0000000000165269

AUTHOR

Raphael Zayadeh

showing 2 related works from this author

From motives to differential equations for loop integrals

2013

In this talk we discuss how ideas from the theory of mixed Hodge structures can be used to find differential equations for Feynman integrals. In particular we discuss the two-loop sunrise graph in two dimensions and show that these methods lead to a differential equation which is simpler than the ones obtained from integration-by-parts.

High Energy Physics - TheoryFor loopHigh Energy Physics - PhenomenologyHigh Energy Physics - Phenomenology (hep-ph)High Energy Physics - Theory (hep-th)Differential equationMathematical analysisFOS: Physical sciencesMathematics
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A second-order differential equation for the two-loop sunrise graph with arbitrary masses

2011

We derive a second-order differential equation for the two-loop sunrise graph in two dimensions with arbitrary masses. The differential equation is obtained by viewing the Feynman integral as a period of a variation of a mixed Hodge structure, where the variation is with respect to the external momentum squared. The fibre is the complement of an elliptic curve. From the fact that the first cohomology group of this elliptic curve is two-dimensional we obtain a second-order differential equation. This is an improvement compared to the usual way of deriving differential equations: Integration-by-parts identities lead only to a coupled system of four first-order differential equations.

Loop (graph theory)Algebra and Number TheoryGroup (mathematics)Differential equationMathematical analysisFOS: Physical sciencesGeneral Physics and AstronomyMathematical Physics (math-ph)CohomologyMomentumElliptic curveHigh Energy Physics - PhenomenologyMathematics - Algebraic GeometryHigh Energy Physics - Phenomenology (hep-ph)FOS: MathematicsGraph (abstract data type)Algebraic Geometry (math.AG)Hodge structureMathematical PhysicsMathematics
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