Abstract
We explore the origins of parameters in adimensional theories — fundamental theories with no classical massive scales. If the parameters originate as draws from a distribution, it should be possible to write a distribution for them that doesn’t depend on or introduce any massive scales. These distributions are the invariant distributions for the renormalization group (RG) and are closely connected to invariant distributions in objective Bayesian analysis. If such distributions can be constructed, adimensional theories could predict the values of their parameters through unique distributions fixed by the RG. If they can’t be constructed, the parameters must originate in a different way. We demonstrate the RG invariant distributions in the Coleman-Weinberg model, though anticipate that they may not exist in more realistic examples.
