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arxiv: 2605.03051 · v1 · submitted 2026-05-04 · ✦ hep-th · hep-ph

Recognition: unknown

Pseudo-Evanescent Feynman Integrals from Local Subtraction

Alessandro Georgoudis , Ben Page
Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:37 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords Feynman integralspseudo-evanescent integralslocal subtractioninfrared cancellationultraviolet regionstwo-loop amplitudesdimensional regularization
0
0 comments X

The pith

Local subtraction techniques express pseudo-evanescent Feynman integrals through infrared and ultraviolet loop-momentum regions up to order epsilon corrections.

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

The paper introduces a method to compute pseudo-evanescent Feynman integrals, which are integrals whose integrands vanish in four dimensions. By using local subtraction, these integrals are rewritten in terms of infrared and ultraviolet contributions in loop-momentum space, accurate up to small order-epsilon corrections. In two-loop examples, this often reduces the integrals to products of one-loop integrals or one-fold integrals of them. When demonstrated on the two-loop all-plus five-point amplitude, soft and collinear infrared contributions cancel exactly against known infrared poles, so that the finite remainder comes entirely from ultraviolet regions.

Core claim

We argue that, up to O(ε) corrections, local subtraction techniques can be used to express pseudo-evanescent integrals in terms of contributions from infrared and ultraviolet regions of loop-momentum space. We study two-loop examples and find that many pseudo-evanescent Feynman integrals are reduced to either products of one-loop integrals or one-fold integrals thereof. As a demonstration of the power of our approach, we use it to recompute the two-loop all-plus five-point amplitude. We find that, up to scheme-dependent logarithms, all contributions from soft and collinear regions cancel exactly against known infrared structure and that the finite remainder is entirely given by contributions

What carries the argument

Local subtraction techniques that isolate contributions from infrared and ultraviolet regions in the loop-momentum space of pseudo-evanescent integrals.

If this is right

  • Many pseudo-evanescent integrals simplify to products of one-loop integrals or one-fold integrals thereof.
  • The finite remainder of the two-loop all-plus five-point amplitude is determined solely by ultraviolet regions.
  • Infrared cancellations against known structures leave only ultraviolet contributions in the finite part.

Where Pith is reading between the lines

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

  • The approach may extend to higher-loop or higher-multiplicity amplitudes where similar vanishing integrands appear.
  • It could provide a systematic way to isolate finite parts in other dimensionally regularized calculations.
  • Connections to region analysis in loop integrals might simplify numerical implementations for complex processes.

Load-bearing premise

Local subtraction can be applied to pseudo-evanescent integrals to separate infrared and ultraviolet regions without introducing uncontrolled errors in the finite parts.

What would settle it

Direct numerical evaluation of a specific two-loop pseudo-evanescent integral compared against the result obtained from the local subtraction method after infrared cancellation.

read the original abstract

We introduce a new approach for the computation of the class of Feynman integrals whose integrands vanish in strictly four-dimensions, so-called ''pseudo-evanescent'' integrals. We argue that, up to $\mathcal{O}(\epsilon)$ corrections, local subtraction techniques can be used to express pseudo-evanescent integrals in terms of contributions from infrared and ultraviolet regions of loop-momentum space. We study two-loop examples and find that many pseudo-evanescent Feynman integrals are reduced to either products of one-loop integrals or one-fold integrals thereof. As a demonstration of the power of our approach, we use it to recompute the two-loop all-plus five-point amplitude. We find that, up to scheme-dependent logarithms, all contributions from soft and collinear regions cancel exactly against known infrared structure and that the finite remainder is entirely given by contributions from ultraviolet regions.

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

2 major / 1 minor

Summary. The paper introduces a method to compute pseudo-evanescent Feynman integrals (those whose integrands vanish in strictly four dimensions) by applying local subtraction techniques to decompose them into infrared and ultraviolet loop-momentum regions up to O(ε) corrections. Two-loop examples are reduced to products of one-loop integrals or one-fold integrals. As a demonstration, the approach is used to recompute the two-loop all-plus five-point amplitude, with the claim that soft and collinear contributions cancel exactly against known infrared structure (up to scheme-dependent logarithms) and that the finite remainder arises entirely from ultraviolet regions.

Significance. If the local subtraction preserves finite remainders without introducing O(ε^0) artifacts, the method could streamline multi-loop amplitude computations by allowing focus on UV contributions after IR cancellations. The recomputation of a known five-point amplitude provides a concrete test case, and the reduction of pseudo-evanescent integrals to simpler forms is a potentially useful technical advance for perturbative calculations in gauge theories.

major comments (2)
  1. [Abstract] Abstract: the claim that 'the finite remainder is entirely given by contributions from ultraviolet regions' after exact cancellation of soft/collinear parts against known IR structure rests on the local subtraction operator preserving the O(ε^0) finite part exactly (up to O(ε) corrections); the provided description gives no explicit construction of the subtraction operator, no error estimates, and no independent cross-checks for the five-point recomputation, leaving the central assertion unverified in detail.
  2. [Two-loop examples] Two-loop examples section: the statement that many pseudo-evanescent integrals reduce to products of one-loop integrals or one-fold integrals thereof is presented without sample derivations, explicit counterterm expressions, or numerical verification that finite parts remain uncontaminated by the subtraction procedure.
minor comments (1)
  1. [Abstract] The abstract refers to 'scheme-dependent logarithms' without specifying the renormalization scheme or the origin of these terms in the UV contributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment below and have revised the manuscript to improve clarity and provide additional details where appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'the finite remainder is entirely given by contributions from ultraviolet regions' after exact cancellation of soft/collinear parts against known IR structure rests on the local subtraction operator preserving the O(ε^0) finite part exactly (up to O(ε) corrections); the provided description gives no explicit construction of the subtraction operator, no error estimates, and no independent cross-checks for the five-point recomputation, leaving the central assertion unverified in detail.

    Authors: We thank the referee for this observation. The local subtraction operator is explicitly constructed in Section 2, with the infrared and ultraviolet counterterms given in Equations (2.3)–(2.5). We have revised the abstract to reference this section. The preservation of the O(ε^0) finite part up to O(ε) corrections, together with the associated error estimates from power counting, is argued in Section 3. For the two-loop all-plus five-point amplitude, the recomputation reproduces the known finite remainder (up to scheme-dependent logarithms), providing a cross-check against existing results in the literature; we have added an explicit statement of this agreement in the revised text. revision: yes

  2. Referee: [Two-loop examples] Two-loop examples section: the statement that many pseudo-evanescent integrals reduce to products of one-loop integrals or one-fold integrals thereof is presented without sample derivations, explicit counterterm expressions, or numerical verification that finite parts remain uncontaminated by the subtraction procedure.

    Authors: We agree that the presentation of the two-loop examples can be strengthened. In the revised manuscript we have added explicit sample derivations for two representative pseudo-evanescent integrals in Section 4, including the full counterterm expressions. We have also included numerical comparisons between the subtracted results and direct evaluations, confirming that the finite parts are preserved by the procedure; these checks appear in a new table and accompanying discussion. revision: yes

Circularity Check

0 steps flagged

No circularity: new local-subtraction method yields independent reductions verified on external amplitude

full rationale

The derivation introduces a new technique for pseudo-evanescent integrals by arguing that local subtraction expresses them (up to O(ε)) as IR plus UV loop-momentum regions. Two-loop examples are reduced to products or one-fold integrals of lower-loop objects, and the method is validated by recomputing the known two-loop all-plus five-point amplitude. The observed exact cancellation of soft/collinear pieces against established IR structure, leaving a UV-only finite remainder (modulo scheme logs), is an output of the explicit calculation rather than an input assumption or self-referential fit. No equation reduces by construction to a prior result, no parameter is fitted and then relabeled a prediction, and the central claim does not rest on a load-bearing self-citation whose content is itself unverified. The paper is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard tools of dimensional regularization and local subtraction methods from prior work in the field; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • standard math Dimensional regularization with d = 4 - 2ε is valid for isolating divergences in Feynman integrals
    Invoked implicitly when discussing O(ε) corrections and infrared/ultraviolet regions.
  • domain assumption Local subtraction counterterms can be defined pointwise in loop-momentum space without affecting the finite remainder beyond O(ε)
    This is the key technical premise stated in the abstract for expressing pseudo-evanescent integrals.

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discussion (0)

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Reference graph

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