A novel approach to the computation of one-loop three- and four-point functions: I. The real mass case

• Published in: Progress of theoretical and experimental physics Vol. 2019; no. 11
• Main Authors: Guillet, J Ph, Pilon, E, Shimizu, Y, Zidi, M S
• Format: Journal Article
• Language: English
• Published: Oxford University Press 01.11.2019; Oxford University Press on behalf of the Physical Society of Japan
• Subjects: High Energy Physics - Phenomenology; Physics; B57; B30; n-point function: 3; n-point function: 4; B30 General; B57 Standard Model; mathematical methods; mass: complex; kinematics; loop integral; algebra; Feynman graph; higher-order: 1
• ISSN: 2050-3911; 2050-3911
• DOI: 10.1093/ptep/ptz114

Abstract This article is the first of a series of three presenting an alternative method of computing the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following ’t Hooft and Veltman adopted previously. It directly proceeds in terms of the quantities driving algebraic reduction methods. It applies to the three-point functions and, in a similar way, to the four-point functions. It also extends to complex masses without much complication. Lastly, it extends to kinematics more general than that of the physical, e.g., collider processes relevant at one loop. This last feature may be useful when considering the application of this method beyond one loop using generalized one-loop integrals as building blocks.