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The one-loop pentagon to higher orders in ϵ

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Abstract

We compute the one-loop scalar massless pentagon integral I 6−2ϵ5 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 (1)5 at \( \mathcal{O} \)(ϵ). In the high energy limit defined by s ≫ s 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 6−2ϵ5 , one therefore gains knowledge of m (1)5 to \( \mathcal{O} \)(ϵ2) 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 \( \mathcal{O} \)(ϵ2) 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 (2)6 remainder function.

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Authors and Affiliations

  1. Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati, 00044, Frascati (Roma), Italy

    Vittorio Del Duca

  2. Institut de Physique Théorique & Centre for Particle Physics and Phenomenology (CP3), Université Catholique de Louvain, Chemin du Cyclotron 2, B-1348, Louvain-la-Neuve, Belgium

    Claude Duhr

  3. Institute for Particle Physics Phenomenology, University of Durham, Durham, DH1 3LE, U.K.

    E. W. Nigel Glover

  4. Nuclear Physics Institute of Moscow State University, Moscow, 119992, Russia

    Vladimir A. Smirnov

Authors
  1. Vittorio Del Duca
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  2. Claude Duhr
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  3. E. W. Nigel Glover
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  4. Vladimir A. Smirnov
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Correspondence to Vittorio Del Duca.

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ArXiv ePrint: 0905.0097

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Del Duca, V., Duhr, C., Nigel Glover, E.W. et al. The one-loop pentagon to higher orders in ϵ. J. High Energ. Phys. 2010, 42 (2010). https://doi.org/10.1007/JHEP01(2010)042

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