Three-loop static potential

Abstract

We compute the three-loop corrections to the potential of two heavy quarks. In particular we consider in this Letter the purely gluonic contribution which provides in combination with the fermion corrections of Ref. \cite{Smirnov:2008pn} the complete answer at three loops.

4 pages, v2: minor changes

References in corpus (8)

• Algorithm FIRE -- Feynman Integral REduction
• Feynman Integral Evaluation by a Sector decomposiTion Approach (FIESTA)
• Static QCD potential at three-loop order
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• Fermionic contributions to the three-loop static potential
• Update: Accurate Determinations of alpha_s from Realistic Lattice QCD
• The QCD static energy at NNNLL
• The Realistic Lattice Determination of alpha_s(M_Z) Revisited

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