The Strong CP Problem

An anomaly-free gauged discrete R symmetry can shield the Peccei-Quinn symmetry from quantum-gravity breaking, yielding a large family of viable axion models once the MSSM is extended by vector-like quarks and singlet fields.

arxiv:1308.1227 · hep-ph · 2013-08

Reviews the theoretical, cosmological, and astrophysical case for axions and axion-like particles and surveys the haloscope, light-shining-through-wall, and helioscope experiments that will probe them.

arxiv:1407.0546 · hep-ph · 2014-07

Several chiral confining gauge theories are constructed in which the Peccei-Quinn symmetry and its axion arise accidentally, protected from explicit breaking up to high operator dimension by the gauge structure or by a moose/deconstruction length.

arxiv:1602.05427 · hep-ph · 2016-02

The axion's couplings to W, Z, and Z-photon pairs inherit a model-independent component from pion and eta-prime mixing, and existing data already exclude broad regions of the axion-W, axion-Z, and axion-Z-photon parameter space.

arxiv:1811.05466 · hep-ph · 2018-11

A nonzero initial velocity of the axion field can enhance or suppress the axion relic abundance relative to the conventional misalignment mechanism, opening new parameter space for axion dark matter.

arxiv:1911.11885 · hep-ph · 2019-11

A single hypercolor strong sector generates a composite Higgs and two dynamical axions, and small instantons of an enlarged color group can push the axion mass up to the TeV scale.

arxiv:2007.10875 · hep-ph · 2020-07

Planck-scale operators that violate Peccei-Quinn symmetry shift the QCD theta angle unless gauge symmetries forbid them below dimension 10, and an E6 x U(1) automatic model can provide that protection.

arxiv:hep-ph/9203206 · hep-ph · 1992-03

A mirror strong interaction inside a grand unified theory can generate a heavy axion, up to roughly a TeV, that still solves the strong CP problem and mixes measurably with the electroweak Higgs.

arxiv:hep-ph/9703409 · hep-ph · 1997-03

An approximate shift symmetry can hide a quintessence scalar from equivalence-principle and constant-variation tests while permitting a polarization-rotating coupling to electromagnetism, bounded here at |beta| <= 3e-2 (M/|dphi|).

arxiv:astro-ph/9806099 · astro-ph · 1998-06

A Peccei-Quinn symmetry shared between the Standard Model and a heavier mirror sector cancels the strong CP phase in both worlds and yields a roughly 1 MeV axion at a decay constant of 10^4 to 10^5 GeV.

arxiv:hep-ph/0009290 · hep-ph · 2000-09

Detecting inflationary gravitational waves with a Hubble scale above about 10^13 GeV would force the axion decay constant above the Planck scale, ruling out a string/M-theory modulus as the QCD axion.

arxiv:hep-th/0409059 · hep-th · 2004-09

The axion solution to the strong CP problem is equivalent to Higgsing a three-form gauge field, and gravity can spoil it only by supplying a second massless three-form such as the Chern-Simons spin connection.

arxiv:hep-th/0507215 · hep-th · 2005-07

The Peccei-Quinn chiral symmetry dynamically cancels QCD's CP-violating vacuum angle and predicts a light, weakly coupled axion whose mass and couplings are fixed by the symmetry-breaking scale.

arxiv:hep-ph/0607268 · hep-ph · 2006-07

The axion remains the most attractive solution to the strong CP problem, with its decay constant bounded to roughly 10^9 to 10^12 GeV by astrophysics and cosmology, and with heavier-decay-constant axions able to supply dark matter if the initial misalignment angle is small.

arxiv:0807.3125 · hep-ph · 2008-07

Sub-eV particles with extremely weak photon couplings are motivated by both the strong CP problem and string compactifications, and a generation of laser, cavity, helioscope and fifth-force experiments can now probe where they would live.

arxiv:1002.0329 · hep-ph · 2010-02

Including quenched QED in a 2+1 flavor domain-wall lattice calculation gives m_u = 2.24(10)(34) MeV, m_d = 4.65(15)(32) MeV, m_s = 97.6(2.9)(5.5) MeV, and a proton-neutron splitting of -2.13(16)(70) MeV.

arxiv:1006.1311 · hep-lat · 2010-06

The review sets quality criteria for lattice QCD calculations and uses them to produce recommended averages for light-quark masses, f+(0), fK/fpi, low-energy constants, and B_K.

arxiv:1011.4408 · hep-lat · 2010-11

A comprehensive review argues that thermally produced WIMPs are increasingly constrained and that mixed axion/supersymmetric dark matter, including axinos and saxions, is a better-motivated target for the next generation of searches.

arxiv:1407.0017 · hep-ph · 2014-06

An A4 x SU(5) supersymmetric grand unified model reproduces all quark and lepton masses and mixings and predicts the full neutrino mixing matrix, including a normal hierarchy and a leptonic CP phase near minus 87 degrees.

arxiv:1503.03306 · hep-ph · 2015-03

A slowly rolling axion during inflation dynamically drives the Higgs mass to the weak scale, stopping when QCD barriers grow large enough, offering a new solution to the hierarchy problem without weak-scale new physics.

arxiv:1504.07551 · hep-ph · 2015-04

Enlarging the color group to SU(3+N') gives the QCD axion a second nonperturbative mass contribution from the hidden SU(N') confinement scale, allowing an electroweak-scale axion searchable at the LHC.

arxiv:1604.01127 · hep-ph · 2016-04

Particle production from an axion-like coupling to weak gauge bosons can supply the friction that stops the relaxion at the observed Higgs mass, removing the need for large field excursions or a long inflationary epoch.

arxiv:1607.01786 · hep-ph · 2016-07

This review compiles the theory and experiment of electric dipole moment searches and shows how current null results constrain CP violation from the QCD theta parameter up to multi-TeV new physics.

arxiv:1710.02504 · physics.atom-ph · 2017-10

Color unification of QCD with a second confining SU(3) group, plus a massless fermion, makes all axions heavy and leaves no light axion, so strong CP is solved at the TeV scale with LHC-visible colored pseudoscalars.

arxiv:1805.06465 · hep-ph · 2018-05

Lattice QCD with a gradient-flow topological charge gives a continuum-extrapolated neutron EDM of -0.00152(71) theta-bar e fm, nonzero at roughly two sigma.

arxiv:1902.03254 · hep-lat · 2019-02

A Z_N-symmetric QCD axion, first trapped in a false high-temperature minimum and then oscillating about the true one, can supply the observed dark matter across a wide mass range while solving the strong CP problem.

arxiv:2102.01082 · hep-ph · 2021-02

Planck polarisation data hint at cosmic birefringence at about 3 sigma, and future CMB experiments could distinguish primordial gravitational waves made by vacuum fluctuations from those made by matter fields.

arxiv:2202.13919 · astro-ph.CO · 2022-02

An instantaneous bulk gauge-field extension replaces the time-nonlocal Euclidean flow in the disk construction of chiral gauge theories, enabling a Hamiltonian route, with exact Abelian solutions and singularities confined to temporal boundaries.

arxiv:2610.11035 · hep-lat · 2026-10

A pedagogical review of the strong CP problem, covering the theta vacuum, axions, alternative solutions, and recent debates.

arxiv:2609.00620 · hep-ph · 2026-09

There is a tension in QCD: solving the U(1) problem prevents solving the strong-CP problem, and vice versa, within the 1PI effective action framework.

arxiv:2608.28253 · hep-th · 2026-08

In N=1 supergravity, modular invariance combined with regularity forces the strong CP angle to vanish and, for positive modular weight, forces the quark Yukawa determinant to vanish at the cusp, generating mass hierarchies.

arxiv:2608.13796 · hep-ph · 2026-08

In natural supersymmetry with discrete R-symmetries, R-parity violation at the 1e-7 level can make the lightest supersymmetric particle decay before nucleosynthesis, leaving only axion dark matter, and LHC non-observation constrains such couplings.

arxiv:2505.09785 · hep-ph · 2025-05

In this chiral U(1)_{B-L} axion model, demanding high axion quality forces a minimal axion-electron coupling that can exceed standard KSVZ-model predictions.

arxiv:2608.01897 · hep-ph · 2026-08

ALPHA Phase I is designed to probe axion dark matter at 40 to 80 micro-eV mass with projected KSVZ-level sensitivity using tunable wire-array plasma resonators.

arxiv:2608.10292 · hep-ex · 2026-08

A review of the strong CP problem and axion mechanisms, with a model-building argument that the axion's Peccei-Quinn symmetry can merge with baryon and lepton number and perhaps explain neutrino masses and baryogenesis.

arxiv:2411.09529 · hep-ph · 2024-11

A bulk axion in flat or warped extra dimensions cannot produce displaced 'QCD maxion' patterns; only a canonical QCD axion plus a decoupled KK plateau survives the combined gravitational, unitarity, and astrophysical constraints.

arxiv:2412.00179 · hep-ph · 2024-11

The BχF five-dimensional regulator for chiral gauge theories simultaneously solves the strong CP problem and the U(1)_A problem for QCD, via bulk fermion zeromodes that quench nontrivial topological vacuum contributions.

arxiv:2412.02024 · hep-lat · 2024-12

The paper defines the QFT path integral using only perturbative boundary conditions and asserts, without a valid proof, that this removes all non-perturbative effects.

arxiv:2412.11246 · physics.gen-ph · 2024-12

A spontaneously broken modular CP symmetry can force the quark mass determinant to be real, solving the strong CP problem without an axion.

arxiv:2501.16427 · hep-ph · 2025-01

In a quantum rotor with a topological term, the proposed order of limits predicts zero topological susceptibility, contradicting both the exact quantum mechanical result and lattice simulations.

arxiv:2502.01217 · hep-lat · 2025-02

For Z_4^R and Z_8^R discrete R-symmetries, R-parity violating couplings of order 10^-7 make the lightest supersymmetric particle decay in 10^-3 to 10 seconds, so the dark matter is entirely axion cold dark matter.

arxiv:2502.06955 · hep-ph · 2025-02

Modular invariance can suppress the QCD theta angle to zero in string-inspired supersymmetric models with positive modular weights and non-trivial gauge kinetic functions, while the CKM phase stays large.

arxiv:2505.20395 · hep-ph · 2025-05

Derivative-coupled gravitational axions cannot solve the strong CP problem; Weyl-invariant Einstein-Cartan gravity is identified as the only promising framework for a gravitational QCD axion.

arxiv:2506.11836 · hep-th · 2025-06

A review of Weyl-invariant Einstein-Cartan gravity claiming that one extra axion-like scalar can unify the strong CP and hierarchy puzzles, with the hierarchy explained by tiny Lorentz gauge couplings.

arxiv:2506.11847 · hep-th · 2025-06

In a supersymmetric Twin Higgs model, light scalars can keep electroweak symmetry broken at high temperature, and a special neutrino sector can suppress dark radiation to match CMB limits.

arxiv:2508.15894 · hep-ph · 2025-08

Leptogenesis can proceed from single-generation gauge-singlet mediator decays in a Universal Seesaw model if parity is broken in the neutrino sector; the lightest right-handed neutrino is a sub-eV dark-radiation relic.

arxiv:2512.19833 · hep-ph · 2025-12

Maximally invisible QCD axions, interacting only via gluons, yield SN 1987A cooling constraints and Cherenkov signals that establish a robust lower bound on QCD axion detectability.

arxiv:2607.12025 · hep-ph · 2026-07

The conventional strong CP problem is contingent on extra global topological assumptions about gauge fields that no established QCD observable is shown to require.

arxiv:2607.10272 · hep-ph · 2026-07

Warped extra-dimensional Wilson-line axions can achieve high quality when non-QCD potential contributions from charged bulk fields are parametrically suppressed by geometry and brane effects.

arxiv:2604.08700 · hep-ph · 2026-04

MeV-scale dark QCD with mixed U(1)_PQ anomaly lifts Z_NDW degeneracy of axion domain walls while preserving the strong-CP solution, yielding PTA-accessible GWs and MeV di-photon signals.

arxiv:2607.04137 · hep-ph · 2026-07

Anomaly-free discrete R-symmetries plus Kim-Nilles regeneration of the mu term force an accidental U(1)_PQ whose spontaneous breaking yields a SUSY DFSZ axion that solves strong CP.

arxiv:2607.07921 · hep-ph · 2026-07

Models with Peccei-Quinn symmetry and vector-like quarks realize one-loop proton decay through the operator u_R u_R d_R e_R while preserving a residual Z2 that forbids tree-level decay, yielding testable axion-photon couplings and an axion-accompanied decay mode.

arxiv:2607.02026 · hep-ph · 2026-07

Multi-axion solutions to the strong CP problem produce varied mass-coupling patterns set by PQ symmetry breaking structure and QCD-EM anomaly alignment, summarized by a general sum rule for N-axion systems.

arxiv:2605.06787 · hep-ph · 2026-05

A mirror GUT model confines dynamically to produce a heavy axion solving the strong CP problem while allowing observable EDMs and a rich hidden sector.

arxiv:2605.28954 · hep-ph · 2026-05

Big axions are axion models from collective spontaneous breaking of a delocalized network of U(1) symmetries that realize high-quality accidental global symmetries, solve the strong CP problem, and may explain dark matter.

arxiv:2606.05276 · hep-ph · 2026-06

A review summarizing theoretical foundations for spin-dependent interactions mediated by ALPs and current experimental constraints on them.

arxiv:2606.13318 · hep-ph · 2026-06

A review of progress in quantifying flavor-diagonal hadronic CP violation effects on EDMs, neutron optics, beta decay, and an attempt to address the strong CP problem without new fields or interactions.

arxiv:2606.23580 · hep-ph · 2026-06

CP conservation in QCD follows from taking the infinite volume limit prior to summing over topological sectors, shown consistent with steepest-descent contours and chiral EFT.

arxiv:2404.16026 · hep-ph · 2024-04

In a parity-symmetric model with TeV-scale lepton number violation, a 10 TeV μ+μ+ collider can probe W' boson masses up to 16 TeV via on-shell and off-shell lepton number violating production.

arxiv:2509.24680 · hep-ph · 2025-09

Type IIA orientifold model with D6-branes stabilizes moduli via STU and KL, predicts axion-neutralino dark matter, and uses four-form flux to address strong CP problem.

arxiv:2603.18566 · hep-th · 2026-03

Dynamical generation of leptonic CP violation and light sterile neutrino masses via radiative breaking of non-invertible selection rules, illustrated in the Inverse Seesaw model.

arxiv:2604.04423 · hep-ph · 2026-04

A chiral U(1) gauge symmetry generates an accidental Peccei-Quinn symmetry broken by mirror QCD, solving the strong CP problem without a light axion while supplying WIMP dark matter, stochastic gravitational waves, and LHC-testable colored pNGBs.

arxiv:2604.24849 · hep-ph · 2026-04

Special embedding of the composite axion and QCD gauge groups into a larger product gauge group reduces the domain wall number to unity and induces a controlled bias term from UV instantons that destabilizes the walls.

arxiv:2604.26010 · hep-ph · 2026-04