Negative dimensional approach for scalar two-loop three-point and three-loop two-point integrals

Abstract

The well-known $D$-dimensional Feynman integrals were shown, by Halliday and Ricotta, to be capable of undergoing analytic continuation into the domain of negative values for the dimension of space-time. Furthermore, this could be identified with Grassmannian integration in positive dimensions. From this possibility follows the concept of negative dimensional integration for loop integrals in field theories. Using this technique, we evaluate three two-loop three-point scalar integrals, with five and six massless propagators, with specific external kinematic configurations (two legs on-shell), and four three-loop two-point scalar integrals. These results are given for arbitrary exponents of propagators and dimension, in Euclidean space, and the particular cases compared to results published in the literature.

6 pages, 7 figures, Revtex

Cited by in corpus (4)

• Modular application of an Integration by Fractional Expansion (IBFE) method to multiloop Feynman diagrams
• General massive one-loop off-shell three-point functions
• Non-planar double-box, massive and massless pentabox Feynman integrals in negative dimensional approach
• Feynman Diagrams and a Combination of the Integration by Parts (IBP) and the Integration by Fractional Expansion (IBFE) Techniques