The one-loop pentagon to higher orders in ϵ

  • Vittorio Del DucaEmail author
  • Claude Duhr
  • E. W. Nigel Glover
  • Vladimir A. Smirnov


We compute the one-loop scalar massless pentagon integral I 5 6−2ϵ in D = 6−2ϵ dimensions in the limit of multi-Regge kinematics. This integral first contributes to the parity-odd part of the one-loop \( \mathcal{N} \) = 4 five-point MHV amplitude m 5 (1) at \( \mathcal{O} \)(ϵ). In the high energy limit defined by ss 1, s 2 ≫ −t 1,−t 2, the pentagon integral reduces to double sums or equivalently twofold Mellin-Barnes integrals. By determining the \( \mathcal{O} \)(ϵ) contribution to I 5 6−2ϵ , one therefore gains knowledge of m 5 (1) to \( \mathcal{O} \)2) which is necessary for studies of the iterative structure of \( \mathcal{N} \) = 4 SYM amplitudes beyond one-loop. One immediate application is the extraction of the one-loop gluon-production vertex to \( \mathcal{O} \)2) and the iterative construction of the two-loop gluon-production vertex including finite terms which is described in a companion paper [1]. The analytic methods we have used for evaluating the one-loop pentagon integral in the high energy limit may also be applied to the hexagon integral and may ultimately give information on the form of the R 6 (2) remainder function.


Supersymmetric gauge theory Gauge Symmetry QCD 


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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Vittorio Del Duca
    • 1
    Email author
  • Claude Duhr
    • 2
  • E. W. Nigel Glover
    • 3
  • Vladimir A. Smirnov
    • 4
  1. 1.Istituto Nazionale di Fisica NucleareLaboratori Nazionali di FrascatiFrascati (Roma)Italy
  2. 2.Institut de Physique Théorique & Centre for Particle Physics and Phenomenology (CP3)Université Catholique de LouvainLouvain-la-NeuveBelgium
  3. 3.Institute for Particle Physics PhenomenologyUniversity of DurhamDurhamU.K.
  4. 4.Nuclear Physics Institute of Moscow State UniversityMoscowRussia

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