dorsal/arxiv
View SchemaPerspectives on QCD, Topology and the Strong CP Problem
| Authors | Anthony G. Williams |
|---|---|
| Categories | |
| ArXiv ID | 2601.07165vv1 |
| URL | https://arxiv.org/abs/2601.07165 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
On the basis of allowed local gauge symmetries, the QCD Lagrangian admits a CP-violating term proportional to the topological charge density, commonly referred to as the $\theta$ term. A priori, any value of $\theta$ is consistent with the local symmetries of the theory, while current experimental limits constrain $\theta \lesssim 10^{-10}$. The apparent extreme smallness of this parameter is known as the strong $CP$ problem. In this work, we provide a careful critical overview of the conceptual assumptions underlying the $\theta$ term, focusing on the roles of topology, the definition of topological charge density, rough gauge field configurations, instantons, and anomalies. We contrast the assumptions required to describe QCD at nonzero $\theta$ with those sufficient at $\theta = 0$, and argue that a vanishing $\theta$ term is compatible with a formulation based solely on local gauge invariance and causal locality, without invoking additional global structure. The perspective developed here is intended as a conceptual analysis of the standard formulation of the strong $CP$ problem. It does not challenge the internal consistency of QCD at nonzero $\theta$, nor does it diminish the independent theoretical and phenomenological motivation for axion and axion-like particle physics, which are well-motivated extensions of the Standard Model.
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"abstract": "On the basis of allowed local gauge symmetries, the QCD Lagrangian admits a CP-violating term proportional to the topological charge density, commonly referred to as the $\\theta$ term. A priori, any value of $\\theta$ is consistent with the local symmetries of the theory, while current experimental limits constrain $\\theta \\lesssim 10^{-10}$. The apparent extreme smallness of this parameter is known as the strong $CP$ problem.\n In this work, we provide a careful critical overview of the conceptual assumptions underlying the $\\theta$ term, focusing on the roles of topology, the definition of topological charge density, rough gauge field configurations, instantons, and anomalies. We contrast the assumptions required to describe QCD at nonzero $\\theta$ with those sufficient at $\\theta = 0$, and argue that a vanishing $\\theta$ term is compatible with a formulation based solely on local gauge invariance and causal locality, without invoking additional global structure.\n The perspective developed here is intended as a conceptual analysis of the standard formulation of the strong $CP$ problem. It does not challenge the internal consistency of QCD at nonzero $\\theta$, nor does it diminish the independent theoretical and phenomenological motivation for axion and axion-like particle physics, which are well-motivated extensions of the Standard Model.",
"arxiv_id": "2601.07165",
"authors": [
"Anthony G. Williams"
],
"categories": [
"hep-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Perspectives on QCD, Topology and the Strong CP Problem",
"url": "https://arxiv.org/abs/2601.07165",
"version": "v1"
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