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Strong CP and the QCD axion lecture notes via effective field theory.

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Title: Strong CP and the QCD axion lecture notes via effective field theory.
Authors: Sannino, Francesco1,2 (AUTHOR) sannino@qtc.sdu.dk
Source: European Physical Journal C -- Particles & Fields. May2026, Vol. 86 Issue 5, p1-57. 57p.
Subjects: Quantum chromodynamics, Axions, Quantum field theory, CP violation, Chiral perturbation theory, Topological property
Abstract: These lecture notes provide a self-contained, graduate-level introduction to the strong CP problem and QCD axion physics from an effective field theory (EFT) viewpoint. We review the construction of the chiral EFT of QCD yielding a θ -dependent potential, from which vacuum alignment, θ periodicity and branch structure follow. We further show how the framework leads to the Witten–Veneziano relation highlighting the role of the pure-glue topological susceptibility in organizing θ -dependent hadronic observables. Using these tools, we show how to extract representative CP-odd mesonic and baryonic amplitudes, including the chiral estimate underlying the neutron EDM bound, and how to generalize the effective framework to confining SU (N) theories with fermions in arbitrary representations. We further show how to employ the Veneziano–Yankielowicz effective Lagrangian for N = 1 supersymmetric Yang–Mills theory to extract salient information on the θ -dependent physics of one-flavour QCD via orientifold planar equivalence. We also revisit a recent no strong CP claim based on an ordering of limits in the sum over topological sectors and show, in the EFT language, that it amounts to introducing an extra non-propagating axion-like degree of freedom not required by QCD. We then present the standard dynamical resolution to the strong CP problem, i.e. the Peccei–Quinn mechanism, the resulting axion potential and mass from chiral EFT and briefly review associated time-honored UV completions, and the axion quality problem from gravitational corrections. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Strong CP and the QCD axion lecture notes via effective field theory.
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  Data: <searchLink fieldCode="AR" term="%22Sannino%2C+Francesco%22">Sannino, Francesco</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> sannino@qtc.sdu.dk</i>
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. May2026, Vol. 86 Issue 5, p1-57. 57p.
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  Data: <searchLink fieldCode="DE" term="%22Quantum+chromodynamics%22">Quantum chromodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Axions%22">Axions</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+field+theory%22">Quantum field theory</searchLink><br /><searchLink fieldCode="DE" term="%22CP+violation%22">CP violation</searchLink><br /><searchLink fieldCode="DE" term="%22Chiral+perturbation+theory%22">Chiral perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Topological+property%22">Topological property</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: These lecture notes provide a self-contained, graduate-level introduction to the strong CP problem and QCD axion physics from an effective field theory (EFT) viewpoint. We review the construction of the chiral EFT of QCD yielding a θ -dependent potential, from which vacuum alignment, θ periodicity and branch structure follow. We further show how the framework leads to the Witten–Veneziano relation highlighting the role of the pure-glue topological susceptibility in organizing θ -dependent hadronic observables. Using these tools, we show how to extract representative CP-odd mesonic and baryonic amplitudes, including the chiral estimate underlying the neutron EDM bound, and how to generalize the effective framework to confining SU (N) theories with fermions in arbitrary representations. We further show how to employ the Veneziano–Yankielowicz effective Lagrangian for N = 1 supersymmetric Yang–Mills theory to extract salient information on the θ -dependent physics of one-flavour QCD via orientifold planar equivalence. We also revisit a recent no strong CP claim based on an ordering of limits in the sum over topological sectors and show, in the EFT language, that it amounts to introducing an extra non-propagating axion-like degree of freedom not required by QCD. We then present the standard dynamical resolution to the strong CP problem, i.e. the Peccei–Quinn mechanism, the resulting axion potential and mass from chiral EFT and briefly review associated time-honored UV completions, and the axion quality problem from gravitational corrections. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1140/epjc/s10052-026-15612-4
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        Text: English
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        Type: general
      – SubjectFull: Axions
        Type: general
      – SubjectFull: Quantum field theory
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      – SubjectFull: CP violation
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      – SubjectFull: Chiral perturbation theory
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      – SubjectFull: Topological property
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              Text: May2026
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              Y: 2026
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