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arxiv: 2606.02485 · v1 · pith:FZAH4EAUnew · submitted 2026-06-01 · ✦ hep-ph · hep-th

On the spanning cuts consistency problem in the IBP reductions of Feynman integrals

Zihao Wu , Yingxuan Xu This is my paper

Pith reviewed 2026-06-28 13:37 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords Feynman integralsIBP reductionspanning cutsconsistency problempinch singularitieshidden relationsFeynman prescription
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0 comments X

The pith

IBP relations are violated on cuts when finite hidden terms proportional to vanishing prescription parameters are omitted due to pinch singularities.

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

This paper identifies why spanning cuts produce inconsistent IBP reduction coefficients across different cuts. The relations contain hidden terms that are normally erased because they are proportional to vanishing Feynman prescription parameters. Cuts can introduce pinch singularities that cancel those parameters, leaving the hidden terms finite and causing violations if they are dropped. The authors supply an algorithm to locate the linear hidden relations between propagators that generate these singularities. Readers care because spanning cuts are used to reduce the cost of multi-loop integral reductions, and undetected inconsistencies undermine the results.

Core claim

The IBP relations can be violated under the cuts if the hidden terms proportional to the vanishing Feynman prescription parameters are blindly erased. In some cases the cut introduces pinch singularities which cancel the vanishing parameters and make the hidden terms finite. The error in various cases comes from omitting such finite hidden terms. The pinch singularities under the cuts are related to hidden linear relations between the propagators, and the paper supplies an algorithm together with its implementation to find those relations.

What carries the argument

Algorithm that detects linear hidden relations between propagators, which produce pinch singularities on cuts and keep otherwise vanishing IBP terms finite.

If this is right

  • Spanning cuts reductions must retain the finite hidden terms once the responsible propagator relations are known.
  • The consistency problem disappears when the algorithm locates and accounts for the hidden relations.
  • Blind erasure of terms proportional to vanishing prescription parameters is invalid on cuts that create pinch singularities.
  • The same hidden relations explain multiple observed inconsistency cases in cut-based reductions.

Where Pith is reading between the lines

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

  • Reduction software could run the hidden-relation algorithm automatically before applying spanning cuts.
  • The mechanism may appear in any cut-based technique that discards terms on the basis of vanishing parameters.
  • The algorithm's output on standard multi-loop integrals could be checked against known analytic results to test completeness.

Load-bearing premise

The inconsistencies originate specifically from omitted finite hidden terms caused by pinch singularities canceling vanishing prescription parameters rather than from numerical instabilities or incomplete IBP sets.

What would settle it

Compute IBP coefficients on a cut that admits a pinch singularity, both with and without the hidden terms identified by the algorithm, and verify whether only the version that retains the terms produces coefficients consistent with those from other cuts.

read the original abstract

The spanning cuts method is a powerful approach to reduce the cost of IBP reduction while computing Feynman integrals. However, its usage is limited due to the so-called consistency problem. It was unclear why the IBP reduction coefficients can be inconsistent with each other between different cuts. In this paper, we report a mechanism behind this inconsistency. We found that the IBP relations can be violated under the cuts, if we blindly erase the hidden terms that are proportional to the ``vanishing'' Feynman prescription parameters in the relations. In some cases, the cut introduces pinch singularities, which cancel the vanishing Feynman prescription parameters, making the hidden terms finite. In various cases, the error comes from omitting such finite hidden terms. We also claimed that the pinch singularity under the cuts are related to some hidden relations between the propagators. In this paper, we provide an algorithm and its implementation to find the linear hidden relations.

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 identifies a mechanism causing the spanning cuts consistency problem in IBP reductions of Feynman integrals. The authors argue that IBP relations can be violated under cuts if hidden terms proportional to vanishing Feynman prescription parameters are omitted, because pinch singularities introduced by the cut can cancel these parameters and render the hidden terms finite. They further claim that these pinch singularities are related to hidden linear relations between propagators and present an algorithm along with its implementation to detect such relations.

Significance. If the proposed mechanism is validated and the algorithm proves effective, this work would address a significant practical obstacle in applying the spanning cuts method, thereby enabling more efficient IBP reductions for multi-loop Feynman integrals. This has direct implications for precision calculations in high-energy physics. The provision of an explicit algorithm and implementation makes the attribution directly testable rather than presupposed.

minor comments (3)
  1. [Abstract] Abstract: the phrase 'in various cases' is used without indicating the number or class of examples examined; adding a short statement on the scope of tested cases would improve clarity.
  2. The manuscript would benefit from including one fully worked low-point example (e.g., a two- or three-propagator integral) that explicitly shows an IBP relation, the hidden term, the pinch singularity, and the resulting finite contribution before and after the cut.
  3. Notation: the distinction between 'vanishing Feynman prescription parameters' and the 'hidden terms' they multiply should be introduced with a short equation or definition in the introductory section to avoid ambiguity for readers unfamiliar with the precise IBP setup.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our manuscript and for recognizing the potential significance of our proposed mechanism and algorithm for resolving the spanning cuts consistency problem in IBP reductions. The recommendation for minor revision is noted with appreciation, as is the acknowledgment of the direct implications for multi-loop calculations in high-energy physics. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper identifies a mechanism for spanning-cuts inconsistencies in IBP reductions (pinch singularities canceling vanishing prescription parameters to produce finite hidden terms) and supplies an explicit algorithm plus implementation to locate the associated linear hidden propagator relations. No derivation step reduces by construction to a fitted input, self-definition, or self-citation chain; the central claim is an empirical identification of a previously unclear source of inconsistency, directly testable via the provided algorithm rather than presupposed. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard assumption that IBP relations hold in the uncut theory and that hidden terms proportional to Feynman prescription parameters exist in those relations; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption IBP relations hold in the uncut theory
    Standard background assumption in the field of Feynman integral reduction invoked when discussing violations under cuts.

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discussion (0)

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