A Feynman Integral and its Recurrences and Associators
arXiv:1511.03630 · doi:10.1016/j.nuclphysb.2016.03.008
Abstract
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations. This epsilon-expansion is identified with the normalized solution of the underlying Fuchs system of four regular singular points. We compute its regularized zeta series (giving rise to two independent associators) whose ratio gives the epsilon-expansion at a specific value. Furthermore, we use the well known one-loop massive bubble integral as an example to demonstrate how to obtain all-order epsilon-expansions for Feynman integrals and how to construct representations for Feynman integrals in terms of generalized hypergeometric functions. We use the method of differential equations in combination with the recently established general solution for recurrence relations with non-commutative coefficients.
29 pages, 1 figure; v2: specified some wording in sect. 1 and at the beginning of sect. 2 & added sect. 4; v3: final and streamlined version published in Nucl. Phys. B
References in corpus (8)
- Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
- Lectures on differential equations for Feynman integrals
- Feynman Diagrams and Differential Equations
- Calculating Three Loop Ladder and V-Topologies for Massive Operator Matrix Elements by Computer Algebra
- Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
- Six Gluon Open Superstring Disk Amplitude, Multiple Hypergeometric Series and Euler-Zagier Sums
- Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
- Differential Equations, Associators, and Recurrences for Amplitudes