Nine-Propagator Master Integrals for Massless Three-Loop Form Factors

Details Nine-Propagator Master Integrals for Massless Three-Loop Form Factors Nine-Propagator Master Integrals for Massless Three-Loop Form Factors

2009-02-20

arxiv.org/abs/0902.3512v2

Phys.Lett.B678:359-366,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

15 pages, 2 figures. Minor modifications and reference added. Matches published version

Scientific paper

10.1016/j.physletb.2009.06.038

We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold Mellin-Barnes representation which we use to compute the coefficients of the Laurent expansion in epsilon. Using Riemann zeta functions of up to weight six, we give fully analytic results for one integral; for a second, analytic results for all but the finite term; for the third, analytic results for all but the last two coefficients in the Laurent expansion. The remaining coefficients are given numerically to sufficiently high accuracy for phenomenological applications.

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