where z is as defined in Eq. (2.20). Note that this result is valid for all values of n$_{2}$ , and that the dimension of the result (2.26) is the same as that of the integral (2.23). The method that we have used to calculate (2.25) cannot be extended to integrals with more than one massive propagator. For instance, suppose that the third propagator in (2.25) contained a mass m . In this case, the k$_{2}$ integral could be evaluated using the one-loop result (2.22). However, the resulting k$_{1}$ integral would involve a hypergeometric function in the argument k$_{2}$ , and this integral cannot be evaluated in closed form. A new method is required in order to consider integrals containing external momenta and more than one massive propagator. Consider a generalization of the integral (2.14) where both propagators are massive This integral can be evaluated using Feynman parameters (see, e.g. Ref. [97]). Instead, we will utilize an approach developed in Ref. [40, 27], which makes use of the Mellin-Barnes contour integral representation of the hypergeometric function $_{1}$F$_{0}$ (B.14) to represent a massive propagator in terms of a massless propagator. In this way, massive propagators can be represented in terms of massless propagators, at the cost of introducing a contour integration. The resulting massless integrals can be evaluated in terms of Gamma functions, and then the contour integrals involving these Gamma functions can be evaluated. The result of the contour integration is typically a generalized hypergeometric function whose argument is a dimensionless ratio of the external momentum and the mass. In order to illustrate the Mellin-Barnes technique, we will use it to evaluate the inte- gral (2.27). Applying the Mellin-Barnes representation to the integral (2.27) gives 60 B ( d ; n$_{1}$ , m ; n$_{2}$ , m ) = 1 Γ ( n$_{1}$ ) Γ ( n$_{2}$ ) ∫ i ∞ − i ∞ ds 2 πi ∫ i ∞ − i ∞ dt 2 πi $^{(}$− m 2 ) s + $^{t}$Γ ( − s ) Γ ( − t ) Γ ( s + n$_{1}$ ) Γ ( t + n$_{2}$ ) 1 µ d − 4 ∫ d $^{d}$k (2 π ) d 1 k 2( n$_{1}$ + s $^{)}$( k − q ) 2( n$_{2}$ + t ) . (2.28) B ( d ; n$_{1}$ , m ; n$_{2}$ , m ) = 1 µ d − 4 ∫ d $^{d}$k (2 π ) d 1 ( k 2 − m $^{2}$) n$_{1}$ [ ( k − q ) 2 − m 2 ] n$_{2}$ . (2.27) 2.3 Integrals with two massive propagators