The analytic value of a 4-loop sunrise graph in a particular kinematical configuration

Abstract

The 4-loop sunrise graph with two massless lines, two lines of equal mass M and a line of mass m, for external invariant timelike and equal to m^2 is considered. We write differential equations in x=m/M for the Master Integrals of the problem, which we Laurent-expand in the regularizing continuous dimension d around d=4, and then solve exactly in x up to order (d-4)^3 included; the result is expressed in terms of Harmonic PolyLogarithms of argument x and maximum weight 7. As a by product, we obtain the x=1 value, expected to be relevant in QED 4-loop static quantities like the electron (g-2). The analytic results were checked by an independent precise numerical calculation

18 pages, 3 figures; minor changes into the Introduction; references added; accepted by Nucl. Phys. B

References in corpus (4)

• Four-loop vacuum energy density of the SU(N_c) + adjoint Higgs theory
• The analytic value of the sunrise self-mass with two equal masses and the external invariant equal to the third squared mass
• High-precision e-expansions of three-loop master integrals contributing to the electron g-2 in QED
• The analytic value of a 3-loop sunrise graph in a particular kinematical configuration

Cited by in corpus (6)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• The Muon g-2
• Feynman Diagrams and Differential Equations
• High-precision calculation of the 4-loop contribution to the electron g-2 in QED
• IBP methods at finite temperature
• The Epsilon Expansion of Feynman Diagrams via Hypergeometric Functions and Differential Reduction