain assumption about the relative size of correlators; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption bar q g q-correlators are much smaller than bar q q-correlators
    Explicitly stated as the definition of the WW-type approximation.

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Reference graph

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