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Impurity moments coupled to fermions with a pseudogap density of statesdisplay a quantum phase transition between a screened and a free moment phaseupon variation of the Kondo coupling. We describe the universal theory of thistransition for the experimentally relevant case of particle-hole asymmetry. Thetheory takes the form of a crossing between effective singlet and doubletlevels, interacting with low-energy fermions. Depending on the pseudogapexponent, this interaction is either relevant or irrelevant underrenormalization group transformations, establishing the existence of anupper-critical "dimension" in this impurity problem. Using perturbativerenormalization group techniques we compute various critical properties andcompare with numerical results.Comment: 4 pages, 2 figs, (v2) title changed, log corrections for r=1 adde

Upper critical dimension in a quantum impurity model: Critical theory of the asymmetric pseudogap Kondo problem