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arxiv: 2601.06245 · v4 · submitted 2026-01-09 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Threshold resummation of Semi-Inclusive Deep-Inelastic Scattering

Stefano Forte , Giovanni Ridolfi , Francesco Ventola
Authors on Pith no claims yet

Pith reviewed 2026-05-16 15:44 UTC · model grok-4.3

classification ✦ hep-ph
keywords threshold resummationsemi-inclusive deep-inelastic scatteringDrell-Yan processnonsinglet channelsoft limitscollinear radiationcoefficient functions
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0 comments X

The pith

Threshold resummation for semi-inclusive deep-inelastic scattering is derived from Drell-Yan crossing symmetry.

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

The paper derives threshold resummation for SIDIS by using crossing relations from the Drell-Yan process at fixed rapidity. It handles both double-soft limits where both scaling variables approach threshold and single-soft limits where only one does. This provides resummed coefficient functions that can be used to improve perturbative predictions for high-energy scattering experiments. A sympathetic reader would care because it extends resummation techniques to a key process for studying nucleon structure.

Core claim

We derive threshold resummation of semi-inclusive deep-inelastic scattering (SIDIS), by building upon previous results by some of us for the resummation of the Drell-Yan process at fixed rapidity, which is related to SIDIS by crossing. We consider both a double-soft limit, in which both the Bjorken and the fragmentation scaling variables tend to their threshold value, and single soft limits in which either of them does. We show that in the former limit only soft radiation contributes, and in the latter limit only collinear radiation, and we derive resummed expressions for the coefficient functions in all cases. We determine explicitly resummation coefficients in the nonsinglet channel up to

What carries the argument

Crossing symmetry relating SIDIS to Drell-Yan at fixed rapidity, determining soft and collinear contributions to threshold resummation.

Load-bearing premise

The crossing symmetry from Drell-Yan at fixed rapidity directly supplies the correct threshold resummation structure for SIDIS in both the double-soft and single-soft limits without additional process-specific corrections.

What would settle it

A next-to-next-to-next-to-leading order calculation of the SIDIS coefficient functions that disagrees with the expansion of the resummed result would show the resummation is incorrect.

read the original abstract

We derive threshold resummation of semi-inclusive deep-inelastic scattering (SIDIS), by building upon previous results by some of us for the resummation of the Drell-Yan process at fixed rapidity, which is related to SIDIS by crossing. We consider both a double-soft limit, in which both the Bjorken and the fragmentation scaling variables tend to their threshold value, and single soft limits in which either of them does. We show that in the former limit only soft radiation contributes, and in the latter limit only collinear radiation, and we derive resummed expressions for the coefficient functions in all cases. We determine explictly resummation coefficients in the nonsinglet channel up to next-to-next-to-leading log by comparing to recent fixed next-to-next-to-leading order results. Expanding out the single-soft resummation we reproduce recent next-to-leading power results.

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 / 2 minor

Summary. The manuscript derives threshold resummation for semi-inclusive deep-inelastic scattering (SIDIS) in the nonsinglet channel by crossing from fixed-rapidity Drell-Yan resummation. It treats the double-soft limit (x, z → 1) where only soft radiation contributes and the single-soft limits (x → 1 or z → 1) where only collinear radiation survives, derives the corresponding resummed coefficient functions, fixes the NNLL coefficients by direct matching to existing NNLO results, and verifies consistency by expanding the single-soft resummation to reproduce known next-to-leading-power corrections.

Significance. If the central results hold, the work supplies a concrete extension of threshold resummation to SIDIS, a process directly relevant to precision phenomenology at facilities such as the EIC. The explicit NNLL coefficients obtained via matching, together with the internal consistency check against known power corrections, provide a practical framework that can be used for higher-order predictions in the threshold region without introducing free parameters.

minor comments (2)
  1. [Abstract] The abstract states that coefficients are fixed by comparison to fixed NNLO results, but the main text should include a short explicit table or equation listing the numerical values of the newly determined NNLL coefficients for immediate reference.
  2. Notation for the scaling variables x and z and the precise kinematic definitions of the double-soft versus single-soft limits should be restated once at the beginning of the resummation section to improve readability for readers unfamiliar with the prior Drell-Yan work.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for recommending minor revision. The report confirms the relevance of our threshold resummation results for SIDIS phenomenology. No specific major comments were raised that require point-by-point rebuttal, so we focus on implementing the minor changes implied by the recommendation.

Circularity Check

0 steps flagged

No significant circularity; derivation anchored by external matching

full rationale

The paper derives the SIDIS threshold resummation structure by crossing from the authors' prior Drell-Yan fixed-rapidity results, then explicitly constructs the double-soft and single-soft limits and fixes the nonsinglet NNLL coefficients through direct comparison to independent recent NNLO fixed-order calculations in the literature. This external matching, together with the reproduction of known next-to-leading-power terms upon expansion, renders the central claim self-contained and independently verifiable rather than reducing to a self-definition or tautology. The self-citation supplies only the starting resummation form, which is then tested against separate benchmarks, satisfying the criteria for non-circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The derivation rests on standard QCD factorization and crossing symmetry; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Crossing symmetry maps the Drell-Yan process at fixed rapidity onto SIDIS threshold kinematics
    Invoked to transfer resummation results from Drell-Yan to SIDIS.
  • standard math Soft and collinear radiation factorize from the hard scattering in the stated threshold limits
    Standard assumption of QCD threshold resummation used to classify contributions in double-soft versus single-soft cases.

pith-pipeline@v0.9.0 · 5448 in / 1420 out tokens · 49345 ms · 2026-05-16T15:44:47.565217+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We derive threshold resummation of semi-inclusive deep-inelastic scattering (SIDIS), by building upon previous results ... for the resummation of the Drell-Yan process at fixed rapidity, which is related to SIDIS by crossing. ... determine explicitly resummation coefficients in the nonsinglet channel up to next-to-next-to-leading log by comparing to recent fixed next-to-next-to-leading order results.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    Resummation is performed in Mellin space ... exp ∫ dk²/k² [A_q(α_s(k²)) ln(NM k²/Q²) − D_ds_qq(α_s(k²))]

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

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

  1. Precision QCD with the Electron-Ion Collider

    hep-ph 2026-04 unverdicted novelty 1.0

    A workshop summary report outlines discussion topics in perturbative QCD, nuclear structure, and related techniques for the upcoming Electron-Ion Collider.

Reference graph

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