Recently, QCD processes involving a heavy quark at energ1es muchsmaller than its mass have been examined in an effective field theory approach. In this'heavy quark theory', the mass of the quark is taken to infinity while its four velocity isheld fixed. The effective theory has a large set of symmetries because of the decoupling ofthe flavor (when the kinematic dependence on masses is removed) and spin of the heavyquark from its interactions with the light degrees of freedom . As a consequence, severalmatrix elements of the theory are determined in terms of a single function, the Isgur-Wisefunction. Being nonperturbative in character, this function is not fully calculable. However,it has a calculable logarithmic dependence on the masses of the heavy particles, arisingfrom QCD effects in the full theory.
Some extensions of the standard model contain heavy color triplet scalars.It is instructive therefore to consider the analogous effective field theory for scalars. Inprocesses where pair production does not occur, the statistics of the heavy particles areirrelevant, and their interactions are identical with those of quarks. Thus there is a 'superflavorsymmetry' that interchanges quarks and scalars, and a flavor symmetry betweenscalars. Again, these symmetries determine several matrix elements involving scalars upto the same Isgur-Wise function. In this thesis, the logarithmic mass dependence of theoperators ϕ_2^†ϕ_1, ϕ_2^† (ὶð^µ ϕ_1), and (ὶð^µ ϕ_2) ^† ϕ_1 is calculated. The latter two operatorsmix under renormalization.
