Feynman Diagrams and Differential Equations

Abstract

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D=4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.

invited review article from Int. J. Mod. Phys. A

References in corpus (2)

• Series and epsilon-expansion of the hypergeometric functions
• Analytical Calculation of Two-Loop Feynman Diagrams

Cited by in corpus (12)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
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• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• NNLO corrections to B --> X_u l nu in the shape-function region
• Perturbation Theory of Coulomb Gauge Yang-Mills Theory Within the First Order Formalism
• Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering
• On a two-loop crossed six-line master integral with two massive lines
• $\mathcal{O}(\alpha {\alpha }_s)$ corrections to the $\gamma t\bar{t}$ vertex at the top quark threshold
• Hypergeometric functions with rational arguments
• Threshold corrections to the gamma t anti-t vertex at O(alpha alpha(s))
• Two-Loop QED Heavy-Flavor Contribution to Bhabha Scattering
• Bhabha Scattering at NNLO