can be expressed as a linear combination of scalar integrals in d + 2 N -dimensions. There- fore, without loss of generality we can focus entirely on scalar integrals. Although this is a very helpful result, it is not the most important use of the T operators. Notice that the loop integral recurrence relations derived from integration by parts identities (2.37) can only alter the indices n$_{i}$ of a given loop integral, and cannot change the number of dimen- sions d . However, T operators effectively lead to loop integral recurrence relations in the number of dimensions. These two distinct forms of recurrence relations can be combined, creating generalized recurrence relations that shift not only the indices n$_{i}$ of loop integrals, but also the dimension d of the loop integrals. In Ref. [118] generalized recurrence rela- tions are developed and used to determine a minimal set of basis integrals for the family of integrals that includes the A , B , J , V , and F type integrals that we have considered so far. These generalized recurrence relations have been implemented in the Mathematica package Tarcer [88]. This package was utilized in the heavy quarkonium hybrid calculations in Chapter 3, and in the heavy-light diquark calculation in Chapter 4. After using Tarcer, all of the Wilson coefficients in the hybrid calculations can be expressed in terms of the following set of integrals: A ( d ; 1 , m )(2.13), B ( d ; 1 , m ; 1 , m ) (2.33), J ( d ; 2 , m ; 1 , m ; 1 , 0) and J ( d ; 1 , m ; 1 , m ; 1 , 0) (2.35). Similarly, the integrals required in the heavy-light di- quark calculation are A ( d ; 1 , m ) (2.13), B ( d ; 1 , m ; 1 , 0) (2.22), J ( d ; 2 , m ; 1 , 0 ; 1 , 0) and J ( d ; 1 , m ; 1 , 0 ; 1 , 0). Note that the last two of these can be calculated using (2.26). Tarcer can be applied to any two-loop calculation, with any combination of masses. We now have explicit d -dimensional results for all of the loop integrals that are encountered in Chapters 3, 4, 5 and 6. Now we shall see that divergent integrals can be regulated by setting d = 4 + 2 ϵ and expanding around ϵ = 0. First we will consider the massive tadpole integral (2.13). Setting n = 1, d = 4 + 2 ϵ and using the properties of the Gamma 69 2.6 The Epsilon Expansion