Reduction of one-loop integrals with higher poles by unitarity cut method

Bo Feng; Hongbin Wang

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Reduction of one-loop integrals with higher poles by unitarity cut method

Bo Feng, Hongbin Wang

High Energy Physics - Theory · Submitted 2 Apr 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,206 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.82 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.15 · mentions code or data availability 0.02.

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arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We show how to use the trick of differentiation over masses to translate the problem to the integrals where all powers are just one. Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole. Using this method, we calculate the reduction of scalar bubble, scalar triangle, scalar box and scalar pentagon with general power of propagators.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Unitarity cut method has been proved to be very useful in the computation of one-loop integrals.	background 1.00	0.06	0.04	asserted 1.00
s1	In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general.	contribution 0.99	0.85	0.14	asserted 0.97
s2	We show how to use the trick of differentiation over masses to translate the problem to the integrals where all powers are just one.	method 0.98	0.82	0.08	asserted 1.00
s3	Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole.	method 0.55	0.94	0.34	asserted 0.97
s4	Using this method, we calculate the reduction of scalar bubble, scalar triangle, scalar box and scalar pentagon with general power of propagators.	result 0.68	0.96	0.31	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.99 · evidence from proof or derivation 0.97.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We show how to use the trick of differentiation over masses to translate the problem to the integrals where all powers are just one. Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole. Using this method, we calculate the reduction of scalar bubble, scalar triangle, scalar box and scalar pentagon with general power of propagators.

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References

Forward citations

Cited by 3 Pith papers

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

Duals of Feynman Integrals, 2: Generalized Unitarity
hep-th 2021-11 accept novelty 7.0 of 10

Intersection numbers between dual forms and Feynman integrands yield master-integral coefficients directly from unitarity cuts, demonstrated on one-loop four- and five-gluon amplitudes.
Cosmology meets cohomology
hep-th 2023-08 conditional novelty 6.0 of 10

Relative twisted cohomology gives a practical algorithm for counting and reducing the integrals behind FRW wavefunction coefficients, yielding a new weight-three correction to the de Sitter four-point correlator.
Duals of Feynman Integrals, I: Differential Equations
hep-th 2021-04 conditional novelty 6.0 of 10

Dual Feynman integrands are identified with a relative cohomology whose representatives sit on unitarity cuts, yielding a one-loop basis and canonical differential equations valid away from integer dimension.

How the literature uses it

6 arXiv papers cite this in 10 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Uses its method or tool 2 papers

For a general one-loop integral, i.e., with general tensor structure and arbitrary power of propagators, we can use a trick as shown in [ref] , i.e.,

Reduction of General One-loop Integrals Using Auxiliary Vector · Introduction · 0.99
Using the unitarity cut method in [ref] , we are able to find reduction coefficients of all basis, except the tadpole.

General One-loop Reduction in Generalized Feynman Parametrization Form · Reduction of one-loop integrals · 0.98

Cites it as background 2 papers

Generalized unitarity [ref] is a powerful technique for constructing loop-level scattering amplitudes.

Duals of Feynman Integrals, I: Differential Equations · Introduction · 0.86
Generalized unitarity [ref] is a powerful technique for constructing loop-level scattering amplitudes.

Duals of Feynman Integrals, 2: Generalized Unitarity · Introduction · 0.86

What it cites · 36 sentences without a confident label

Uses the method or tool of 5 papers

The power of this method is that using the holomorphic anomaly [ref] , one can analytically carry out the reduced phase space integration with double cuts, thus to extract the wanted reduction coefficients of master basis.

Twistor Space Structure Of One-Loop Amplitudes In Gauge Theory · Motivation · 0.80
All coefficients have been checked using LiteRed [ref] numerically.

LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals · Cut $K_1$ of $I_2(1,1,1,1,2)$ · 0.87
One can use the technique developed in [ref] or the familiar IBP method to calculate them to complete the whole reduction program for higher poles.

Solving for tadpole coefficients in one-loop amplitudes · Conclusion · 0.95

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