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

This article is the first of a series of three presenting an alternative method to compute 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 the one of 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 generalised one-loop integrals as building blocks.