Axion Scale Research Articles

Removing the cosmological bound on the axion scale in the Kim-Shifman-Vainshtein-Zakharov and Dine-Fischler-Srednicki-Zhitnitsky models

It is known for some time that the cosmological bound on the invisible axion scale can be avoided by an early phase of strong QCD. While most approaches rely on theories where the strong coupling constant is determined through the expectation value of some scalar field, we show that this mechanism can also be implemented into the benchmark KSVZ and DFSZ models when the early phase of strong QCD emerges by the modification of the running coupling during inflation. For both models the physics that are responsible for making QCD strong do not displace the axions minimum by too much, so that the efficiency of the relaxation is controlled by parameters of the theory and the number of inflationary e-folds. In particular, we consider the case of very efficient relaxation where the axion abundance is dominated by inflationary quantum and post-inflationary thermal fluctuations. Within this situation we identify the parameter space compatible with all cosmological constrains and derive conditions on the reheating temperature and the QCD scale during inflation that result in the axion making up all the dark matter. Due to duality below the Peccei-Quinn scale and a minor influence of the KSVZ and DFSZ fields on the running, our findings also apply to a minimal 2-form implementation of the axion.

Axion quality straight from the GUT

Composite axion scenarios offer a robust field theoretic justification for the existence of a Peccei–Quinn symmetry of high quality. We present a new class of realizations that are naturally embedded in Grand-Unified Theories, retain asymptotic freedom for all gauge groups, and protect the axion shift symmetry up to operators of dimension 12. Our setup leads to a number of distinctive signatures at low energies. First, additional composite scalars are predicted; some of these are viable dark matter candidates for values of the decay constant that are likely too low for the QCD axion abundance to be relevant. Second, an approximate unification of the Standard Model gauge couplings takes place at the axion scale, while leaving the actual quark-lepton unification at much higher energies as usual. This suggests the existence of GUT relics with Standard Model gauge quantum numbers at potentially accessible scales.

An even lighter QCD axion

We explore whether the axion which solves the strong CP problem can naturally be much lighter than the canonical QCD axion. The {Z}_{mathcal{N}} symmetry proposed by Hook, with mathcal{N} mirror and degenerate worlds coexisting in Nature and linked by the axion field, is considered in terms of generic effective axion couplings. We show that the total potential is safely approximated by a single cosine in the large mathcal{N} limit, and we determine the analytical formula for the exponentially suppressed axion mass. The resulting universal enhancement of all axion interactions relative to those of the canonical QCD axion has a strong impact on the prospects of axion-like particle experiments such as ALPS II, IAXO and many others: experiments searching for generic axion-like particles have in fact discovery potential to solve the strong CP problem. The finite density axion potential is also analyzed and we show that the {Z}_{mathcal{N}} asymmetric background of high-density stellar environments sets already significant model-independent constraints: 3 ≤ mathcal{N} ≲ 47 for an axion scale fa ≲ 2.4 × 1015 GeV, with tantalizing discovery prospects for any value of fa and down to mathcal{N} ∼ 9 with future neutron star and gravitational wave data, down to the ultra-light mass region. In addition, two specific ultraviolet {Z}_{mathcal{N}} completions are developed: a composite axion one and a KSVZ-like model with improved Peccei-Quinn quality.

Diagonal reflection symmetries and universal four-zero texture * *This study is financially Supported by JSPS Grants-in-Aid for Scientific Research (JP18H01210, 20K14459) and MEXT KAKENHI (JP18H05543)

In this paper, we consider a set of new symmetries in the SM: diagonal reflection symmetries with diag . These generalized symmetries predict the Majorana phases to be or . Realization of diagonal reflection symmetries implies a broken chiral symmetry only for the first generation. The axion scale is suggested to be [GeV]. By combining the symmetries with the four-zero texture, the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well. This scheme predicts the normal hierarchy, the Dirac phase and or [meV]. In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix completely determine the structure of the right-handed neutrino mass . A unification predicts the mass eigenvalues to be [GeV].

Axion scales and couplings with St\xfcckelberg mixing

We study the axion field range and low energy couplings in models with Stückelberg mixing between axions and U(1) gauge bosons. It is noted that the gauge- invariant axion combination ξ in the model is periodic modulo an appropriate shift of gauge-variant axions eaten by the massive U(1) gauge bosons, which in some cases makes the connection between the field range and the low energy couplings less transparent. We derive the field range of ξ for generic forms of the axion kinetic metric and U(1) charges, and identify the field basis for which all non-derivative couplings of ξ are quantized in a manner manifestly consistent with the periodicity of ξ. Generically Stückelberg mixing reduces the axion field range. In particular, the mixings between N axions and (N − 1) U(1) gauge bosons typically result in an exponentially reduced field range {M}_{xi }=mathcal{O}left({k}^{-left(N-1right)}f/sqrt{N!}right) for the residual gauge-invariant axion ξ in the limit N ≫ 1, where f and k denote the typical decay constant and the root mean square of the U(1) gauge charges of the original N axions. Using simple examples, we study also the reparameterization-invariant physical quantities such as the axion effective potential and 1PI couplings to gauge bosons, which are determined by the reparameterization-dependent axion couplings in the model.

Unification of inflation with dark energy in f(R) gravity and axion dark matter

In this work we introduce an effective model of $f(R)$ gravity containing a non-minimal coupling to the axion scalar field. The axion field is described by the misalignment model, in which the primordial $U(1)$ Peccei-Quinn symmetry is broken during inflation and the $f(R)$ gravity is described by the $R^2$ model, and in addition, the non-minimal coupling has the form $\sim h(\phi)R^{\gamma}$, with $0<\gamma<0.75$. By appropriately constraining the non-minimal coupling at early times, the axion field remains frozen in its primordial vacuum expectation value, and the $R^2$ gravity dominates the inflationary era. As the Universe expands, when $H$ equals the axion mass $m_a$ and for cosmic times for which $m_a\gg H$, the axion field oscillates. By assuming a slowly varying evolution of the axion field, the axion energy density scales as $\rho_a\sim a^{-3}$, where $a$ is the scale factor, regardless of the background Hubble rate, thus behaving as cold dark matter. At late times, the axion still evolves as $\rho_a\sim a^{-3}$, however the Hubble rate of the expansion and thus the dynamical evolution of the Universe is controlled by terms containing the higher derivatives of $\sim R^{\gamma}$, which are related to the non-minimal coupling, and as we demonstrate, the resulting solution of the Friedman equation at late times is an approximate de Sitter evolution. The late-time de Sitter Hubble rate scales as $H\sim \Lambda^{1/2}$, where $\Lambda$ is an integration constant of the theory, which has its allowed values very close to the current value of the cosmological constant. Finally, the theory has a prediction for the existence of a pre-inflationary primordial stiff era, in which the energy density of the axion scales as $\rho_a\sim a^{-6}$.

Axion couplings to electroweak gauge bosons

We determine the model-independent component of the couplings of axions to electroweak gauge bosons, induced by the minimal coupling to QCD inherent to solving the strong CP problem. The case of the invisible QCD axion is developed first, and the impact on W and Z axion couplings is discussed. The analysis is extended next to the generic framework of heavy true axions and low axion scales, corresponding to scenarios with enlarged confining sector. The mass dependence of the coupling of heavy axions to photons, W and Z bosons is determined. Furthermore, we perform a two-coupling-at-a-time phenomenological study where the gluonic coupling together with individual gauge boson couplings are considered. In this way, the regions excluded by experimental data for the axion-WW, axion-ZZ and axion-Zgamma couplings are determined and analyzed together with the usual photonic ones. The phenomenological results apply as well to ALPs which have anomalous couplings to both QCD and the electroweak bosons.

Color unified dynamical axion

We consider an enlarged color sector which solves the strong CP problem via new massless fermions. The spontaneous breaking of a unified color group into QCD and another confining group provides a source of naturally large axion mass m_a due to small size instantons. This extra source of axion mass respects automatically the alignment of the vacuum, ensuring a low-energy CP-conserving vacuum. The mechanism does not appeal to a Z_2 “mirror” copy of the SM, nor does it require any fine-tuning of the axion-related couplings at the unification scale. There is no very light axion and uncharacteristically the lighter spectrum contains instead sterile fermions. The axion scale f_a can be naturally brought down to a few TeV, with an exotic spectrum of colored pseudoscalars lighter than this scale, observable at colliders exclusively via strong interactions. The {m_a, f_a} parameter space which allows a solution of the strong CP problem is thus enlarged well beyond that of invisible axion models.

Accidental Peccei–Quinn symmetry from discrete flavour symmetry and Pati–Salam

We show how an accidental U(1) Peccei–Quinn (PQ) symmetry can arise from a discrete A4 family symmetry combined with a discrete flavour symmetry Z3×Z52, in a realistic Pati–Salam unified theory of flavour. Imposing only these discrete flavour symmetries, the axion solution to the strong CP problem is protected from PQ-breaking operators to the required degree. A QCD axion arises from a linear combination of A4 triplet flavons, which are also responsible for fermion flavour structures due to their vacuum alignments. We find that the requirement of an accidental PQ symmetry arising from a discrete flavour symmetry constrains the form of the Yukawa matrices, providing a link between flavour and the strong CP problem. Our model predicts specific flavour-violating couplings of the flavourful axion and thus puts a strong limit on the axion scale from kaon decays.

Ultralight axion in supersymmetry and strings and cosmology at small scales

Dynamical mechanisms to generate an ultralight axion of mass $\sim 10^{-21}-10^{-22}$ eV in supergravity and strings are discussed. An ultralight particle of this mass provides a candidate for dark matter that may play a role for cosmology at scales $10\, {\rm kpc}$ or less. An effective operator approach for the axion mass provides a general framework for models of ultralight axions, and in one case recovers the scale $10^{-21}-10^{-22}$ eV as the electroweak scale times the square of the hierarchy with an $O(1)$ Wilson coefficient. We discuss several classes of models realizing this framework where an ultralight axion of the necessary size can be generated. In one class of supersymmetric models an ultralight axion is generated by instanton like effects. In the second class higher dimensional operators involving couplings of Higgs, standard model singlets, and axion fields naturally lead to an ultralight axion. Further, for the class of models considered the hierarchy between the ultralight scale and the weak scale is maintained. We also discuss the generation of an ultralight scale within string based models. Here it is shown that in the single modulus KKLT moduli stabilization scheme an ultralight axion would require an ultra-low weak scale. However, within the Large Volume Scenario, the desired hierarchy between the axion scale and the weak scale is achieved. A general analysis of couplings of Higgs fields to instantons within the string framework is discussed and it is shown that the condition necessary for achieving such couplings is the existence of vector-like zero modes of the instanton. Some of the phenomenological aspects of these models are also discussed.

Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry

We discuss a scheme to implement the relaxion solution to the hierarchy problem with multiple axions, and present a UV-completed model realizing the scheme. All of the $N$ axions in our model are periodic with a similar decay constant $f$ well below the Planck scale. In the limit $N\gg 1$, the relaxion $\phi$ corresponds to an exponentially long multi-helical flat direction which is shaped by a series of mass mixing between nearby axions in the compact field space of $N$ axions. With the length of flat direction given by $\Delta \phi =2\pi f_{\rm eff} \sim e^{\xi N} f$ for $\xi={\cal O}(1)$, both the scalar potential driving the evolution of $\phi$ during the inflationary epoch and the $\phi$-dependent Higgs boson mass vary with an exponentially large periodicity of ${\cal O}(f_{\rm eff})$, while the back reaction potential stabilizing the relaxion has a periodicity of ${\cal O}( f)$. A natural UV completion of our scheme can be found in high scale or (mini) split supersymmetry (SUSY) scenario with the axion scales generated by SUSY breaking as $f\sim \sqrt{m_{\rm SUSY}M_*}$, where the soft SUSY breaking scalar mass $m_{\rm SUSY}$ can be well above the weak scale, and the fundamental scale $M_*$ can be identified as the Planck scale or the GUT scale.

Aligned natural inflation with modulations

The weak gravity conjecture applied for the aligned natural inflation indicates that generically there can be a modulation of the inflaton potential, with a period determined by sub-Planckian axion scale. We study the oscillations in the primordial power spectrum induced by such modulation, and discuss the resulting observational constraints on the model.

Diluting the inflationary axion fluctuation by a stronger QCD in the early Universe

We propose a new mechanism to suppress the axion isocurvature perturbation, while producing the right amount of axion dark matter, within the framework of supersymmetric axion models with the axion scale induced by supersymmetry breaking. The mechanism involves an intermediate phase transition to generate the Higgs μ-parameter, before which the weak scale is comparable to the axion scale and the resulting stronger QCD yields an axion mass heavier than the Hubble scale over a certain period. Combined with that the Hubble-induced axion scale during the primordial inflation is well above the intermediate axion scale at present, the stronger QCD in the early Universe suppresses the axion fluctuation to be small enough even when the inflationary Hubble scale saturates the current upper bound, while generating an axion misalignment angle of order unity.

Trajectories with suppressed tensor-to-scalar ratio in Aligned Natural Inflation

In Aligned Natural Inflation, an alignment between different potential terms produces an inflaton excursion greater than the axion scales in the potential. We show that, starting from a general potential of two axions with two aligned potential terms, the effective theory for the resulting light direction is characterized by four parameters: an effective potential scale, an effective axion constant, and two extra parameters (related to ratios of the axion scales and the potential scales in the 2−field theory). For all choices of these extra parameters, the model can support inflation along valleys (in the 2−field space) that end in minima of the potential. This leads to a phenomenology similar to that of single field Natural Inflation. For a significant range of the extra two parameters, the model possesses also higher altitude inflationary trajectories passing through saddle points of the 2−field potential, and disconnected from any minimum. These plateaus end when the heavier direction becomes unstable, and therefore all of inflation takes place close to the saddle point, where—due to the higher altitude—the potential is flatter (smaller ϵ parameter). As a consequence, a tensor-to-scalar ratio r = O ( 10−4 − 10−2 ) can be easily achieved in the allowed ns region, well within the latest 1 σ CMB contours.

Implications of an axino LSP for naturalness

Both the naturalness of the electroweak symmetry breaking and the resolution of the strong CP problem may require a small Higgsino mass $\mu$ generated by a realization of the DFSZ axion model. Assuming the axino is the lightest supersymmetric particle, we study its implications on $\mu$ and the axion scale. Copiously produced light Higgsinos at collider (effectively only neutral NLSP pairs) eventually decay to axinos leaving prompt multi-leptons or displaced vertices which are being looked for at the LHC. We use latest LHC7+8 results to derive current limits on $\mu$ and the axion scale. Various Higgsino-axino phenomenology is illustrated by comparing with a standard case without lightest axinos as well as with a more general case with additional light gauginos in the spectrum.

String theoretic QCD axions in the light of PLANCK and BICEP2

The QCD axion solving the strong CP problem may originate from antisymmetric tensor gauge fields in compactified string theory, with a decay constant around the GUT scale. Such possibility appears to be ruled out now by the detection of tensor modes by BICEP2 and the PLANCK constraints on isocurvature density perturbations. A more interesting and still viable possibility is that the string theoretic QCD axion is charged under an anomalous U(1)_A gauge symmetry. In such case, the axion decay constant can be much lower than the GUT scale if moduli are stabilized near the point of vanishing Fayet-Illiopoulos term, and U(1)_A-charged matter fields get a vacuum value far below the GUT scale due to a tachyonic SUSY breaking scalar mass. We examine the symmetry breaking pattern of such models during the inflationary epoch with the Hubble expansion rate 10^{14} GeV, and identify the range of the QCD axion decay constant, as well as the corresponding relic axion abundance, consistent with known cosmological constraints. In addition to the case that the PQ symmetry is restored during inflation, there are other viable scenarios, including that the PQ symmetry is broken during inflation at high scales around 10^{16}-10^{17} GeV due to a large Hubble-induced tachyonic scalar mass from the U(1)_A D-term, while the present axion scale is in the range 10^{9}-5\times 10^{13} GeV, where the present value larger than 10^{12} GeV requires a fine-tuning of the axion misalignment angle. We also discuss the implications of our results for the size of SUSY breaking soft masses.

Axion dark matter with high-scale inflation

We show that supersymmetric axion models breaking the PQ symmetry by the interplay of non-renormalizable supersymmetric terms and soft supersymmetry breaking terms provide a natural framework not only for generating the axion scale from soft supersymmetry breaking scale m3/2 but also for enhancing it during inflation by factor of order HI/m3/2 where HI≃1014 GeV according to the recent BICEP2 result. In this scheme, the PQ symmetry can stay broken throughout the whole history of the Universe if the reheat temperature is below 1010 GeV, or m3/2 when the PQ fields couple strongly to thermal (Standard Model) particles. It is also shown that parametric resonance during preheating is not effective enough to induce non-thermal PQ symmetry restoration. As a consequence, axion models with the QCD anomaly NDW>1 can be made free from the domain wall problem while the axion isocurvature perturbation is suppressed sufficiently for the axion scale during inflation larger than about MP(Ωah2/0.12)1/2(Fa/1012 GeV)0.6 GeV.

Gravity and axions from a random UV QFT

It is postulated that the UV QFT is enormous and random. The coupling of the Standard Model to such QFT is analyzed. It is argued that massless 4d gravity and axions are general avatars of the postulate. The equivalence principle emerges naturally as well as a concrete set of sources for its breaking. The axion scale is related to the 4d Planck scale as $f=M_P/N$, where $N$ is the "number of colors" of the (almost) hidden UV CFT.

SUPERSYMMETRIC AXION-NEUTRINO MODEL WITH A HIGGS HYBRID

In 2001, a supersymmetric model was proposed to relate the axion scale to that of neutrino mass seesaw. Whereas this scenario is realistic, the particles associated with this mechanism are either too heavy or too weakly coupled for them to be observed (other than the axion itself or perhaps the axino). A variation of that model is here proposed which allows significant mixing of the Higgs boson with a new singlet related to the saxion (the scalar partner of the pseudoscalar axion), rendering it possible to be observed at the large hadron collider (LHC). With the addition of exotic color superfields, this also becomes a specific realization of how the production of such a Higgs hybrid may be suppressed or enhanced at the LHC, which is very relevant to ongoing experimental efforts to find the Higgs boson.

Dark matter in the Kim-Nilles mechanism

The Kim-Nilles mechanism relates the $\mu$ term with the axion scale $f_a$, leading to the axino-Higgsino-Higgs Yukawa coupling of order $\mu/f_a$. This can bring a dangerous thermal production of axinos. If the axino is stable, its mass has to be as small as ${\cal O}$(0.1keV), or the reheat temperature should be lower than ${\cal O}$(10GeV) taking the lower axion scale $10^{10}$ GeV in order not to overclose the Universe. If the axino decays to a neutralino, the overproduced neutralinos can re-annihilate appropriately to saturate the observed dark matter density if the annihilation rate is of order $10^{-8}{GeV}^{-2}$ for the axion scale larger than about $10^{11}$ GeV. Thus, a light Higgsino-like lightest supersymmetric particle with a sizable bino mixture becomes a good dark matter candidate whose nucleonic cross-section is of order $10^{-45}$cm$^2$.