Analytic result for the one-loop scalar pentagon integral with massless propagators

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Erscheinungsjahr:
2010
Medientyp:
Text
Schlagworte:
  • Loops
  • Integrals
  • Master integrals
  • Decay
  • Quarks
  • Neutrinos
  • Feynman integrals
  • Multi-Regge kinematics
  • Appell hypergeometric functions
  • Loops
  • Integrals
  • Master integrals
  • Decay
  • Quarks
  • Neutrinos
Beschreibung:
  • The method of dimensional recurrences proposed by Tarasov (1996, 2000) [1,2] is applied to the evaluation of the pentagon-type scalar integral with on-shell external legs and massless internal lines. For the first time, an analytic result valid for arbitrary space-time dimension d and five arbitrary kinematic variables is presented. An explicit expression in terms of the Appell hypergeometric function F3 and the Gauss hypergeometric function 2F1, both admitting one-fold integral representations, is given. In the case when one kinematic variable vanishes, the integral reduces to a combination of Gauss hypergeometric functions 2F1. For the case when one scalar invariant is large compared to the others, the asymptotic values of the integral in terms of Gauss hypergeometric functions 2F1 are presented in d=2-2ε, 4-2ε, and 6-2ε dimensions. For multi-Regge kinematics, the asymptotic value of the integral in d=4-2ε dimensions is given in terms of the Appell function F3 and the Gauss hypergeometric function 2F1. © 2010 Elsevier B.V.
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Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/e230c46e-af5e-496d-82dc-c677cc78d4db