Two-loop master integrals for jets: the non-planar topologies

By Thomas Gehrmann, Ettore Remiddi. 2001

179 citations recorded by the source corpus.

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 ϵ =(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.

Subfields: Mechanics of Materials, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d60b7caa2ac2df8865f588c6c99fffd9ceb3018f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

1. Stefan Weinzierl
2. Erik Panzer
3. Gudrun Heinrich

In Nuclear and High Energy Physics

1. Erik Panzer
2. Gudrun Heinrich
3. L. Dixon
4. J. Drummond
5. J. Henn
6. Stefan Weinzierl
7. S. Caron-Huot
8. Claude Duhr

Citations in the corpus

• Feynman integrals and hyperlogarithms (2015, methodology): “Two-dimensional harmonic polylogarithms The two-loop four-point functions with one leg off-shell were calculated in [85, 86].”
• Sector Decomposition (2008, background): “[16] were predictions which played a major role to validate the subsequent analytical calculations [45,46], finally allowing the calculation of the full two-loop QCD matrix element for ee → 3 jets [47].”