The independence of mass scales in inverse hierarchy models

Abstract

In inverse hierarchy models, one attempts to “solve” the hierarchy problem by generating a large scale X from a theory with only a smaller scale M. Einhorn and Jones have argued, however, that M and X are essentially independent scales, even though the ratio appears to be calculable. We consider a model in which the same phenomenon occurs, and show that it is identical to the more familiar “near-Coleman-Weinberg” models. As the latter clearly have two independent scales, one put in by hand and the other generated by dimensional transmutation, we argue that inverse hierarchy models also have two independent scales, thus agreeing with the more detailed analysis of Einhorn and Jones.