We study Nelson–Barr models with a discrete Z_N symmetry that solve the strong CP problem through spontaneous CP violation, and show that they naturally predict a light axion-like particle (ALP) without introducing any additional ingredients. Unlike the QCD axion, this ALP is anomaly-free: its couplings to photons and gluons are highly suppressed, rendering it naturally long-lived. Instead, it couples to quarks through flavor-violating interactions whose structure is dictated by the CKM matrix. These interactions induce rare meson decays, providing a unique probe of the Nelson–Barr mechanism. We study the cosmological production of the ALP through both freeze-in and misalignment mechanisms. We show that the parameter space in which the observed relic abundance is explained by the freeze-in mechanism is subject to stringent constraints from precision flavor experiments and stellar cooling bounds from SN1987A, leaving only a small viable region that will be comprehensively tested by future structure-formation observations such as the Vera Rubin Observatory and next-generation X-ray missions like Athena, GECCO and THESEUS. In contrast, misalignment production remains a robust and viable mechanism for explaining the observed dark matter abundance over a broad region of parameter space. Our results demonstrate that precision flavor measurements, cosmological observations, and X-ray searches provide complementary probes of this anomaly-free ALP and, consequently, of the Nelson–Barr solution to the strong CP problem.

An interesting proposal suggests that a QCD axion (a) coupling to the up quark, down quark, and electron remains viable for an axion mass near 10 MeV. In this paper, this possibility is reexamined by deriving new bounds from kaon decays. In particular, we perform a detailed analysis of the K_L → π^0 π^0 e^+ e^- measurement reported by the KTeV experiment, and reinterpret K^+ decay measurements at the E949 and NA62 experiments to constrain both the diphoton decay and effectively invisible decay modes of the axion. We find that, combined with the previously known bounds, the viable window for the MeV-scale QCD axion is excluded, primarily due to the KTeV bound. Uncertainties associated with the chiral Lagrangian are further examined, and the scenario remains excluded even after accounting for these uncertainties, except for a tiny region of parameter space where higher-order corrections must finely cancel the leading-order contribution, suppressing the branching ratio of K_L→ π^0π^0 a by three orders of magnitude.

We study the Sommerfeld enhancement of the annihilation cross section of dark matter into heavier unstable particles. In this process, the annihilation products become non-relativistic near the kinematical threshold. If they experience long-range interactions with each other, their wave function is distorted from a plane wave, and the annihilation cross section can be significantly enhanced. When evaluating the Sommerfeld enhancement from the long-range interactions between the annihilation products, the decay of the products needs to be taken into account. We treat this issue by including the decay width in the Schrödinger equations of the two-body wave function of the annihilation products. We find that bound states of the annihilation products with a narrow decay width enhance the annihilation cross section through a resonant effect. At the same time, this formulation automatically includes the annihilation process with off-shell final state particles, which is relevant for a wide decay width. We show that the resonant effect significantly affects the prediction of the dark matter relic abundance.

We discuss a novel mechanism for generating dark matter from a fast-rolling scalar field, relevant for both inflation and rotating axion models, and apply it specifically to the (QCD) axion. Dark matter comes from scalar field fluctuations generated by the product of the curvature perturbation and the fast-rolling background field. These fluctuations can explain the totality of dark matter in a vast axion parameter space, particularly for the QCD axion, which will be targeted by upcoming experiments. We review the constraints on this mechanism and potential gravitational-wave signatures.

We show that primordial adiabatic curvature fluctuations generate an instability of the scalar field sourcing a kination era. We demonstrate that the generated higher Fourier modes constitute a radiation-like component dominating over the kination background after about 11 e-folds of cosmic expansion. Current constraints on the extra number of neutrino flavors ΔN_ eff thus imply the observational bound of approximately 10 e-folds, representing the most stringent bound to date on the stiffness of the equation of state of the pre-Big-Bang-Nucleosynthesis universe.

Long-range attractive interactions between dark matter particles can significantly enhance their annihilation, particularly at low velocities. This “Sommerfeld enhancement” is typically computed by evaluating the deformation of the two-particle wavefunction due to the long-range potential, while ignoring the physics associated with the annihilation, and then scaling the appropriate annihilation matrix elements by factors that depend on the wavefunction in the limit where the particles approach zero relative separation. It has long been recognized that this approach is a valid approximation only in the limit where the annihilation rate is small, and breaks down in the regime where the enhanced annihilation rate approaches the unitarity bound, in which case ignoring the impact of the annihilation physics on the two-particle wavefunction cannot be justified and leads to apparent violations of unitarity. In the case where the physics relevant to annihilation occurs at a parametrically shorter distance scale (higher energy scale) compared with the long-range potential, we provide a simple prescription for correcting the Sommerfeld enhancement for the effects of the short-range physics, valid for all partial waves and for systems where multiple states are coupled by the long-range potential.

The axion kinetic misalignment mechanism (KMM) opens the possibility of explaining dark matter for almost any axion mass and decay constant that is not accessible by the standard misalignment mechanism, in particular at low values of the axion decay constant (i.e. large coupling). This is a new opportunity for most axion experiments which could be sensitive to dark matter and probe new regimes of axion cosmology. We scrutinise UV completions that lead to the KMM mechanism. These mainly rely on the early dynamics of the axion partner, the radial mode of the complex scalar field, from which the axion inherits kinetic energy. The damping of the radial-mode energy density is then a necessary ingredient. We study in detail thermal damping from interactions in the plasma. A minimal and rather natural implementation consists of a KSVZ-type model with a nearly-quadratic potential for the radial mode extended by U(1)-breaking higher-dimensional operators. Furthermore, we study Higgs portal interactions as an alternative damping mechanism and improve upon previously proposed implementations based on quartic potentials. These implementations can lead to the QCD axion being dark matter and in the reach of IAXO, while MADMAX, IAXO and ALPS II can be sensitive to a generic Axion-Like-Particle (ALP) as dark matter. Such models typically feature a kination era. We also show that ALP dark matter from KMM points to a particular realization of inflation.

We present models of axion based on supersymmetric chiral gauge theories. In these models, the PQ symmetry is spontaneously broken by the non-perturbative dynamics of chiral gauge theory. Thanks to supersymmetry, IR dynamics of the models are calculable. We also present an example of a QCD axion model that is compatible with SU(5) grand unification. We find that the PQ breaking scale should be higher than ∼ 10^13 GeV for the successful GUT unification. In addition, the PQ breaking scale should be higher than the GUT scale to avoid a Landau pole of gauge coupling below the Planck scale.

A dark matter model based on QCD-like $SU(N_c)$ gauge theory with electroweakly interacting dark quarks is discussed. Assuming the dark quark mass $m$ is smaller than the dynamical scale $\Lambda_d \sim 4\pi f_d$, the main component of the dark matter is the lightest $G$-parity odd dark pion associated with chiral symmetry breaking in the dark sector. We show that nonzero dark quark mass induces the universal mass contribution to both $G$-parity odd and even pions, and their masses tend to be degenerate. As a result, dark pion annihilation into heavier $G$-parity even dark pion also affects the dark matter relic abundance. Thus, our setup naturally accommodates forbidden dark matter scenario and realizes heavy dark matter whose mass is ${\cal O}(1$-$100)~{\rm TeV}$, which is different from conventional electroweakly interacting dark matter such as minimal dark matter. We also discuss CP-violation from $\theta$-term in the dark gauge sector and find that the predicted size of electron electric dipole moment can be as large as $\sim 10^{-32}~e~{\rm cm}$.

A bstract We explore a model of dark matter (DM) that can explain the reported discrepancy in the muon anomalous magnetic moment and predict a large electric dipole moment (EDM) of the muon. The model contains a DM fermion and new scalars whose exclusive interactions with the muon radiatively generate the observed muon mass. Constraints from DM direct and indirect detection experiments as well as collider searches are safely evaded. The model parameter space that gives the observed DM abundance and explains the muon g – 2 anomaly leads to the muon EDM of d μ ≃ (4-5) × 10 − 22 e cm that can be probed by the projected PSI muEDM experiment. Another viable parameter space even achieves $$ {d}_{\mu }=\mathcal{O}\left({10}^{-21}\right) $$ d μ = O 10 − 21 e cm reachable by the ongoing Fermilab Muon g − 2 experiment and the future J-PARC Muon g − 2/EDM experiment.

Abstract We investigate cosmological phase transitions in various composite Higgs models consisting of four-dimensional asymptotically-free gauge field theories. Each model may lead to a confinement-deconfinement transition and a phase transition associated with the spontaneous breaking of a global symmetry that realizes the Standard Model Higgs field as a pseudo-Nambu-Goldstone boson. Based on the argument of universality, we discuss the order of the phase transition associated with the global symmetry breaking by studying the renormalization group flow of the corresponding linear sigma model at finite temperature, which is calculated by utilizing the ϵ-expansion technique at the one-loop order. Our analysis indicates that some composite Higgs models accommodate phenomenologically interesting first-order phase transitions. We also explore the confinement-deconfinement transition in a UV-completed composite Higgs model based on a Sp(2N c ) gauge theory. It is found that the first-order phase transition is favored when the number of degrees of freedom for the Sp(2N c ) gauge field is much larger than that of matter fields in the fundamental representation of Sp(2N c ). We comment on the gravitational wave signal generated by the confinement-deconfinement transition and its detectability at future observations. Our discussions motivate further studies on phase transitions in composite Higgs models with the use of lattice simulations.

Electric dipole moments (EDMs) of elementary particles are powerful probes of new physics with flavor-diagonal CP violation. The reported discrepancy in the muon anomalous magnetic moment motivates us to explore to what extent new physics with flavor-diagonal CP violation to address the discrepancy is probed by searches for the muon EDM. As a benchmark, we focus on a CP-violating two-Higgs-doublet model to explain the muon g−2 anomaly where the muon exclusively couples to one Higgs doublet. Since contributions to flavor violating processes as well as the electron EDM are suppressed, the muon EDM becomes an essential probe of the model. Our result shows that some viable parameter space leads to the muon EDM of around dμ≃6×10−23e cm probed by the PSI experiment and most of the parameter space is covered by the proposed J-PARC experiment.

Spontaneous CP violation, such as the Nelson-Barr (NB) mechanism, is an attractive scenario for addressing the strong CP problem while realizing the observed phase of the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix. However, not only the CKM phase but also the baryon asymmetric Universe requires sources of CP violation. In this study, we show that a supersymmetric NB mechanism can naturally accommodate the Affleck-Dine (AD) baryogenesis within a CP-invariant Lagrangian. The model provides flat directions associated with new heavy quarks. Focusing on one of the directions, we find that the correct baryon asymmetry is obtained with a sufficiently low reheating temperature which does not cause the gravitino problem. Some parameter space is consistent with the gravitino dark matter. We assess radiative corrections to the strong CP phase induced by gauge-mediated supersymmetry breaking and CP-violating heavy fields and show that the strong CP problem is solved in a viable parameter space where the visible sector supersymmetric particles must be lighter than O(100) TeV. Even in the case that they are heavier than the TeV scale, our model predicts the neutron electric dipole moment within the reach of the near future experiments. Our model addresses the electroweak naturalness problem, strong CP problem, baryon asymmetric Universe, and dark matter. Then, the model may give a new compelling paradigm of physics beyond the Standard Model.

We discuss spontaneous chiral symmetry breaking and the quark bilinear condensate in large-N-c quantum chromodynamics (QCD). It is known that the existence of the eta ' meson is implied in large-N-c QCD, as pointed out by Witten[] and Veneziano[]. First, we show that the existence of eta ' and the Ward-Takahashi identities implies the existence of Nambu-Goldstone bosons from chiral symmetry breaking SU(N-f)(L) x SU(N-f)(R) -> SU(N-f)(V). Second, we show that a QCD inequality implies a non-zero lower bound on the quark bilinear condensate.

The main mechanism responsible for Axion-Like-Particle (ALP) production in the early universe is the so-called misalignment mechanism. Three regimes have been investigated in this context: standard misalignment, large misalignment and kinetic misalignment. The latter applies if the axion inherits a large initial velocity in the early universe, such that the field rolls through many wiggles during its evolution, before it gets trapped in one minimum. This largely opens the region of parameter space for ALP dark matter towards higher values for the axion-photon coupling, which can be probed by the whole set of next decade's upcoming experiments. In fact, almost the entire parameter space in the [mass, decay constant] plane can now accommodate dark matter. In this paper, we show that in kinetic misalignment, the axion field is almost always entirely fragmented, meaning that the energy density of the homogeneous field is redistributed over higher-mode axions. We present a general model-independent analytical description of kinetic fragmentation, including discussion of the modified initial conditions for the mode functions due to the axion's initial velocity, and how they impact the growth of the adiabatic fluctuations. We calculate precisely the parameter regions corresponding respectively to standard misalignment, kinetic misalignment with weak fragmentation, fragmentation after trapping and fragmentation before trapping. While axion fragmentation can impact the precise determination of the relic abundance, another main observational implication is the formation of much denser compact axion halos, that is described in a companion paper. We also point out a new gravitational-wave signature that arises in the large misalignment regime with complete fragmentation and could be seen in measurements of μ distortions in the Cosmic Microwave Background.

We use Super-K data to place new strong limits on interactions of sub-GeV Dark Matter (DM) with nuclei, that rely on the DM flux inevitably induced by cosmic-ray upscatterings. We derive analogous sensitivities at Hyper-K and DUNE and compare them with others, e.g. at JUNO. Using simplified models, we find that our proposal tests genuinely new parameter space, allowed both by theoretical consistency and by other direct detection experiments, cosmology, meson decays and our recast of monojet. Our results thus motivate and shape a new physics case for any large volume detector sensitive to nuclear recoils.

We correct a minor point in section 3.2 of “Relaxion Fluctuations (Self-stopping Relaxion) and Overview of Relaxion Stopping Mechanisms”, JHEP 05 (2020) 080. Furthermore, we clarify the origin of equation (4.25). Finally, we add some plots that are of interest.

We study negative modes around the Coleman-de Luccia bounce solution. The conditions for the appearance of an infinite number of the negative modes do not coincide between Lagrangian and Hamiltonian formulations in the literature, and we discuss the origin of this difference in detail. We show how different choices of the variable for the fluctuation around the bounce solution affect the negative mode condition in the Hamiltonian approach, and point out that there exists a choice which gives the same negative mode condition as the Lagrangian approach.

We analyze the phenomenon of axion fragmentation when an axion field rolls over many oscillations of a periodic potential. This is particularly relevant for the case of relaxion, in which fragmentation provides the necessary energy dissipation to stop the field evolution. We compare the results of a linear analysis with the ones obtained from a classical lattice simulation, finding an agreement in the stopping time of the zero mode between the two within an O(1) difference. We finally speculate on the generation of bubbles with different VEVs of the axion field, and discuss their cosmological consequences.