Direct Extraction of One-loop Integral Coefficients

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We present a general procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted by considering two-particle and triple unitarity cuts of the corresponding bubble and triangle integral functions. After choosing a specific parameterization of the cut loop momentum we can uniquely identify the coefficients of the desired integral functions simply by examining the behavior of the cut integrand as the unconstrained parameters of the cut loop momentum approach infinity. In this way we can produce compact forms for scalar integral coefficients. Applications of this method are presented for both QCD ... continued below

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42 pages

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Forde, Darren April 16, 2007.

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Description

We present a general procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted by considering two-particle and triple unitarity cuts of the corresponding bubble and triangle integral functions. After choosing a specific parameterization of the cut loop momentum we can uniquely identify the coefficients of the desired integral functions simply by examining the behavior of the cut integrand as the unconstrained parameters of the cut loop momentum approach infinity. In this way we can produce compact forms for scalar integral coefficients. Applications of this method are presented for both QCD and electroweak processes, including an alternative form for the recently computed three-mass triangle coefficient in the six-photon amplitude A{sub 6}(1{sup -}, 2{sup +}, 3{sup -}, 4{sup +}, 5{sup -}, 6{sup +}). The direct nature of this extraction procedure allows for a very straightforward automation of the procedure.

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42 pages

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  • Journal Name: Physical Review D

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  • Report No.: SLAC-PUB-12455
  • Grant Number: AC02-76SF00515
  • DOI: 10.1103/PhysRevD.75.125019 | External Link
  • Office of Scientific & Technical Information Report Number: 902482
  • Archival Resource Key: ark:/67531/metadc889328

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  • April 16, 2007

Added to The UNT Digital Library

  • Sept. 22, 2016, 2:13 a.m.

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  • Dec. 9, 2016, 9:18 p.m.

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Forde, Darren. Direct Extraction of One-loop Integral Coefficients, article, April 16, 2007; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc889328/: accessed April 24, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.