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arxiv: 2606.27454 · v1 · pith:EOIUSMPZnew · submitted 2026-06-25 · ✦ hep-ph

The one-point charge correlator in deep inelastic scattering

Haotian Cao , Frank Petriello This is my paper

Pith reviewed 2026-06-29 01:55 UTC · model grok-4.3

classification ✦ hep-ph
keywords one-point charge correlatordeep inelastic scatteringTMD factorizationSCETIRC safetylogarithm resummationnucleon structure
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The pith

A one-point charge correlator defined in the Breit frame for deep inelastic scattering is infrared and collinear safe and corresponds directly to transverse momentum dependent distributions in the back-to-back limit.

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

The paper defines a one-point charge correlator adapted to the Breit frame in DIS and proves it is infrared and collinear safe, so it admits perturbative calculations. In the forward limit the definition yields a new non-perturbative nucleon charge correlator that encodes multi-dimensional nucleon structure. In the back-to-back limit the same observable maps onto standard TMD factorization, with singular distributions computed in SCET, cross-checked against full QCD through order alpha_s squared, and with collinear logarithms resummed to NLL while TMD logarithms are resummed to N3LL (unpolarized) or N2LL (Sivers). A reader cares because the construction supplies both a fresh non-perturbative object and a practical bridge between inclusive observables and TMD physics.

Core claim

The one-point charge correlator is defined in the Breit frame for DIS and shown to be IRC safe. In the forward limit it introduces the nucleon charge correlator as a novel non-perturbative object encoding the multi-dimensional microscopic structure of the nucleon. In the back-to-back limit it establishes a direct correspondence with TMDs, with singular distributions derived in SCET and verified by full QCD to O(alpha_s^2); collinear logarithms are resummed to NLL while TMD logarithms are resummed to N3LL for the unpolarized case and N2LL for the Sivers asymmetry.

What carries the argument

The one-point charge correlator (QC) in the Breit frame, which maps to TMD factorization in the back-to-back limit and to a new nucleon charge correlator in the forward limit.

If this is right

  • The QC is perturbatively calculable because it is IRC safe.
  • Singular distributions obtained in SCET match full QCD through O(alpha_s^2).
  • Collinear logarithms can be resummed to NLL accuracy.
  • TMD logarithms can be resummed to N3LL (unpolarized) or N2LL (Sivers).
  • The forward limit supplies a new non-perturbative object for nucleon structure studies.

Where Pith is reading between the lines

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

  • Measurements of the QC at future DIS facilities could furnish an independent experimental handle on TMDs.
  • The construction may be extended to other hard processes where similar one-point observables can be defined.
  • If power corrections remain small, the QC offers a concrete route to test factorization theorems that link inclusive and differential observables.

Load-bearing premise

SCET factorization in the forward and back-to-back limits captures all relevant physics without power-suppressed corrections that would invalidate the claimed direct correspondence to TMDs or the nucleon charge correlator.

What would settle it

A full QCD calculation of the one-point charge correlator at order alpha_s^3 that produces singular terms differing from the SCET result beyond the stated accuracy.

Figures

Figures reproduced from arXiv: 2606.27454 by Frank Petriello, Haotian Cao.

Figure 1
Figure 1. Figure 1: FIG. 1: Sketch of the one point charge correlator measurement showing the angle and the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Sketch of the relevant angular regions in the Breit frame. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Potential IRC-unsafe measurement of soft quark that originate from the branching [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Comparison between the ln [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Resummed [PITH_FULL_IMAGE:figures/full_fig_p022_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: presents the resummed distributions in the TFR. We choose µh = µ, allowing us to evaluate the resummed cross section by evolving the QC from µ0 to µ. In this case, we select the canonical resummation scales as follows: µ = Q, µ0 = Qθ 2 . (99) The scale uncertainties are evaluated by varying µ0 up and down by a factor of 2 indepen￾dently. LL(APFEL) NLL(APFEL) LL(analytic) NLL(analytic) 0.3 0.4 0.5 0.6 0.7 0… view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Comparison of the distributions between the N [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Resummed y distributions for the Sivers asymmetry. The error band corresponds [PITH_FULL_IMAGE:figures/full_fig_p024_8.png] view at source ↗
read the original abstract

In this work, we propose a novel definition of the one-point charge correlator (QC) adapted to the Breit frame in deep-inelastic scattering (DIS). We demonstrate that this observable is infrared and collinear (IRC) safe, ensuring its perturbative calculability. Utilizing soft-collinear effective theory (SCET), we systematically analyze the QC in both the forward and back-to-back limits. In the forward limit, we introduce the nucleon charge correlator as a novel non-perturbative object that encodes the multi-dimensional microscopic structure of the nucleon. In the back-to-back limit, the QC establishes a direct correspondence with transverse momentum-dependent distributions (TMDs), enabling its description within the standard TMD factorization formalism. The singular distributions are derived within SCET and are verified by the full QCD calculations up to $\mathcal{O}(\alpha_s^2)$. The corresponding collinear logarithms are resummed to all orders with the accuracy of NLL (${\cal{O}}(\alpha_s^n L^{n-1})$), while the transverse momentum-dependent logarithms are resummed to all orders with the accuracy of $N^3$LL for the unpolarized distribution and N$^2$LL for the Sivers asymmetry.

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

1 major / 1 minor

Summary. The manuscript proposes a novel one-point charge correlator (QC) adapted to the Breit frame in deep-inelastic scattering. It demonstrates that the QC is infrared and collinear safe and thus perturbatively calculable. SCET is used to analyze the QC in the forward limit, where a new non-perturbative nucleon charge correlator is introduced, and in the back-to-back limit, where the QC corresponds directly to TMDs and can be described by standard TMD factorization. Singular distributions are derived in SCET and verified by full QCD calculations to O(α_s²). Collinear logarithms are resummed to NLL accuracy while TMD logarithms are resummed to N³LL (unpolarized) and N²LL (Sivers).

Significance. If the central claims hold, the work introduces an IRC-safe observable that links DIS to TMD physics and defines a new non-perturbative object (nucleon charge correlator) for nucleon structure. The O(α_s²) verification against full QCD and the stated resummation accuracies constitute concrete calculational advances that could support phenomenological studies. The SCET treatment of the two kinematic limits is a clear organizational strength.

major comments (1)
  1. [Abstract] Abstract (back-to-back limit paragraph): the claim of a 'direct correspondence' to standard TMD factorization is load-bearing for the central result, yet the manuscript provides no explicit power-counting argument or bound showing that O(Λ/Q) or O(k_T/Q) corrections remain negligible in the claimed regime; the O(α_s²) fixed-order verification alone does not establish that higher-power terms can be neglected for the all-order resummations.
minor comments (1)
  1. The abstract introduces the QC and its limits without a brief statement of the precise operator definition or the kinematic variables used in the Breit frame; adding one sentence would improve accessibility before the SCET analysis begins.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying an important point regarding the presentation of the back-to-back limit. We address the comment below and will incorporate revisions to strengthen the discussion of power counting.

read point-by-point responses

  1. Referee: [Abstract] Abstract (back-to-back limit paragraph): the claim of a 'direct correspondence' to standard TMD factorization is load-bearing for the central result, yet the manuscript provides no explicit power-counting argument or bound showing that O(Λ/Q) or O(k_T/Q) corrections remain negligible in the claimed regime; the O(α_s²) fixed-order verification alone does not establish that higher-power terms can be neglected for the all-order resummations.

    Authors: The SCET derivation in the manuscript establishes the factorization at leading power in the expansion parameter λ ∼ k_T/Q ∼ Λ/Q, with the QC matching onto standard TMD factorization in this limit; higher-power corrections are parametrically suppressed by O(λ). The O(α_s²) verification confirms the leading singular structure obtained from SCET. We agree, however, that an explicit statement of this power counting and the associated regime of validity is not sufficiently highlighted in the abstract. We will revise the abstract to qualify the correspondence as holding at leading power and add a short clarifying paragraph in the main text (near the discussion of the back-to-back limit) that recalls the SCET power counting and the suppression of O(Λ/Q) and O(k_T/Q) terms. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation introduces new observable with external verification

full rationale

The paper defines a novel one-point charge correlator adapted to the Breit frame, demonstrates its IRC safety, and analyzes its behavior in forward and back-to-back limits via SCET. The back-to-back correspondence to TMDs is presented as a derived property within standard TMD factorization, with singular distributions explicitly calculated in SCET and cross-verified against full QCD to O(α_s²). Resummations follow established accuracy orders. No self-definitional reductions, fitted inputs renamed as predictions, or load-bearing self-citations appear in the provided text; the central claims rest on independent perturbative calculations and matching rather than circular equivalence to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on SCET factorization theorems (standard in the field) plus the assumption that the new correlator definition remains IRC safe after the Breit-frame adaptation; no new free parameters or invented entities are introduced beyond the definition of the observable itself.

axioms (1)
  • domain assumption SCET factorization applies in both forward and back-to-back limits of the defined correlator
    Invoked when mapping the QC to the nucleon charge correlator and to TMDs (abstract).

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discussion (0)

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