Renormalization corrections in heavy colored scalar effective field theory

Citation

Sharma, Murali (1993) Renormalization corrections in heavy colored scalar effective field theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/k333-2a97. https://resolver.caltech.edu/CaltechTHESIS:01082013-134838904

Abstract

Recently, QCD processes involving a heavy quark at energ1es much smaller 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 is held fixed. The effective theory has a large set of symmetries because of the decoupling of the flavor (when the kinematic dependence on masses is removed) and spin of the heavy quark from its interactions with the light degrees of freedom . As a consequence, several matrix elements of the theory are determined in terms of a single function, the Isgur-Wise function. Being nonperturbative in character, this function is not fully calculable. However, it has a calculable logarithmic dependence on the masses of the heavy particles, arising from 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. In processes where pair production does not occur, the statistics of the heavy particles are irrelevant, and their interactions are identical with those of quarks. Thus there is a 'superflavor symmetry' that interchanges quarks and scalars, and a flavor symmetry between scalars. Again, these symmetries determine several matrix elements involving scalars up to the same Isgur-Wise function. In this thesis, the logarithmic mass dependence of the operators ϕ_2^†ϕ_1, ϕ_2^† (ὶð^µ ϕ_1), and (ὶð^µ ϕ_2) ^† ϕ_1 is calculated. The latter two operators mix under renormalization.

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