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arXiv · 1712.05173

DREAM, a program for arbitrary-precision computation of dimensional recurrence relations solutions, and its applications

Roman N. Lee·Kirill T. Mingulov
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Abstract

We present the Mathematica package DREAM for arbitrarily high precision computation of multiloop integrals within the DRA (Dimensional Recurrence & Analyticity) method as solutions of dimensional recurrence relations. Starting from these relations, the package automatically constructs the inhomogeneous solutions and reduces the manual efforts to setting proper homogeneous solutions. DREAM also provides means to define the homogeneous solutions of the higher-order recurrence relations (and can construct those of the first-order recurrence relations automatically). Therefore, this package can be used to apply the DRA method to the topologies with sectors having more than one master integral. Two nontrivial examples are presented: four-loop fully massive tadpole diagrams of cat-eye topology and three-loop cut diagrams which are necessary for computation of the width of the para-positronium decay into four photons. The analytical form of this width is obtained here for the first time to the best of our knowledge.

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Roman N. Lee, Kirill T. Mingulov. 2017-12-14. DREAM, a program for arbitrary-precision computation of dimensional recurrence relations solutions, and its applications. https://arxiv.org/abs/1712.05173

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