New N= 2 superconformal field theories in four dimensions

New examples of N = 2 supersymmetric conformal field theories are found as fixed points of SU(2) N = 2 supersymmetric QCD. Relations among the scaling dimensions of their relevant chiral operators, global symmetries, and Higgs branches are understood in terms of the general structure of relevant deformations of non-trivial N = 2 conformal field theories. The spectrum of scaling dimensions found are all those compatible with relevant deformations of a y2 = x3 singular curve.