Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale symmetry breaking, quantum anomalous energy and proton mass
  decomposition   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.

21
The categories of this paper are: adap-org
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
1
The categories of this paper are: cs
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an