Harmonic scaling laws and underlying structures

TL;DR

This paper introduces a universal framework based on effective field theory that derives harmonic scaling laws, clarifies anomalies as decoupling effects, and unifies renormalization group equations within a broader underlying physics perspective.

Contribution

It presents a novel approach to derive harmonic scaling laws and unify various renormalization equations through an underlying theory framework.

Findings

Derivation of a universal form of scaling laws

Clarification of anomalies as decoupling effects

Reproduction of RG and Callan-Symanzik equations as special cases

Abstract

Based on the effective field theory philosophy, a universal form of the scaling laws could be easily derived with the scaling anomalies naturally clarified as the decoupling effects of underlying physics. In the novel framework, the conventional renormalization group equations and Callan-Symanzik equations could be reproduced as special cases and a number of important and difficult issues around them could be clarified. The underlying theory point of view could envisage a harmonic scaling law that help to fix the form of the loop amplitudes through anomalies, and the heavy field decoupling can be incorporated in this underlying theory approach in a more unified manner.