One-loop three-point Feynman integrals with Appell $F_1$ hypergeometric functions

Abstract

New analytic formulas for one-loop three-point Feynman integrals in general space-time dimension ($d$) are presented in this paper. The calculations are performed at general configurations for internal masses and external momenta. The analytic results are expressed in terms of hypergeometric series ${}_2{F}_1$, ${}_3{F}_2$ for special cases and Appell $F_1$ for general cases. Furthermore, we cross-check our analytic results with other references which have carried out the integrals in several special cases.

22 pages, 1 figure

References in corpus (12)

• Connection between Feynman integrals having different values of the space-time dimension
• Scalar one-loop integrals for QCD
• Massive Feynman diagrams and inverse binomial sums
• A geometrical angle on Feynman integrals
• Scalar One-Loop Integrals using the Negative-Dimension Approach
• A New Hypergeometric Representation of One-Loop Scalar Integrals in $d$ Dimensions
• Reduction of One-loop Tensor Form-Factors to Scalar Integrals: A General Scheme
• A complete algebraic reduction of one-loop tensor Feynman integrals
• Scalar 1-loop Feynman integrals as meromorphic functions in space-time dimension d
• One-loop N-point equivalence among negative-dimensional, Mellin-Barnes and Feynman parametrization approaches to Feynman integrals
• Scalar one-loop vertex integrals as meromorphic functions of space-time dimension d
• General $\epsilon$-representation for scalar one-loop Feynman integrals

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