arxiv: 2605.13256 · v1 · submitted 2026-05-13 · ✦ hep-ph

Recognition: unknown

Factorization of denominators as a `fuel' for Feynman integral reduction

Alexander V. Smirnov , Vladislav. A. Fokin , Egor Yu. Chuvashov

Authors on Pith no claims yet

Pith reviewed 2026-05-14 18:40 UTC · model grok-4.3

classification ✦ hep-ph

keywords Feynman integralsIBP reductiondenominator factorizationrational function simplificationcomputational efficiencyFUEL interface

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The pith

Factorization patterns in denominators of IBP coefficients can be exploited to lower the cost of rational-function simplification in Feynman integral reductions.

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

The paper examines recurring factorization patterns that appear in the denominators of coefficients generated during integration-by-parts reductions of Feynman integrals. It develops algorithms to detect these patterns and incorporate them into the FUEL interface. This targets the rational-function simplification step that forms a major computational bottleneck. If the patterns prove common and reliably detectable, the approach would make large-scale reductions faster and more stable.

Core claim

By treating factorized denominators as fuel within the FUEL interface, the workflow extracts these structures from IBP coefficients and exploits them to streamline rational-function simplification, thereby reducing reconstruction costs and improving robustness for large-scale reductions of Feynman integrals.

What carries the argument

Algorithms for extracting and exploiting factorized denominator structure in IBP coefficients, implemented inside the FUEL interface.

If this is right

Lower time and resources spent on the rational-function simplification step
Increased stability when reductions involve large numbers of integrals
Better scalability for multi-loop calculations in particle physics

Where Pith is reading between the lines

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

Similar detection methods could be adapted for other symbolic tasks involving rational functions in theoretical physics
Integration into general reduction packages would allow broader testing across integral families
Empirical surveys of how often factorization appears in standard benchmark integrals would clarify the practical scope

Load-bearing premise

Denominator factorization patterns occur frequently enough in generic IBP problems and can be detected reliably enough to deliver measurable efficiency gains.

What would settle it

Directly comparing reconstruction time, memory use, and success rate on the same large set of Feynman integrals run once with the factorization exploitation enabled and once disabled.

Figures

Figures reproduced from arXiv: 2605.13256 by Alexander V. Smirnov, Egor Yu. Chuvashov, Vladislav. A. Fokin.

**Figure 2.** Figure 2: The nonplanar double pentagon diagram. The list of eight propagator denominators and [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: The three-loop forward-scattering diagram with massive internal lines, with [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

read the original abstract

Rational-function simplification is key bottlenecks in integration-by-parts (IBP) reduction of Feynman integrals. We study denominator factorization patterns appearing in IBP coefficients and develop practical algorithms for extracting and exploiting factorized denominator structure within the FUEL interface. The resulting workflow reduces reconstruction cost and improves robustness of large-scale reductions.

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

The paper builds practical algorithms to detect and use factorized denominators in IBP coefficients inside the FUEL interface, targeting a known cost in rational reconstruction.

read the letter

The main point is a set of concrete algorithms that pull out factorized denominator structure from the rational functions generated during IBP reduction and feed it back into the FUEL workflow. The authors argue this lowers reconstruction effort and makes large-scale runs more stable. That is the core engineering move they describe. It sits on top of existing IBP machinery rather than replacing it, which keeps the scope focused. The work is useful because rational simplification remains one of the slower steps when the number of loops or legs grows, and any reliable pattern that can be automated helps. The authors have turned an observed regularity into something the code can act on without manual intervention each time. The soft spot is the absence of reported benchmarks or frequency counts. The abstract states that the workflow reduces cost and improves robustness, but without numbers on how often the factorizations appear in realistic problems or how much time is actually saved, it is hard to know whether the gains are modest or decisive. The detection rules themselves are not laid out in enough detail here to judge edge cases. This is written for people who already run automated IBP reductions on collider integrals and are looking for incremental speed-ups inside tools they use. A reader who needs to push to higher multiplicity or loop order will see the most direct relevance. I would send it to referees. The idea is clear, the target is real, and the implementation details are exactly what peer review should check against working examples.

Referee Report

0 major / 2 minor

Summary. The manuscript studies denominator factorization patterns that appear in the rational coefficients generated during integration-by-parts (IBP) reductions of Feynman integrals. It develops practical algorithms to detect and exploit these patterns inside the FUEL interface, producing a workflow that is stated to lower the cost of rational-function reconstruction while increasing robustness for large-scale reductions.

Significance. If the reported gains are reproducible, the work would supply a concrete, pattern-driven improvement to a persistent computational bottleneck in multi-loop calculations. The focus on algorithmic exploitation of existing denominator structure rather than new reduction identities makes the contribution potentially portable to other IBP frameworks.

minor comments (2)

A quantitative benchmark table (e.g., wall-time or memory usage for a standard set of four-loop integrals with and without the factorization step) would allow readers to judge the magnitude of the claimed cost reduction.
The manuscript should state the precise criteria used to decide when a detected factorization is retained versus discarded, as this choice directly affects the robustness claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript, the positive assessment of its significance, and the recommendation for minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper describes an algorithmic workflow for detecting and exploiting denominator factorization patterns in IBP coefficients inside the FUEL interface. No load-bearing derivation step reduces by construction to its own inputs, fitted parameters, or self-citation chains; the central claim is a practical pattern-based improvement whose validity rests on observable algebraic structure rather than self-referential definitions or unverified uniqueness theorems. The abstract and available description present the method as an independent algorithmic contribution without evidence of circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No free parameters, axioms, or invented entities are described in the abstract; the work is presented as algorithmic pattern exploitation rather than new theoretical postulates.

pith-pipeline@v0.9.0 · 5346 in / 936 out tokens · 41767 ms · 2026-05-14T18:40:17.303464+00:00 · methodology

discussion (0)

Reference graph

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