Strong CP Problem Research Articles

Strong CP problem in the quantum rotor

Recent studies have claimed that the strong CP problem does not occur in QCD, proposing a new order of limits in volume and topological sectors when studying observables on the lattice. In order to shed light on this issue, we study the effect of the topological θ-term on a simple quantum mechanical rotor that allows a lattice description. The topological susceptibility and the θ-dependence of the energy spectrum are both computed using local lattice correlation functions. The sign problem is overcome by considering Taylor expansions in θ, exploiting automatic differentiation methods for Monte Carlo processes. Our findings confirm the conventional wisdom on the strong CP problem. Published by the American Physical Society 2024

Revisiting the minimal Nelson-Barr model

Abstract We revisit the minimal Nelson-Barr model for solving the strong CP problem through the idea of spontaneous CP breaking. The minimal model suffers from the quality problem, which means that the strong CP angle is generated by higher-dimensional operators and one-loop effects. Consequently, it has been considered that there is a cosmological domain wall problem and that leptogenesis does not work. We point out that just imposing an additional approximate global symmetry solves the quality problem. We also propose a simple solution to the domain wall problem and show that the thermal leptogenesis scenario works.

Finite modular symmetries and the strong CP problem

Recently, it was shown that modular symmetry may solve the strong CP problem without axions, by producing a vanishing QCD angle while generating a large quark CP violation phase. We extend this framework to finite modular groups, systematically identifying the allowed mass textures. We find quark fields must furnish 1D representations and scan the minimal model landscape.

Constraints for scalars and pseudoscalars from (g−2)l and existing e+e− colliders

Scalars and pseudoscalars with masses in the MeV–GeV range are of interest in different extensions of the Standard Model. Such particles are often associated with dark matter, the strong CP problem, and the (g−2)μ anomaly. In this work we investigate limits for masses of such particles and their couplings to photons and leptons which can be derived from present and currently operating e+e− collider experiments and recent (g−2)l measurements. Our work expands upon previous studies in several ways, demonstrating that the interplay of both couplings is a decisive factor in these type of analyses. Published by the American Physical Society 2024

Bringing the Peccei-Quinn mechanism down to Earth

It is conventionally assumed that the physics underlying the Peccei-Quinn (PQ) mechanism for addressing the strong CP problem is at very high energies, orders of magnitude above the weak scale. However, this may not be the case in general and the associated PQ boson ϕ, besides the signature state, i.e., the ultralight axion a, may emerge well below the weak scale. We consider this possibility and examine some of the conditions for its viability. The example model proposed here may also provide the requisite Standard Model Higgs mass parameter, without invoking new scalars above the giga-electron-volt (GeV) scale. The corresponding parameter space can maintain against quantum corrections. This scenario, depending on the choice of parameters, can potentially be constrained by flavor data. We point out that the current mild excess in B+→K+νν¯, reported by the Belle II experiment, could in principle be explained in this setup as B+→K+ϕ and B+→K+a, with both ϕ and a escaping the detector as missing energy. For a sufficiently heavy PQ boson, in the GeV regime (as the preferred explanation of the Belle II excess), one can separate these two contributions, due to the difference in K+ momenta. In this case, the axion may also affect lighter meson, e.g., kaon, decays while ϕ would not be a kinematically allowed final state. Published by the American Physical Society 2024

Singlet–doublet Dirac Fermion dark matter from Peccei–Quinn symmetry

Weakly interacting massive particles (WIMPs) and axions are arguably the most compelling dark matter (DM) candidates in the literature. Here, we consider a model where the Peccei–Quinn (PQ) symmetry solves the strong CP problem, generates radiatively Dirac neutrino masses and gives origin to a multicomponent dark sector. Specifically, scotogenic Dirac neutrino masses arise at one-loop level. The lightest fermionic mediator acts as the second DM candidate due to a residual [Formula: see text] symmetry resulting from the PQ symmetry breaking. The WIMP DM component resembles the well-known singlet–doublet fermion DM. While the lower WIMP dark mass region is usually excluded, our model reopens that portion of the parameter space (for DM masses below [Formula: see text][Formula: see text]GeV). Therefore, we perform a phenomenological analysis that addresses the constraints from direct searches of DM, neutrino oscillation data and charged lepton flavor violating processes. The model can be tested in future facilities where neutrino telescopes search for DM annihilation into Standard Model particles.

Axion detection via superfluid 3He ferromagnetic phase and quantum measurement techniques

We propose to use the nuclear spin excitation in the ferromagnetic A1 phase of the superfluid 3He for the axion dark matter detection. This approach is striking in that it is sensitive to the axion-nucleon coupling, one of the most important features of the QCD axion introduced to solve the strong CP problem. We review a quantum mechanical description of the nuclear spin excitation and apply it to the estimation of the axion-induced spin excitation rate. We also describe a possible detection method of the spin excitation in detail and show that the combination of the squeezing of the final state with the Josephson parametric amplifier and the homodyne measurement can enhance the sensitivity. It turns out that this approach gives good sensitivity to the axion dark matter with the mass of O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(1) μeV depending on the size of the external magnetic field. We estimate the parameters of experimental setups, e.g., the detector volume and the amplitude of squeezing, required to reach the QCD axion parameter space.

A light QCD axion with hilltop misalignment

We study the cosmological evolution of a light QCD axion and identify the parameter space to obtain the correct relic dark matter abundance. The axion potential is flattened at the origin, corresponding to the only minimum, while it is unsuppressed at π. These potential features arise by assuming a mirror sector with the strong CP phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} shifted by π compared to the SM sector, which allows the mirror axion potential to be tuned against the usual QCD axion potential. Before the QCD phase transition, assuming the mirror sector is decoupled and much colder than the SM thermal bath, the mirror sector potential dominates, causing the axion to initially roll to a temporary minimum at π. However, after the QCD phase transition, the potential minimum changes, and the axion relaxes from the newly created “hilltop” near π to the CP-conserving minimum at the origin. As the axion adiabatically tracks this shift in the potential minimum through the QCD phase transition, with non-adiabatic evolution near π and 0, it alters the usual prediction of the dark matter abundance. Consequently, this “hilltop” misalignment mechanism opens new regions of axion parameter space, with the correct relic abundance while still solving the strong CP problem, that could be explored in future experiments.

Spontaneous CP violation in supersymmetric QCD

We investigate a composite model of spontaneous CP violation based on a new supersymmetric QCD as a solution to the strong CP problem. The scalar components of the meson chiral superfields obtain complex vacuum expectation values to break CP symmetry spontaneously. Then, wavefunction renormalization for the quark kinetic terms provides the Cabibbo-Kobayashi-Maskawa (CKM) phase, while the strong CP phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} is protected by nonrenormalization of the superpotential and hermiticity of the wavefunction renormalization factor. In our model, the right-handed down-type quark multiplets are given by composite states, enhancing their couplings to CP breaking fields, which is essential to realize the observed CKM phase. The non-perturbative dynamics generates the scale of spontaneous CP violation hierarchically lower than the Planck scale. We discuss potential corrections to θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} and find a viable parameter space of the model to solve the strong CP problem without fine-tuning.

A4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_4$$\\end{document} modular invariance and the strong CP problem

We present simple effective theory of quark masses, mixing and CP violation with level N=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=3$$\\end{document} (A4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_4$$\\end{document}) modular symmetry, which provides solution to the strong CP problem without the need for an axion. The vanishing of the strong CP-violating phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{\ heta }}$$\\end{document} is ensured by assuming CP to be a fundamental symmetry of the Lagrangian of the theory. The CP symmetry is broken spontaneously by the vacuum expectation value (VEV) of the modulus τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}. This provides the requisite large value of the CKM CP-violating phase while the strong CP phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\bar{\ heta }}$$\\end{document} remains zero or is tiny. Within the considered framework we discuss phenomenologically viable quark mass matrices with three types of texture zeros, which are realized by assigning both the left-handed and right-handed quark fields to A4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_4$$\\end{document} singlets 1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{1}$$\\end{document}, 1′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbf{1'}}$$\\end{document} and 1′′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbf{1''}$$\\end{document} with appropriate weights. The VEV of τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document} is restricted to reproduce the observed CKM parameters. We discuss cases in which the modulus VEV is close to the fixed points i, ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} and i∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$i\\infty $$\\end{document}. In particular, we focus on the VEV of τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}, which gives the absolute minima of the supergravity-motivated modular- and CP-invariant potentials for the modulus τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document}, so called, modulus stabilisation. We present a successful model, which is consistent with the modulus stabilisation close to τ=ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au =\\omega $$\\end{document}.

Solving the strong CP problem without axions

We formulate general conditions under which the strong CP problem is solved by spontaneous CP violation. Quark-mass matrix elements are polynomials in the CP-breaking order parameters, engineered such that their determinant is a real constant. This scheme permits only a limited number of textures. These conditions can be realized in supersymmetric theories with CP as an anomaly-free local flavor symmetry, suggesting a unified solution to the strong CP problem and the flavor puzzle. Our solution can be implemented using either modular invariance or a local U(1) symmetry. We present modular-invariant realizations where matter fields are assigned small modular weights ±2 (±1), utilising higher levels N = 2 (N = 3). Heavy quarks are in general not required, but their presence allows for models where colored particles fill non-singlet representations of the flavor group.

Cosmological dynamics of string theory axion strings

The quantum chromodynamics (QCD) axion may solve the strong CP problem and explain the dark matter (DM) abundance of our Universe. The axion was originally proposed to arise as the pseudo-Nambu-Goldstone boson of global U(1)PQ Peccei-Quinn (PQ) symmetry breaking, but axions also arise generically in string theory as zero modes of higher-dimensional gauge fields. In this work we show that string theory axions behave fundamentally differently from field theory axions in the early Universe. Field theory axions may form axion strings if the PQ phase transition takes place after inflation. In contrast, we show that string theory axions do not generically form axion strings. In special inflationary paradigms, such as D-brane inflation, string theory axion strings may form; however, their tension is parametrically larger than that of field theory axion strings. We then show that such QCD axion strings overproduce the DM abundance for all allowed QCD axion masses and are thus ruled out, except in scenarios with large warping. A loop-hole to this conclusion arises in the axiverse, where an axion string could be composed of multiple different axion mass eigenstates; a heavier eigenstate could collapse the network earlier, allowing for the QCD axion to produce the correct DM abundance and also generating observable gravitational wave signals. Published by the American Physical Society 2024

An attractive model: simulating fuzzy dark matter with attractive self-interactions

Abstract Fuzzy Dark Matter (FDM) comprised of ultralight ($m \sim 10^{-22}~\rm {eV}$) boson particles has received significant attention as a viable alternative to Cold Dark Matter (CDM), as it approximates CDM on large scales (≳ 1 Mpc) while potentially resolving some of its small-scale problems via kiloparsec-scale quantum interference. However, the most basic FDM model, with one free parameter (the boson mass), is subject to a tension: small boson masses yield the desired cores of dwarf galaxies but underpredict structure in the Lyman-α forest, while large boson masses render FDM effectively identical to CDM. This Catch-22 problem may be alleviated by considering an axion-like particle with attractive particle self-interactions. We simulate an idealized FDM halo with self-interactions parameterized by an energy decay constant $f \sim 10^{15}~\rm {GeV}$ related to the axion symmetry-breaking conjectured to solve the strong-CP problem in particle physics. We observe solitons, a hallmark of FDM, condensing within a broader halo envelope, and find that the density profile and soliton mass depend on self-interaction strength. We propose generalized formulae to extend those from previous works to include self-interactions. We also investigate a critical mass threshold predicted for strong interactions at which the soliton collapses into a compact, unresolved state. We find that the collapse happens quickly and its effects are initially contained to the central region of the halo.

The quality/cosmology tension for a post-inflation QCD axion

It is difficult to construct a post-inflation QCD axion model that solves the axion quality problem (and hence the Strong CP problem) without introducing a cosmological disaster. In a post-inflation axion model, the axion field value is randomized during the Peccei-Quinn phase transition, and axion domain walls form at the QCD phase transition. We emphasize that the gauge equivalence of all minima of the axion potential (i.e., domain wall number equals one) is insufficient to solve the cosmological domain wall problem. The axion string on which a domain wall ends must exist as an individual object (as opposed to a multi-string state), and it must be produced in the early universe. These conditions are often not satisfied in concrete models. Post-inflation axion models also face a potential problem from fractionally charged relics; solving this problem often leads to low-energy Landau poles for Standard Model gauge couplings, reintroducing the quality problem. We study several examples, finding that models that solve the quality problem face cosmological problems, and vice versa. This is not a no-go theorem; nonetheless, we argue that it is much more difficult than generally appreciated to find a viable post-inflation QCD axion model. Successful examples may have a nonstandard cosmological history (e.g., multiple types of cosmic axion strings of different tensions), undermining the widespread expectation that the post-inflation QCD axion scenario predicts a unique mass for axion dark matter.

Axion dark matter and additional BSM aspects in an extended 2HDM setup

We illustrate and discuss the phenomenology of a model featuring a two-Higgs doublet sector augmented by two SU(2) singlet scalars. The gauge symmetry group is extended as well with a U(1)Lμ−Lτ component whose spontaneous breaking leads to the gauge boson which has an important effect in the muon (g−2). A global PQ symmetry is introduced upon its breaking; we have the axion particle which is also dark matter (DM) in our work. In particular, we have focused on type-X and type-II 2HDM models and found out that (g−2) cannot be explained only by the scalar sector for type-II 2HDM mainly due to stringent constraint from b→sγ resulted in MH±>800 GeV. For type-II 2HDM, we can have axion coupling with the gluons which generates the axion potential and possible explanation for the strong CP problem. The proposed model accommodates neutrino masses via the type-I seesaw mechanism with an upper bound on the right-handed neutrino mass 1 GeV (1 TeV) for type-II (type-X) 2HDM due to the presence of Planck scale suppressed operators. Moreover, we also have additional scalars which affect the oblique parameters and hence the W-boson mass which leads us to explain the W-boson mass observed at the CDF-II detector. The most stringent constraints on the masses and quartic couplings come from the perturbativity and potential bound from the below conditions which leads to fine-tuning among the parameters in part of the parameter space. Finally, we discuss the possible detection prospects of the axion DM and the additional gauge boson. Published by the American Physical Society 2024

Primordial black holes from axion domain wall collapse

The QCD axion can solve the Strong CP Problem and be the dark matter of our universe. If the PQ symmetry breaking scale associated with the axion is below the inflationary reheating temperature, axion strings and domain walls populate the universe. Most of these strings and walls decay away into axion dark matter, but a small subset of the walls will be self-enclosed surfaces that are not attached to any strings. These enclosed walls can collapse in on themselves, compressing a large amount of energy into a small volume and potentially forming primordial black holes (PBHs). We study the number density and dynamics of these self-enclosed walls, taking into account their size distribution, Hubble expansion, asphericities, and all stages of domain wall dynamics using a combination of semi-analytic and numerical approaches. We find that axion models with a high axion decay constant fa, such as those of interest in early matter-dominated cosmologies, yield a PBH abundance potentially observable by future gravitational lensing surveys. We note that the formalism developed here is also useful for predicting relic PBH abundances in other models that exhibit unstable domain walls.

Leptogenesis in parity solutions to the strong CP problem and Standard Model parameters

We study the simplest theories with exact spacetime parity that solve the strong CP problem and successfully generate the cosmological baryon asymmetry via decays of right-handed neutrinos. Lower bounds are derived for the masses of the right-handed neutrinos and for the scale of spontaneous parity breaking, vR. For generic thermal leptogenesis, vR ≳ 1012 GeV, unless the small observed neutrino masses arise from fine-tuning. We compute vR in terms of the top quark mass, the QCD coupling, and the Higgs boson mass and find this bound is consistent with current data at 1σ. Future precision measurements of these parameters may provide support for the theory or, if vR is determined to be below 1012 GeV, force modifications. However, modified cosmologies do not easily allow reductions in vR — no reduction is possible if leptogenesis occurs in the collisions of domain walls formed at parity breaking, and at most a factor 10 reduction is possible with non-thermal leptogenesis. Standard Model parameters that yield low values for vR can only be accommodated by having a high degree of degeneracy among the right-handed neutrinos involved in leptogenesis. If future precision measurements determine vR to be above 1012 GeV, it is likely that higher-dimensional operators of the theory will yield a neutron electric dipole moment accessible to ongoing experiments. This is especially true in a simple UV completion of the neutrino sector, involving gauge singlet fermions, where the bound from successful leptogenesis is strengthened to vR ≳ 1013 GeV.

Two-loop contributions of axion-like particles to electromagnetic and chromomagnetic form factors

Axions and axion-like particles emerge in many models for physics beyond the Standard Model. Thus, they have gained increasing research interest in both experimental and theoretical physics apart from their original proposition as a solution to the strong CP-problem. Among other aspects it has recently been shown that ALPs can potentially provide a solution to the long-lasting discrepancy between theory and experiment of the anomalous magnetic moment of the muon. Provided that the ALP has flavor-violating couplings to leptons, they can also mediate flavor-violating decays like μ→eγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu \\rightarrow e\\gamma $$\\end{document}. Both processes are mediated through related form factors that we compute to two-loop order. We further show numerical implications of our calculations and how they might affect constraints on ALP couplings derived from experiments.

Improved constraints for axion-like particles from 3-photon events at e+e-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^-$$\\end{document} colliders

Axions and axion-like particles (ALPs) are one of the most widely discussed extensions of the Standard Model when it comes to the strong CP problem and dark matter candidates. Current experiments are focused on the indirect searches of invisible pseudoscalars in a wide parameter range. In this paper we investigate limits on ALP mass, and its couplings to photons and leptons from 3-photon annihilation at e+e-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$e^+e^-$$\\end{document} colliders. We provide detailed calculations and apply them to the particular kinematics of the Belle II experiment, covering the ALP mass range from few hundred MeV to around 10 GeV. Our results, which improve upon previous analyses by also including the ALP coupling to electrons, show that such future analyses will allow to significantly extend the ALP search range and impose much more stringent restrictions on their couplings.

Axion dark matter

Axions have a double motivation: they solve the ‘strong CP problem’ of the Standard Model of elementary particles and they are a candidate for the dark matter of the Universe. Dark matter axions can be detected on Earth by converting them to photons in an electromagnetic cavity permeated by a strong magnetic field. A signal in such a detector, called an axion haloscope, would immediately reveal the velocity spectrum of dark matter axions on Earth in great detail. This prospect motivated the study of the special properties that axions have in large scale structure formation. It is shown that cold dark matter axions thermalize through their gravitational self-interactions, and form a Bose-Einstein condensate. As a result, axion dark matter behaves differently from the other proposed forms of dark matter. The differences are observable.