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A tree-loop duality relation at two loops and beyond

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Abstract

The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary + i0 prescription of the Feynman propagators, which compensates for the absence of the multiple-cut contributions that appear in the Feynman tree theorem. We rederive the duality theorem at one-loop order in a form that is more suitable for its iterative extension to higher-loop orders. We explicitly show its application to two-and three-loop scalar master integrals, and we discuss the structure of the occurring cuts and the ensuing results in detail.

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Authors and Affiliations

  1. Instituto de Física Corpuscular, Universitat de València – Consejo Superior de Investigaciones Científicas, Apartado de Correos 22085, E-46071, Valencia, Spain

    Isabella Bierenbaum, Petros Draggiotis & Germán Rodrigo

  2. INFN, Sezione di Firenze and Dipartimento di Fisica, Università di Firenze, I-50019, Sesto Fiorentino, Florence, Italy

    Stefano Catani

Authors
  1. Isabella Bierenbaum
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  2. Stefano Catani
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  3. Petros Draggiotis
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  4. Germán Rodrigo
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Correspondence to Isabella Bierenbaum.

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ArXive Print: 1007.0194

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Bierenbaum, I., Catani, S., Draggiotis, P. et al. A tree-loop duality relation at two loops and beyond. J. High Energ. Phys. 2010, 73 (2010). https://doi.org/10.1007/JHEP10(2010)073

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  • DOI: https://doi.org/10.1007/JHEP10(2010)073

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