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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2601.07165 |
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| _version_ | 1866910069986164736 |
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| author | Williams, Anthony G. |
| author_facet | Williams, Anthony G. |
| contents | 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 $θ$ term. A priori, any value of $θ$ is consistent with the local symmetries of the theory, while current experimental limits constrain $θ\lesssim 10^{-10}$. 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 $θ$ 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 $θ$ with those sufficient at $θ= 0$, and argue that a vanishing $θ$ 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 $θ$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07165 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Perspectives on QCD, Topology and the Strong CP Problem Williams, Anthony G. High Energy Physics - Phenomenology 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 $θ$ term. A priori, any value of $θ$ is consistent with the local symmetries of the theory, while current experimental limits constrain $θ\lesssim 10^{-10}$. 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 $θ$ 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 $θ$ with those sufficient at $θ= 0$, and argue that a vanishing $θ$ 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 $θ$, 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. |
| title | Perspectives on QCD, Topology and the Strong CP Problem |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2601.07165 |