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Simple one-dimensional integral representations for two-loop self-energies: the master diagram

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arxiv hep-ph/9501201 v1 pith:ONESSDQO submitted 1995-01-02 hep-ph

classification hep-ph
keywords diagrammasterintegralone-dimensionalrepresentationtwo-loopanalyticalappell-functions
verification ladder T0 review T1 audit T2 compute T3 formal
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The scalar two-loop self-energy master diagram is studied in the case of arbitrary masses. Analytical results in terms of Lauricella- and Appell-functions are presented for the imaginary part. By using the dispersion relation a one-dimensional integral representation is derived. This representation uses only elementary functions and is thus well suited for a numerical calculation of the master diagram.

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Cited by 2 Pith papers

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

  1. TVID 2: Evaluation of planar-type three-loop self-energy integrals with arbitrary masses

    hep-ph 2019-08 conditional novelty 5.0 of 10

    TVID 2 computes all master integrals for planar three-loop self-energy diagrams with two closed fermion loops using at most two-dimensional numerical integrations.

  2. Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations

    hep-ph 2025-10 unverdicted novelty 4.0 of 10

    Connects recurrence techniques and dispersive methods with dimension shifts to reduce multi-point functions to two-point basis, minimizing dispersive integrals for one- and two-loop calculations.

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