Scale symmetry breaking, quantum anomalous energy and proton mass decomposition

TL;DR

This paper investigates how quantum fluctuations and scale symmetry breaking contribute to the proton mass in QCD, introducing the concept of quantum anomalous energy (QAE) as a scheme-independent component that acts like a dynamical Higgs mechanism.

Contribution

It identifies and characterizes the quantum anomalous energy (QAE) as a novel, scheme-independent contribution to the proton mass arising from anomalous scale symmetry breaking effects.

Findings

QAE is a scheme- and scale-independent component of the proton mass.

QAE originates from quantum fluctuations at ultraviolet scales.

QAE plays a role similar to a dynamical Higgs mechanism in mass generation.

Abstract

We study the anomalous scale symmetry breaking effects on the proton mass in QCD due to quantum fluctuations at ultraviolet scales. We confirm that a novel contribution naturally arises as a part of the proton mass, which we call the quantum anomalous energy (QAE). We discuss the QAE origins in both lattice and dimensional regularizations and demonstrate its role as a scheme-and-scale independent component in the mass decomposition. We further argue that QAE role in the proton mass resembles a dynamical Higgs mechanism, in which the anomalous scale symmetry breaking field generates mass scales through its vacuum condensate, as well as its static and dynamical responses to the valence quarks. We demonstrate some of our points in two simpler but closely related quantum field theories, namely the 1+1 dimensional non-linear sigma model in which QAE is non-perturbative and scheme-independent, and QED where the anomalous energy effect is perturbative calculable.