Origins of parameters in adimensional models

TL;DR

This paper investigates the origins of parameters in adimensional theories by exploring RG invariant distributions, demonstrating their existence in QCD, Coleman-Weinberg model, and asymptotically free theories, which could enable parameter predictions.

Contribution

It introduces the concept of RG invariant distributions for parameters in adimensional theories and demonstrates their existence in specific models, offering a new perspective on parameter origins.

Findings

RG invariant distributions exist in QCD, Coleman-Weinberg model, and asymptotically free theories.

Such distributions can potentially predict parameter values in adimensional theories.

The existence of these distributions constrains the possible origins of parameters.

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). If there exist RG invariant combinations of parameters, the RG invariant distributions are specified up to arbitrary functions of the RG invariants. If such distributions can be constructed, adimensional theories could predict the values of their parameters through distributions that are constrained by the RG. If they can't be constructed, the parameters must originate in a different way. We demonstrate the RG invariant distributions in QCD, the Coleman-Weinberg model and a totally asymptotically free theory.