Status of the strong CP problem

arXiv:2609.00620 · hep-ph, astro-ph.CO, hep-lat, hep-th · Submitted 2026-09-01 · Read on arXiv

hep-ph, astro-ph.CO, hep-lat, hep-th

Submitted: 2026-09-01

Updated: 2026-09-01

Comments: 125 pages including refs, 6 figures, 4 tables; comments are welcome

License: http://creativecommons.org/licenses/by/4.0/

The gist: The strong CP problem remains one of the major open questions in the Standard Model of particle physics.

Terminology

• Abundance — 28× in this paper · explained in 1 episode
• Symmetry Breaking — 24× in this paper · explained in 3 episodes
• Alignment — 19× in this paper · explained in 1 episode
• Benchmark — 15× in this paper · explained in 2 episodes
• Core — 12× in this paper · explained in 2 episodes
• Domain Walls — 12× in this paper · explained in 2 episodes
• Hilbert Space — 10× in this paper · explained in 2 episodes
• Redundancy — 9× in this paper · explained in 2 episodes
• Superradiance — 8× in this paper · explained in 3 episodes
• Degeneracy — 5× in this paper · explained in 3 episodes
• Robustness — 5× in this paper · explained in 5 episodes
• Trace — 5× in this paper · explained in 2 episodes
• Accuracy — 4× in this paper · explained in 1 episode
• Consistency — 4× in this paper · explained in 3 episodes
• Reheating — 3× in this paper · explained in 2 episodes
• Ab Initio — 2× in this paper · explained in 1 episode
• Topological Defects — 2× in this paper · explained in 2 episodes
• alpha — 2× in this paper · explained in 1 episode
• Aperture — 1× in this paper · explained in 1 episode
• Bayesian Framework — 1× in this paper · explained in 3 episodes
• Boltzmann Equation — 1× in this paper · explained in 2 episodes
• CERN Axion Solar Telescope — 1× in this paper
• Calibration — 1× in this paper · explained in 7 episodes
• Center for Axion and Precision Physics Research — 1× in this paper
• Decoupling — 1× in this paper · explained in 2 episodes
• Effective Field Theory (EFT) — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 3 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Many-Body Effects — 1× in this paper · explained in 2 episodes
• Microlensing — 1× in this paper · explained in 2 episodes
• Momentum transfer — 1× in this paper · explained in 2 episodes
• Quantization — 1× in this paper · explained in 12 episodes
• Relic Axion Dark-Matter Exploratory Setup — 1× in this paper
• Unified Framework — 1× in this paper · explained in 5 episodes
• Velocity Dispersion — 1× in this paper · explained in 2 episodes

Abstract

Sources

• An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
• Measurement of the permanent electric dipole moment of the neutron
• Absence of $CP$ violation in the strong interactions
• The strong CP problem solved by itself due to long-distance vacuum effects
• The limits of the strong $CP$ problem
• The QCD theta-parameter in canonical quantization
• Absence of strong CP violation
• CP conservation in the strong interactions
• Regulated chiral gauge theory and the strong CP problem
• Perspectives on QCD, Topology and the Strong CP Problem
• The strong CP problem, general covariance, and horizons
• Unobservability of topological charge in nonabelian gauge theory
• Unobservability of the topological charge in nonabelian gauge theory: Ward-Takahashi identity and phenomenological aspects
• Strong CP problem in the quantum rotor
• Clearing up the Strong $CP$ problem
• Reply to "Clearing up the Strong $CP$ problem"
• A note on instantons, $\theta$-dependence and strong CP
• CP, or not CP, that is the question...
• A particle on a ring or: how I learned to stop worrying and love $\theta$-vacua
• Strong CP and the QCD Axion: Lecture Notes via Effective Field Theory

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