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

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.

17 pages, minor changes

References in corpus (7)

• Connection between Feynman integrals having different values of the space-time dimension
• Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• High-precision calculation of the 4-loop contribution to the electron g-2 in QED
• High-precision e-expansions of massive four-loop vacuum bubbles
• Quark and gluon form factors to four loop order in QCD: the $N_f^3$ contributions
• The $n_f^2$ contributions to fermionic four-loop form factors
• Introducing SummerTime: a package for high-precision computation of sums appearing in DRA method

Cited by in corpus (2)

• Multi-loop techniques for massless Feynman diagram calculations
• Electron-positron annihilation to photons at $O({\alpha }^3)$ revisited