arxiv: 2601.04309 · v2 · submitted 2026-01-07 · ✦ hep-ph

Recognition: 1 theorem link

· Lean Theorem

Threshold resummation of rapidity distributions at fixed partonic rapidity

Lorenzo De Ros , Stefano Forte , Giovanni Ridolfi , Davide Maria Tagliabue

Authors on Pith no claims yet

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

classification ✦ hep-ph

keywords threshold resummationrapidity distributionsDrell-Yan processHiggs productionNNLL accuracyquark nonsinglet channelfixed-order matchingdirect QCD

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The pith

A general expression for threshold resummation of rapidity distributions at fixed partonic rapidity is derived for processes with colorless final states.

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

The paper establishes a resummation formula for the rapidity distribution of a colorless particle such as the Higgs or Z boson when the partonic center-of-mass energy approaches threshold while the rapidity in that frame stays fixed. This is achieved by extending a renormalization-group method previously used for threshold resummation. The result holds to all orders in logarithms with coefficients fixed by matching to known fixed-order calculations. For the Drell-Yan process matching to NNLO determines the coefficients up to NNLL for the quark-antiquark channel. It also translates an earlier SCET result into direct QCD and confirms agreement between the approaches.

Core claim

The central claim is that a general all-order resummation expression for rapidity distributions at fixed partonic rapidity can be obtained by generalizing the renormalization-group based threshold resummation approach, with explicit coefficients determined up to NNLL by comparison to NNLO fixed-order results for Drell-Yan in the quark nonsinglet channel.

What carries the argument

The generalized renormalization-group based approach to threshold resummation, which organizes the logarithms arising when the partonic threshold is approached at fixed rapidity.

If this is right

Resummation coefficients up to NNLL accuracy are determined for the Drell-Yan quark-antiquark coefficient function in the nonsinglet channel.
The result applies to Higgs production and other processes with colorless final states.
A translation to direct QCD of the SCET-based resummation result is provided and shown to agree with the new expression.
The expression is valid to all logarithmic orders once the coefficients are known from fixed-order data.

Where Pith is reading between the lines

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

Similar resummation can be extended to other colorless final states at higher logarithmic accuracy once corresponding fixed-order results are available.
These resummed distributions could improve differential cross-section predictions near threshold in collider phenomenology.
Further matching to N3LO would determine N3LL coefficients if the fixed-order calculation becomes available.

Load-bearing premise

The renormalization-group based approach can be generalized to fixed partonic rapidity without introducing additional uncontrolled terms, and matching to NNLO suffices to determine the coefficients reliably up to NNLL.

What would settle it

A calculation of the Drell-Yan rapidity distribution at N3LO that deviates from the logarithmic terms predicted by the NNLL resummation formula would falsify the claim.

read the original abstract

We derive a general expression for the resummation of rapidity distributions for processes with a colorless final state, such as Drell-Yan or Higgs production, in the limit in which the center-of-mass energy goes on threshold, but with fixed rapidity of the Higgs or gauge boson in the partonic center-of-mass frame. The result is obtained by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by us. The ensuing expression is valid to all logarithmic orders but the resummation coefficients must be determined by comparing to fixed order results. We perform this comparison for the Drell-Yan process using the fixed-order next-to-next-to-leading (NNLO) result, thereby determining resummation coefficients up to next-to-next-to-leading logarithmic (NNLL) accuracy, for the quark-antiquark coefficient function in the quark nonsinglet channel. We provide a translation to direct QCD of a result for this resummation previously obtained using SCET methods, and we show that it agrees with our own.

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

This generalizes the authors' RG threshold resummation to rapidity distributions at fixed partonic rapidity, with NNLL coefficients fixed by NNLO Drell-Yan matching and verified by SCET translation.

read the letter

This paper extends the renormalization-group approach to threshold resummation that the authors have developed in earlier work. The new piece is an all-order expression for the resummation of rapidity distributions when the partonic rapidity is kept fixed as the threshold limit is taken. It applies to processes with colorless final states such as Drell-Yan or Higgs production. They do the generalization in direct QCD and then fix the coefficients up to NNLL by matching to the known NNLO result for Drell-Yan in the quark-antiquark nonsinglet channel. They also translate an existing SCET result into their framework and confirm agreement, which is a useful independent check. The central derivation appears consistent with the checks they provide. Using fixed-order results to determine the coefficients avoids circularity, and the agreement with SCET supports that the generalization is under control. The main limitation is the need for those fixed-order inputs to get the coefficients; the expression itself is general but not self-contained for higher orders without them. The explicit results are given only for the nonsinglet quark channel, so extension to other channels would require additional matching. This work is aimed at theorists and phenomenologists who need improved precision on differential cross sections near threshold at hadron colliders. It refines an existing technique rather than introducing a completely new method. I would send it for peer review. The claim is well-supported by the matching and cross-check, and it addresses a specific gap in the literature on threshold resummation.

Referee Report

0 major / 1 minor

Summary. The manuscript derives a general all-order expression for threshold resummation of rapidity distributions for colorless final states (Drell-Yan, Higgs) at fixed partonic rapidity by generalizing the authors' prior renormalization-group approach. The resummation coefficients are fixed up to NNLL accuracy via explicit matching to NNLO fixed-order results in the Drell-Yan quark-antiquark nonsinglet channel, and the direct-QCD result is shown to agree with a translated SCET expression.

Significance. If the central result holds, the work supplies a practical framework for all-order resummation of rapidity distributions near threshold, with concrete NNLL coefficients available for phenomenology. The explicit NNLO matching to determine coefficients and the independent cross-check against the SCET derivation are clear strengths that support the reliability of the generalization.

minor comments (1)

[§4] §4: the extraction of the NNLL coefficients from the NNLO Drell-Yan result would be easier to follow if the individual logarithmic contributions at each order were collected in a short table.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive evaluation of our manuscript, for highlighting its strengths in providing a practical framework for threshold resummation of rapidity distributions, and for recommending acceptance. No major comments were raised in the report.

Circularity Check

0 steps flagged

Derivation self-contained via independent NNLO matching and SCET cross-check

full rationale

The paper generalizes the authors' prior RG-based threshold resummation framework to fixed partonic rapidity, yielding an all-order expression whose coefficients are explicitly fixed by matching to independent NNLO fixed-order results for Drell-Yan (quark-antiquark nonsinglet channel). The resulting NNLL coefficients are then shown to agree with a separate SCET derivation. No equation or step reduces the claimed resummation result to its inputs by construction; the fixed-order data and external SCET result function as independent benchmarks rather than tautological fits.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on generalizing the authors' prior renormalization-group threshold resummation framework to fixed partonic rapidity and determining coefficients via standard matching to fixed-order results, with no new free parameters or invented entities introduced.

axioms (2)

standard math Renormalization-group evolution organizes threshold logarithms to all orders
Generalizes the RG-based approach previously pursued by the authors, invoked in the derivation of the general expression.
domain assumption Matching to fixed-order NNLO results determines resummation coefficients up to NNLL
Standard procedure in resummation techniques, used explicitly for the Drell-Yan quark-antiquark channel.

pith-pipeline@v0.9.0 · 5484 in / 1497 out tokens · 43280 ms · 2026-05-16T16:05:18.962827+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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Relation between the paper passage and the cited Recognition theorem.

We derive a general expression for the resummation of rapidity distributions ... by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by us.

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 2 Pith papers

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

Threshold resummation of Semi-Inclusive Deep-Inelastic Scattering
hep-ph 2026-01 unverdicted novelty 6.0

Derives resummed coefficient functions for SIDIS in double-soft and single-soft threshold limits, with explicit NNLL coefficients extracted in the nonsinglet channel by matching to fixed-order results.
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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