The Polonyi problem and upper bound on inflation scale in supergravity

We reconsider the Polonyi problem in gravity-mediation models for supersymmetry (SUSY) breaking. It has been argued that there is no problem in the dynamical SUSY breaking scenarios, since the Polonyi field acquires a sufficiently large mass of the order of the dynamical SUSY-breaking scale ΛSUSY${\Lambda }_{\mathrm{SUSY}}$. However, we find that a linear term of the Polonyi field in the Kähler potential brings us back to the Polonyi problem, unless the inflation scale is sufficiently low, Hinf?¹⁰⁸ GeV$H_{\inf }?{10}^8\text{GeV}$, or the reheating temperature is extremely low, TR?100 GeV$T_R?100\text{GeV}$. Here, this Polonyi problem is more serious than the original one, since the Polonyi field mainly decays into a pair of gravitinos.     

Petrov classification of supergravity

N = 1 supergravity is analyzed in light of the Petrov classification scheme. It is found that the ($\text{2,}\text{3}\text{2}$) chiral multiplet obtained must be recognized as the Weyl submultiplet, W_abα, where only $\text{(}\text{3}\text{2}\text{, 0) + (0,}\text{3}\text{2}\text{)}$ components contribute. Due to the SUSY transformation laws the classes of solutions allowed for various Petrov types are shown to be restrictive — indeed, in certain instances there can be no consistent solution. The freedom left in the solutions and their possible interpretation are discussed. One-loop invariants are also considered by resorting to non-covariant forms.     

A complete calculation for direct detection of Wino dark matter

In the anomaly-mediated supersymmetry (SUSY) breaking scenario, neutral gaugino of SUL₍₂₎$\mathit{SU}{(2)}_L$ multiplet, Wino, can be the lightest SUSY particle and become a candidate for dark matter. We calculated scattering cross section of Wino dark matter with nucleon, which is responsible for direct detection of the dark matter, on the assumption that the SUSY particles and the heavier Higgs bosons have masses of the order of the gravitino mass in the SUSY standard model. In such a case, the Wino–nucleon coupling is generated by loop processes. We have included two-loop contribution to Wino–gluon interaction in the calculation, since it is one of the leading contributions to the Wino–nucleon coupling. It was found that the spin-independent scattering cross section with proton is ^{10−(46–48)} cm²${10}^{-(46\text{–}48)}{\text{cm}}^2$. While it is almost independent of the Wino mass, the result is quite sensitive to the Higgs boson mass due to the accidental cancellation.     

Chiral symmetry breaking in lattice electrodynamics

Chiral symmetry breaking is studied in lattice quantum electrodynamics in the quenched approximation by computer simulation methods. Simulations at zero temperature show that $\text{〈}\text{Ψ}\text{Ψ〉}$ is non-zero for all couplings e² greater than a critical value e_c². The sensitivity of $\text{〈}\text{Ψ}\text{Ψ〉}$ to short-distance features of the lattice action is studied by simulating variant gauge actions. Simulations on asymmetric lattices do not reveal significant temperature dependence in the symmetry breaking dynamics. Subtle effects and limitations of quenched calculations are discussed.     

SU (4) × SU (4) symmetry breaking and its implications for SU (3) × SU (3) breaking

We investigate models where the SU (4) × SU (4) symmetry breaking Hamiltonian, $\text{H}$_SB, belongs to the (15, 15) and $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ representations, and show how they are equivalent to models of SU (3) × SU (3) breaking where $\text{H}$_SB belongs to a mixture of different representations. The results for the ππ scattering lengths in the (15, 15) model are outside the experimental limits, but the $\text{(10,}\text{10}\text{) + (}\text{10}\text{, 10)}$ model yields solutions with a wide range of values for the scattering lengths within the experimental bounds.     

Calculated isospin-mixing corrections to Fermi β-decays in 1s0d-shell nuclei with emphasis on A = 34

Corrections to the Fermi matrix element due to analogue symmetry breaking are evaluated for the superallowed β-decays of ²²Mg, ³⁴Cl, and ³⁴Ar by considering the effects of Coulomb and other isospin-nonconserving potentials. Analogue symmetry breaking is calculated within the shell-model formalism by considering: (i) the deviations from unity of the radial overlap between the proton and neutron single-particle wave functions, and (ii) isospin mixing between states within the 0d$\text{5}\text{2}$0d$\text{3}\text{2}$0d$\text{1}\text{2}$ shell. The radial-overlap corrections for several cases of interest in the sd shell are evaluated with single-particle wave functions obtained from a self-consistent Hartree-Fock calculation. The sd-shell isospin-mixing corrections are calculated with an isospin-non-conserving potential which reproduces the experimental isobaric mass shifts. Comparisons with previous calculations are made. The Fermi matrix elements for the isospin-forbidden (β-decays of ³⁴Cl and ³⁴Ar to excited 0⁺ states are also calculated.     

Dynamical approach to supersymmetry

Using new techniques for deriving bounds satisfying the requirements of unitarity and analiticity, optimal constraints on the scalar K_?3 form factor are obtained, given the s-wave, $\text{I =}\text{1}\text{2}\text{,}\text{K}\text{π}$ elastic phase shift. It is assumed that the propagators of current divergences satisfy unsubtracted dispersion relations, that axial divergences are dominated by pion and kaon poles and that the chiral symmetry breaking Hamiltonian transforms as $\text{(3,}\text{3}\text{) + (}\text{3}\text{,3)}$. Recent SLAC-Santa Cruz data satisfy these constraints, as does the Callan-Treiman relation. The constraint on the slope of the form factor, given either the Callan-Treiman relation or the data, is badly violated by the current algebra prediction of Dashen and Weinstein. This violation suggests the necessity for subtraction, corresponding to a chiral symmetry breaking Hamiltonian density with scale dimension greater than or equal to two. The results depend only weakly on the elastic phase shift.     

Supersymmetric flavon-chromon models

Using the supersymmetry and R-breaking mechanism induced by N=1 supergravity, we develop the minimal flavon-chromon preonic model where $\text{spin}\text{-}\text{1}\text{2}$ and spin-0 components of four preonic chiral multiplets correspond to flavons and chromons, from which quarks and leptons are made as composites. The emergence of the concepts of flavour and colour, in this minimal model, is synonymous with R and supersymmetry breaking. This breaking also gives a heavy mass to the gaugino, which is necessary for the implementation of the model.     

Conformal gauge mediation

We propose a one-parameter theory for gauge mediation of supersymmetry (SUSY) breaking. The spectrum of SUSY particles such as squarks and sleptons in the SUSY standard-model and the dynamics of SUSY-breaking sector are, in principle, determined only by one parameter in the theory, that is, the mass of messengers. Above the messenger threshold all gauge coupling and Yukawa coupling constants in the SUSY-breaking sector are on the infrared fixed point. We find that the present theory may predict a split spectrum of the standard-model SUSY particles, mgaugino<msfermion$m_{\mathrm{gaugino}}<m_{\mathrm{sfermion}}$, where mgaugino$m_{\mathrm{gaugino}}$ and msfermion$m_{\mathrm{sfermion}}$ are SUSY-breaking masses for gauginos and squarks/sleptons, respectively.     

A conformal gauge mediation and dark matter with only one mass parameter

If the supersymmetry (SUSY) is a solution to the hierarchy problem, it is puzzling that any SUSY particle has not been discovered yet. We show that there is a low-scale conformal gauge mediation model which contains all necessary ingredients, i.e. not only a SUSY-breaking dynamics and a gauge mediation mechanism, but also a candidate for the dark matter. The model has only one free mass parameter, that is, the mass for messengers. In this model, the dark matter is provided by a composite particle in the SUSY-breaking sector, and the observed value of the dark matter density uniquely fixes the mass of messengers at the order of 10² TeV. Then, the sfermion and gaugino masses are fixed to be of order ¹⁰²–¹⁰³ GeV${10}^2\text{–}{10}^3\text{GeV}$ without any arbitrariness, thus the SUSY particles are expected not to be discovered at the Tevatron or LEP, while having a discovery possibility at the LHC.     

The SU(3) noninvariant vacuum and the Cabibbo angle

A connection between chiral symmetry breaking and the Cabibbo angle is formulated in a new way within the framework of the $\text{(3,}\text{3}\text{) ? (}\text{3}\text{, 3)}$ model. The essential feature of this formulation is the assumption about the SU(3) noninvariance of the vacuum. In such a way it is shown that no isopin symmetry breaking of the hadron world is needed to explain the magnitude of the Cabibbo angle.     

Superconductivity in singlet La-Pr and in nonmagnetic La-rare earth alloys

We show that concentration dependence of the superconducting transition temperature of d.h.c.p. $\text{La}$Pr alloys is almost identical to that of $\text{La}$Y and $\text{La}$Lu alloys. This suggests that Pr is in a singlet ground state and that lifetime broadening caused by the 4? electrons of Pr have little effect on the superconducting process in $\text{La}$Pr. The depression of the transition temperature arises largely from pair weakening (or possibly crystal field effects) rather than pair breaking effects.     

Glueballs versus quarkonium-flavor symmetry signatures

Flavor symmetry selection rules provide unambiguous signatures for glueball decays at masses above 1500 MeV where many channels are open. For example, a 2⁺⁺ glueball should decay into ππ, K$\text{K}$, ηη, η'η', ωω, ?? and ψψ, but not into K¹$\text{K}$ nor ηη'. A quarkonium or a four-quark state cannot go into all channels allowed for a glueball; at least one is OZI-forbidden for any choice of flavors. But any quarkonium state that goes to K$\text{K}$ should also go to K¹$\text{K}$ and ηη'. These selection rules are shown to be stable against SU(3) symmetry breaking.     

Moduli stabilization in stringy ISS models

We present a stringy realization of the ISS metastable SUSY breaking model with moduli stabilization. The mass moduli of the ISS model is stabilized by gauging of a U(1)$U(1)$ symmetry and its D-term potential. The SUSY is broken both by F-terms and D-terms. It is possible to obtain de Sitter vacua with a vanishingly small cosmological constant by an appropriate fine-tuning of flux parameters.     

Index theorems and supersymmetry in the soliton sector

For arbitrary two-dimensional supersymmetric theories with soliton solutions, we use the Callias-Bott-Seeley trace theorem to calculate the O(?) correction to the soliton mass. At the same order the Bogomolny bound is shown, by an explicit computation, to be saturated. The non-vanishing of the mass correction is traced to the existence of supersymmetry violating surface terms in the soliton lagrangian, while the saturation of the Bogomolny bound is a consequence of the absence of spontaneous breaking of $\text{N =}\text{1}\text{2}$ supersymmetry in a related lagrangian. We argue that this supersymmetry remains unbroken to all orders in perturbation theory. Topological arguments à la Witten are not able to exclude non-perturbative breaking.     

Features of dynamically broken gauge theories

We discuss several features of dynamical symmetry breaking in gauge theories of strong, weak and electromagnetic interactions. We speculate that in some such theories the fine structure constant calculable. A possible solution of the strong P and T violation problem in QCD by dynamical symmetry breaking is indicated. Self-energy divergences are absent in such models and we compute the finite electromagnetic self-energy of a quark in QCD. The mass hierarchy problem is examined. We find models in which the fermion-gauge boson mass ratio is $\text{M}{}_{\mathrm{<mtext>F</mtext>}}{}^2\text{M}{}_{\mathrm{<mtext>B</mtext>}}{}^2\text{～}\text{exp}$ ($\text{?1}\text{g}{}^2$), where g is a gauge boson coupling, which could account for the origin of weak interactions.     

SU(5) Higgs problem with adjoint + vector representations

Recently Kim has given a general method, using group-invariant orbit parameters, for determining the energy and residual symmetry of the Higgs potential minimum. In this paper we illustrate the method by working out the case of a quartic SU(5) Higgs potential with $\text{5}$ and $\text{24}$ higgsons. In this method the Gell-Mann-Slansky conjecture concerning possible little groups of the potential minimum takes a geometric form, which is verified for our case. The results are used to discuss the hierarchical symmetry breaking of SU(5) grand unification theory. We generalize our results to the SU(N) adjoint + vector models, which are all closely related.     

Gravitational effects on the SU(5) breaking phase transition for a Coleman-Weinberg potential

The gravitational coupling Rφ² plays a crucial role in determining the fate of the symmetric, high temperature state in a graud unified model with Coleman-Weinberg type symmetry breaking. If this term enters in the lagrangian with a negative sign, it drives the SU(5) breaking phase transition at a temperature of about 10¹⁰ GeV. If it enters with a positive sign, and in particular with the coefficient $\text{1}\text{12}$ which is required for a conformally invariant classical theory, this term prevents the phase transition from being completed, at least until temperatures are reached for which the SU(5) coupling becomes large.     

Cosmological constraints on supergravity models

We delineate the domain of supersymmetry breaking parameters in minimal supergravity models for which the cosmological relic photino density is no larger than the closure density. Demanding that the relic density equal the closure density as suggested by inflationary cosmology suggests $\text{m}{}_{\mathrm{<mtext>q</mtext><mtext>?</mtext>}}\text{～ 42}\text{GeV}\text{+ 0.89 m}{}_{\mathrm{<mtext>g</mtext><mtext>?</mtext>}}$. We point out that several supergravity scenarios for the monojet events at the CERN $\text{p}$p Collider would yield a relic density considerably greater than the closure density.