Axion Scale Research Articles

GLUINO AXION, NEUTRINO SEESAW, DYNAMICAL GAUGINO MASS, AND A≃0 SUPERSYMMETRY

In the axionic solution of the strong CP problem, fermions which transform under quantum chromodynamics (QCD) are required. In supersymmetry, by equating U (1)PQ with U (1)R, the natural candidates are the gluinos, as pointed out some years ago. A new specific implementation of this idea is proposed, linking the gluino axion scale to that of the canonical seesaw mechanism for neutrinos. Gaugino masses are generated dynamically and the A term is predicted to be very small.

Cosmological consequences of string axions

Axion fluctuations generated during inflation lead to isocurvature and non-Gaussian temperature fluctuations in the cosmic microwave background radiation. Following a previous analysis for the model independent string axion we consider the consequences of a measurement of these fluctuations for two additional string axions. We do so independent of any cosmological assumptions except for the axions being massless during inflation. The first axion has been shown to solve the strong CP problem for most compactifications of the heterotic string while the second axion, which does not solve the strong CP problem, obeys a mass formula which is independent of the axion scale. We find that if gravitational waves interpreted as arising from inflation are observed by the PLANCK polarimetry experiment with a Hubble constant during inflation of H{sub inf} {approx}> 10{sup 13} GeV the existence of the first axion is ruled out and the second axion cannot obey the scale independent mass formula. In an appendix we quantitatively justify the often held assumption that temperature corrections to the zero temperature QCD axion mass may be ignored for temperatures T {approx}< {Lambda}{sub QCD}.

Some recent work on the curvaton paradigm

I review the simplest curvaton scenario. Using a pseudo Nambu-Goldstone boson as curvaton avoids the η -problem of inflation which plagues most curvaton candidates. Then I report on a collaboration with E. J. Chun and K. Dimopoulos, describing a concrete realization of the curvaton mechanism. It uses a pseudo Nambu-Goldstone boson can be found in the supersymmetric Peccei-Quinn mechanism resolving the strong CP problem. In the flaton models of Peccei-Quinn symmetry breaking, the angular degree of freedom associated with the QCD axion can naturally be a flat direction during inflation and provides successful curvature perturbations. In this scheme, the preferred values of the axion scale and the Hubble parameter during inflation turn out to be about 10 10 GeV and 10 12 GeV, respectively. Moreover, it is found that a significant isocurvature component, (anti)correlated to the overall curvature perturbation, can be generated, which is a smoking-gun for the curvaton scenario. Finally, non-Gaussianity in the perturbation spectrum at potentially observable level is also possible.

Model of cosmology and particle physics at an intermediate scale

We propose a model of cosmology and particle physics in which all relevant scales arise in a natural way from an intermediate string scale. We are led to assign the string scale to the intermediate scale ${M}_{*}\ensuremath{\sim}{10}^{13}\text{ }\text{ }\mathrm{GeV}$ by four independent pieces of physics: electroweak symmetry breaking; the $\ensuremath{\mu}$ parameter; the axion scale; and the neutrino mass scale. The model involves hybrid inflation with the waterfall field $N$ being responsible for generating the $\ensuremath{\mu}$ term, the right-handed neutrino mass scale, and the Peccei-Quinn symmetry breaking scale. The large scale structure of the Universe is generated by the lightest right-handed sneutrino playing the r\^ole of a coupled curvaton. We show that the correct curvature perturbations may be successfully generated providing the lightest right-handed neutrino is weakly coupled in the seesaw mechanism, consistent with sequential dominance.

Inflationary solution to the strong CP and μ problems

We show that the vacuum expectation value of the inflaton at the Peccei–Quinn axion scale can generate the supersymmetric Higgs mass μ term. This provides an inflationary simultaneous solution to the strong CP problem and the μ problem of the minimal supersymmetric Standard Model, and gives a testable prediction for the μ parameter: μ2≈(0.25–0.5)m02, where m0 is the soft Higgs scalar mass. Our model involves a very small Yukawa coupling of order 10−10, which could originate from an extra-dimensional scenario or type I string theory.

Completing natural inflation

If the inflaton is a pseudo-scalar axion, the axion shift symmetry can protect the flatness ofits potential from too large radiative corrections. This possibility, known as naturalinflation, requires an axion scale which is greater than the (reduced) Planck scale. It isunclear whether such a high value is compatible with an effective field theoreticaldescription, and whether the global axionic symmetry survives quantum gravity effects. Wepropose a mechanism which provides an effective large axion scale, although the originalone is sub-Planckian. The mechanism is based on the presence of two axions, with apotential provided by two anomalous gauge groups. The effective large axion scale is due toan almost exact symmetry between the couplings of the axions to the anomalousgroups. We also comment on a possible implementation in heterotic string theory.

Curvaton and QCD axion in supersymmetric theories

A pseudo Nambu-Goldstone boson as curvaton avoids the eta-problem of inflation which plagues most curvaton candidates. We point out that a concrete realization of the curvaton mechanism with a pseudo Nambu-Goldstone boson can be found in the supersymmetric Peccei-Quinn mechanism resolving the strong CP problem. In the flaton models of Peccei-Quinn symmetry breaking, the angular degree of freedom associated with the QCD axion can naturally be a flat direction during inflation and provides successful curvature perturbations. In this scheme, the preferred values of the axion scale and the Hubble parameter during inflation turn out to be about 10^{10} GeV and 10^{12} GeV, respectively. Moreover, it is found that a significant isocurvature component, (anti)correlated to the overall curvature perturbation, can be generated, which is a smoking-gun for the curvaton scenario. Finally, non-Gaussianity in the perturbation spectrum at potentially observable level is also possible.

QCD axion from a higher dimensional gauge field theory.

We point out that a QCD axion solving the strong CP problem can arise naturally from a parity-odd gauge field in five-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all other unwanted U(1)PQ breaking axion couplings can be avoided naturally by the 5D gauge symmetry and locality. If the fifth dimension is warped, the resulting axion scale is suppressed by a small warp factor compared to the Planck scale, thereby the model can generate naturally an intermediate axion scale fa = 10(10)-10(12) GeV.

Stabilizing the axion by discrete gauge symmetries

The axion solution to the strong CP problem makes use of a global Peccei–Quinn U(1) symmetry which is susceptible to violations from quantum gravitational effects. We show how discrete gauge symmetries can protect the axion from such violations. PQ symmetry emerges as an approximate global symmetry from discrete gauge symmetries. Simple models based on ZN symmetries with N=11,12, etc., are presented realizing the DFSZ axion and the KSVZ axion. The discrete gauge anomalies are canceled by a discrete version of the Green–Schwarz mechanism. In the supersymmetric extension our models provide a natural link between the SUSY breaking scale, the axion scale, and the SUSY-preserving μ term.

Making neutrinos massive with an axion in supersymmetry

The minimal supersymmetric standard model (MSSM) of particle interactions is extended to include three singlet (right-handed) neutrino superfields together with three other singlet superfields. The resulting theory is assumed to be invariant under an anomalous global U(1) (Peccei-Quinn) symmetry with one fundamental mass $m_2$. The soft breaking of supersymmetry at the TeV scale is shown to generate an axion scale $f_a$ of order $m_2$. Neutrino masses are generated by $f_a$ according to the usual seesaw mechanism.

Cosmological constraints on a Peccei-Quinn flatino as the lightest supersymmetric particle

In an interesting class of models, nonrenormalizable terms of the superpotential are responsible for the spontaneous breaking of Peccei-Quinn (PQ) symmetry as well as the generation of the \ensuremath{\mu} term. The flaton fields that break PQ symmetry are accompanied by flatinos, and the lightest flatino [the lightest supersymmetric particle (LSP)] can be stable, while the decay of the lightest neutralino [the next-to-lightest supersymmetric particle (NLSP)] might be visible at colliders with a low axion scale. We examine the cosmology of these models involving thermal inflation just after the PQ phase transition. The branching ratio of flatons into axions must be small so as not to interfere with nucleosynthesis, and flatons must not decay into the LSP or it will be overabundant. We explore a simple model, with light flatons that can decay into Z or W bosons, or into a light Higgs boson ${(h}^{0})$ plus a Z boson, to show that such features can be realized in a wide range of parameter space. The mass of the NLSP can be as low as ${(m}_{{h}^{0}}{+m}_{Z})/2,$ with an axion scale of order ${10}^{10}\mathrm{GeV}$ and a final reheat temperature typically of order 10 GeV. Thus, the flatino LSP is a good dark matter candidate because the reheat temperature can be high enough to allow its production from the decay of the thermalized LSP, while low enough to prevent its overproduction from the decay of sfermions.

Phenomenology of low quantum gravity scale models

We study some phenomenological implications of models where the scale of quantum gravity effect lies much below the four-dimensional Planck scale. These models arise from M-theory vacua where either the internal space volume is large or the string coupling is very small. We provide a critical analysis of ways to unify electroweak, strong, and gravitational interactions in M theory. We discuss the relations between different scales in two M vacua: type I strings and Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Witten supergravity models. The latter allows possibilities for an 11-dimensional scale at TeV energies with one large dimension below separating our four-dimensional world from a hidden one. Different mechanisms for breaking supersymmetry (gravity mediated, gauge mediated, and Scherk-Schwarz mechanisms) are discussed in this framework. Some phenomenological issues such as dark matter (with masses that may vary in time), origin of neutrino masses, and axion scale are discussed. We suggest that these are indications that the string scale may be lying in the ${10}^{10}--{10}^{14 }$GeV region.

Cosmological implications of radiatively generated axion scale

We study cosmological implications of supersymmetric axion models in which the axion scale is generated radiatively. Such models lead to the so-called thermal inflation and subsequent reheating should be constrained not to yield to a too large axion energy density at the time of nucleosynthesis. We examine how plausible it is that this nucleosynthesis constraint is satisfied for both hadronic and Dine-Fischler-Srednicki-Zhitnitskii type axion models. Baryogenesis and the possibility for raising up the cosmological upper bound on the axion scale in thermal inflation scenario are also discussed.

Is a heavy quark axion necessarily a hadronic axion?

We show that a heavy quark axion is not necessarily a hadronic axion, which manifests itself in the quark and lepton seesaw mechanism. We introduce a heavy SU(2) singlet fermion for each known fermion in order to unify the axion scale and the seesaw scale. The light qaurks and leptons gain their masses by the seesaw mechanism. Even though our axion model gives a kind of heavy quark axion, the axion has a tree level lepton-axion coupling suppressed by {ital F}{sub {ital a}}, contrary to a widely known belief that heavy quark axions are hadronic.

Cosmological constraints on pseudo Nambu-Goldstone bosons.

Particle-physics models with pseudo Nambu-Goldstone bosons (PNGB's) are characterized by two mass scales: a global spontaneous-symmetry-breaking scale $f$ and a soft (explicit) symmetry-breaking scale $\ensuremath{\Lambda}$. We investigate general model-insensitive constraints on this two-dimensional parameter space arising from the cosmological and astrophysical effects of PNGB's. In particular, we study constraints arising from vacuum misalignment and thermal production of PNGB's, topological defects, and the cosmological effects of PNGB decay products, as well as astrophysical constraints from stellar PNGB emission. Bounds on the Peccei-Quinn axion scale, ${10}^{10}\mathrm{GeV}\ensuremath{\lesssim}{f}_{\mathrm{PQ}}\ensuremath{\lesssim}{10}^{10}\ensuremath{-}{10}^{12}\mathrm{GeV}$, emerge as a special case, where the soft breaking scale is fixed at ${\ensuremath{\Lambda}}_{\mathrm{QCD}}\ensuremath{\simeq}100$ MeV.

Axions and stars.

The emission of light, noninteracting particles, such as axions and Majorons, modifies the structure and evolution of stars. We show that the main effects of such an energy loss are to raise the central temperature and luminosity of stars and to reduce their lifetimes. We clarify previous discussions of stellar axion bounds by directly relating the effects of axions to observable stellar parameters. The concordance of the standard model of the Sun with observations yields a self-consistent bound on the coupling of light pseudoscalars to electrons: ${g}_{\ensuremath{\varphi}e}$5.4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$. This corresponds to a lower limit on the Peccei-Quinn scale, (F/2${X}_{e}^{\mathcal{'}}$)\ensuremath{\ge}${10}^{7}$ GeV, comparable to the usually quoted solar bound. The lifetime of helium-burning stars can be used to place a very stringent and confident bound on the axion scale, (F/2${X}_{e}^{\mathcal{'}}$)\ensuremath{\ge}5.2\ifmmode\times\else\texttimes\fi{}${10}^{8}$ GeV, corresponding to ${g}_{\ensuremath{\varphi}e}$9.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$. We also discuss the consequences of axion emission for the solar-neutrino problem, for the ages of globular clusters, and for terrestrial solar axion detectors. Since the axion luminosity scales as a lower power of temperature than the nuclear-energy-generation rate, axion emission has a stronger influence on cool stars. We discuss the resultant changes in the mass-luminosity relation for low-mass stars and the effects on the low-mass cutoff for main-sequence stars.

An attempt to extend the standard model to include invisible axions and majorons

We present a modest extension of the standard model to include a Peccei-Quinn symmetry and a global lepton-number symmetry both of which are spontaneously broken at the same invisible axion scale, thus eliminating the strong CP problem and generating masses for the light neutrinos that could explain the observed depletion of the solar neutrino flux. The model has no apparent difficulties with known constraints.

Light neutrino masses and mixing angles in SO(10) from the flavor structure of quarks, and the solar neutrino problem

The light neutrino masses and their mixing angles are investigated in a class of SO(10) models with the GRSY seesaw mechanism. The models are motivated by a recent proposal on the structure of the Yukawa couplings postulated from the observed KM angles and the strong- CP problem. The scale of the seesaw mechanism is found to be bounded from above by the invisible axion scale, leading to a lower bound on the light neutrino masses. The main results are: 0.18 eV⩽m v3 ⩽100 eV, m v1 m v2 = O( m u m c ) , and m v2 m v3 = O(( m c m t )( m u m c m t )) for the non-hierarchical structure of the right-handed neutrino mass matrix ( M N), and m v2 m v3 = O( m c m t ) for the hierarchical structure of M N , θ eμ ≅| m e m μ + exp( iη l′ ) O( m u m c )|, θ μt≅| m μ m t - exp( iη 2) O( m c m t )| , and θ e/ m t θ μt , where η 1′ and η 2 are some phases. With present experimental constraints on the mixing angles, ν μ − ν τ and ν e − ν μ oscillations may be observable in the next generation of experiments. Regarding the solution to the solar neutrino problem with the MSW amplification mechanism, we find that the relevant neutrino oscillation in the sun should be in the ν e − ν μ channel, instead of the ν e − ν t channel which the “naive seesaw” model at the GUT scale predicts. Moreover, we also find that, for the structure of M N similar to those of quarks, the existence of a light fourth generation neutrino is inevitable, if the cosmological mass density bound is to be saturated by the light neutrino masses and the solar neutrino problem is solved by the MSW mechanism.

Light neutrino masses and mixing angles in SO(10) with realistic flavor structure, and the solar neutrino problem

The light neutrino mass spectrum and their mixing angles are investigated in a class of SO(10) models with GRSY seesaw mechanism. The models are motivated by a recent proposal on the structure of the Yukawa couplings postulated from the observed KM angles and the strong CP problem. The scale of GRSY seesaw mechanism is found to be bounded from above by the invisible axion scale, leading to a lower bound on the light neutrino masses, if the strong CP problem is solved by the standard Peccei-Quinn mechanism with the invisible axion. The main results on the light neutrino masses are: 0.18 eV ⩽ m ν 3 ⩽ 100 eV, m ν 1 / m ν 2 = O( m u/ m c) , and m ν 2 /m ν 3 = O((m c /m t )( m u m c /m t )) for the non-hierarchical structure of the right-handed neutrino mass matrix ( M N), and m ν 2 / m ν 3 = O( m c/ m t) for the hierarchical structure of M N. The mixing angles are predicted to be: θ eμ ⋍ | m e /m μ + e iη' 1 O( m u /m c ) | , θ μ⊥ ⋍ | m μ /m ⊥ − e iη 2 O( m c /m t ) | and θ e⊥ ⋍ m e /m μθ μ⊥, where η' 1 and η/ 2 are some phases. Present experimental constraints on the mixing angles suggest that the phase structures of the lepton mass matrices are similar to those for the quarks if the sum of the light neutrino masses saturates the cosmological mass density bound of 100 eV, implying that ν μ − ν ⊥ and ν e− ν μ oscillations may be observable in the next generation of experiments. Regarding the solution to the solar neutrino problem with MSW amplification mechanism, we find that the relevant neutrino oscillation in the sun should be in the ν e− ν μ channel, instead of the ν e− ν ⊥ channel which the “naive seesaw” model at the GUT scale predicts. Moreover, for the structure of M N similar to those of quarks, the existence of the fourth generation light neutrino is inevitable, if the cosmological mass density bound is to be saturated by the light neutrino masses and the solar neutrino problem is solved by MSW mechanism. The results obtained in this paper are quite different from and far more interesting than those of the “naive” seesaw model in which M N is assumed to be proportional to the identity matrix and/or the scale of seesaw mechanism is taken to be the GUT scale.

Fermion mass hierarchy, Kobayashi-Maskawa matrix, and weak and strong CP solution with a non-Abelian family symmetry.

We present a prototype model in which the observed family structure is entirely due to the family symmetry and its breaking patterns present at the axion scale. The model is based upon an SU(3) global family group and an Abelian group, in which U(1${)}_{\mathrm{PQ}}$ is a subgroup. The model successfully explains the observed fermion mass hierarchy, the Kobayashi-Maskawa (KM) matrix, and the weak and strong-CP problem on the same footing. The observed fermion mass hierarchy is naturally obtained from the smallest dimensionless parameter of order of the Cabibbo angle (theta\ensuremath{\simeq}(1/5)) while the weak-CP phase of \ensuremath{\pi}/2 is generated by spontaneous symmetry breaking at the axion scale. The entire KM angles are correctly produced in terms of the observed quark mass ratios from the Fritzsch ``texture'' of quark mass matrices. Three generations of superheavy Dirac fermions are predicted to exist at the axion scale. These fermions are in one-to-one correspondence with the three generations of ordinary quarks and leptons, and can be regarded as their ``mirror image''. The best way of testing the scenario presented in the model would be to detect some of the familons predicted by the model.