Two loop master integrals for gamma* --> 3 jets: The Nonplanar topologies

Gehrmann, T.; Remiddi, E.

doi:10.1016/S0550-3213(01)00074-8

Two loop master integrals for gamma* --> 3 jets: The Nonplanar topologies

T. Gehrmann
(
- CERN
)
,
E. Remiddi
(
- Bologna U. and
- INFN, Bologna
)

Jan, 2001

22 pages

Published in:

Nucl.Phys.B 601 (2001) 287-317

e-Print:

hep-ph/0101124 [hep-ph]

DOI:

10.1016/S0550-3213(01)00074-8

Report number:

CERN-TH-2001-005

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Abstract:

The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three on-shell legs. Up to now, only those master integrals corresponding to planar topologies were known. In this paper, we compute the yet outstanding non-planar master integrals by solving differential equations in the external invariants which are fulfilled by these master integrals. We obtain the master integrals as expansions in \e=(4-d)/2, where

d

is the space-time dimension. The fully analytic results are expressed in terms of the two-dimensional harmonic polylogarithms already introduced in the evaluation of the planar topologies.

Note:

22 pages, LaTeX, version to be published, Note added on numerical checks of the results, typos corrected Report-no: CERN-TH/2001-005

12.38.Bx
12.20.Ds
02.30.Hq
Two-loop integrals
Box diagrams
electron positron: annihilation
jet: electroproduction
final state: (3jet)
event shape analysis
Feynman graph: higher-order

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