Fine-tuning Problem Research Articles

Erratum: Neutron and electron electric dipole moment inN=1supergravity unification [Phys. Rev. D57, 478 (1998)

An analysis of the neutron EDM and of the electron EDM in minimal N=1 supergravity unification with two CP violating phases is given. For the neutron the analysis includes the complete one loop gluino, chargino, and neutralino exchange diagrams for the electric dipole and the chromoelectric dipole operators, and also the contribution of the purely gluonic dimension six operator. It is shown that there exist significant regions in the six dimensional parameter space of the model where cancellations between the gluino and the chargino exchanges reduce the electric and the chromoelectric contributions, and further cancellations among the electric, the chromoelectric, and the purely gluonic parts lead to a dramatic lowering of the neutron EDM sometimes below the electron EDM value. This phenomenon gives a new mechanism, i.e., that of internal cancellations, for the suppression of the neutron EDM in supersymmetric theories. The cancellation mechanism can significantly reduce the severe fine tuning problem associated with CP violating phases in SUSY and SUGRA unified models.

EXACT RENORMALIZATION GROUP EQUATION FOR SU(2) GAUGE FIELDS INTERACTING WITH MASSIVE FERMIONS

We show an application of the Wilson renormalization group (RG) method to a SU(2) gauge field theory in interaction with a massive fermion doublet. We succeed in implementing the local gauge symmetry up to one loop by choosing suitable boundary conditions to the RG equation: we require the relevant monomials not present in the classical action to satisfy the Slavnov–Taylor identities once the cutoffs are removed. In this way the so called fine-tuning problem, due to the assignation of boundary conditions in terms of the bare parameters, is avoided. In this framework, loop expansion is equivalent to the iterative solution of the RG equation; one loop calculations are performed in order to determine whether and, if so, how much the fermionic matter modifies the infrared and ultraviolet asymptotic form of the couplings. The analysis of the infrared behavior allows to verify the regularity of the Λ-flow equation at Λ=0. Then we compute the β-function and we check gluon transversality. Finally, we outline a proof of perturbative renormalizability.

Cosmological fine tuning, supersymmetry and the gauge hierarchy problem

We study the extent to which the cosmological fine-tuning problem – why the relic density of neutralino cold dark matter particles χ is similar to that of baryons – is related to the fine-tuning aspect of the gauge hierarchy problem – how one arranges that M W ≪ M P without unnatural choices of MSSM parameters. Working in the minimal supergravity framework with universal soft supersymmetry-breaking parameters as inputs, we find that the hierarchical fine tuning is minimized for Ω χh 2∼0.1 . Conversely, imposing Ω χh 2<1 does not require small hierarchical fine tuning, but the exceptions to this rule are rather special, with parameters chosen such that m χ ∼ M Z /2 or M h /2, or else m χ ≳ m t . In the first two cases, neutralino annihilation receives a large contribution from a direct-channel pole, whereas in the third case it is enhanced by the large top Yukawa coupling.

Fine Tuning of Rational B-Spline Motions

This paper presents two algorithms for fine-tuning rational B-spline motions suitable for Computer Aided Design. The problem of fine-tuning of rational motions is studied as that of fine-tuning rational curves in a projective dual three-space, called the image curves. The path-smoothing algorithm automatically detects and smoothes out the third order geometric discontinuities in the path of a cubic rational B-spline image curve. The speed-smoothing algorithm uses a quintic rational spline image curve to obtain a second-order geometric approximation of the path of a cubic rational B-spline image curve while allowing specification of the speed and the rate of change of speed at the key points to obtain a near constant kinetic energy parameterization. The results have applications in Cartesian trajectory planning in robotics, spatial navigation in visualization and virtual reality systems, as well as mechanical system simulation.

Testing the Dark Matter Hypothesis with Low Surface Brightness Galaxies and Other Evidence

The severity of the mass discrepancy in spiral galaxies is strongly correlated with the central surface brightness of the disk. Progressively lower surface brightness galaxies have ever larger mass discrepancies. No other parameter (luminosity, size, velocity, morphology) is so well correlated with the magnitude of the mass deficit. The rotation curves of low surface brightness disks thus provide a unique data set with which to probe the dark matter distribution in galaxies. The mass discrepancy is apparent from $R = 0$ giving a nearly direct map of the halo mass distribution. The luminous mass is insignificant. Interpreting the data in terms of dark matter leads to troublesome fine-tuning problems. Different observations require contradictory amounts of dark matter. Structure formation theories are as yet far from able to explain the observations.

Neutron and electron electric dipole moment inN=1supergravity unification

An analysis of the neutron EDM and of the electron EDM in minimal $N=1$ supergravity unification with two $\mathrm{CP}$-violating phases is given. For the neutron the analysis includes the complete one loop gluino, chargino, and neutralino exchange diagrams for the electric dipole and the chromoelectric dipole operators, and also the contribution of the purely gluonic dimension-six operator. It is shown that there exist significant regions in the six-dimensional parameter space of the model where cancellations between the gluino and the chargino exchanges reduce the electric and the chromoelectric contributions, and further cancellations among the electric, the chromoelectric, and the purely gluonic parts lead to a dramatic lowering of the neutron EDM sometimes below the electron EDM value. This phenomenon gives a new mechanism, i.e., that of internal cancellations, for the suppression of the neutron EDM in supersymmetric theories. The cancellation mechanism can significantly reduce the severe fine-tuning problem associated with $\mathrm{CP}$-violating phases in SUSY and SUGRA unified models.

The fine tuning problem in pre-big-bang inflation

We examine the effect of spatial curvature in the pre-big-bang inflationary model suggested by string theory. We study $O(\alpha ')$ corrections and we show that, independently of the initial curvature, they lead to a phase of exponential inflation. The amount of inflation in this phase is long enough to solve the horizon and flatness problems if the evolution starts deeply into the weak coupling regime. There is a region of the parameter space of the model where such a long inflationary phase at the string scale is consistent with COBE anisotropies, millisecond pulsar timing and nucleosynthesis constraints. We discuss implications for the spectrum of relic gravitational waves at the frequencies of LIGO and Virgo.

Improving the fine tuning in models of low energy gauge mediated supersymmetry breaking

The fine tuning in models of low energy gauge mediated supersymmetry breaking required to btain the correct Z mass is quantified. To alleviate the fine tuning problem, a model with split ( 5 + 5 ) messenger fields is presented. This model has additional triplets in the low energy theory which get a mass of O(500) GeV from a coupling to a singlet. The improvement in fine tuning is quantified and the spectrum in this model is discussed. The same model with the above singlet coupled to the Higgs doublets to generate the μ term is also discussed. A Grand Unified version of the model is constructed and a known doublet-triplet splitting mechanism is used to split the messenger (5 + 5)' s . A complete model is presented and some phenomenological constraints are discussed.

Inflation and the fine-tuning problem

I describe a recently derived stochastic approach to inflaton dynamics which can address some serious problems associated with conventional inflationary theory. Using this theory I derive an exact solution to the stochastic dynamics for the case of a $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ potential and use it to study the generated primordial density fluctuations. It is found that on both subhorizon and superhorizon scales the theory predicts Gaussian fluctuations to a very high accuracy along with a near-scale-invariant spectrum. Of most interest is that the amplitude constraint is found to be satisfied for $\ensuremath{\lambda}\ensuremath{\sim}{10}^{\ensuremath{-}5}$ rather than for $\ensuremath{\lambda}\ensuremath{\sim}{10}^{\ensuremath{-}14}$ of the conventional theory. This represents a dramatic easing of the fine-tuning constraints, a feature likely to generalize to a wide range of potentials.

Phenomenology of a Supersymmetric Model for Fermion Mass Hierarchy

Some phenomenological aspects of a supersymmetric model for fermion mass hierarchy proposed previously are discussed. It is required that the lepton universality violation is near to its current experimental bound. The lepton number violation decay modes τ→2eμ and 3μ maybe observable in the near future. The Majorana mass of electron-neutrino is predicted to be about 0.1 eV. The fine-tuning problem is discussed.

On the observability of Majoron emitting double beta decays

Because of the fine-tuning problem in classical Majoron models in recent years several new models were invented. It is pointed out that double beta decays with new Majoron emission depend on new matrix elements, which have not been considered in the literature. A calculation of these matrix elements and phase space integrals is presented. We find that for new Majoron models extremely small decay rates are expected.

Taming the scalar mass problem with a singlet Higgs boson.

We investigate the fine-tuning problem in the standard model and show that Higgs boson and top quark masses consistent with current experimental bounds cannot be obtained unless one extends the particle spectrum. A minimal extension which achieves this involves the addition of a singlet real scalar but this model is not very predictive. With a discrete symmetry and the further addition of one generation of vectorlike fermions one can get a solution which leads to a phenomenologically viable prediction for the mass of the standard model Higgs boson. \textcopyright{} 1996 The American Physical Society.

The mass spectrum in a model with calculable dynamical supersymmetry breaking

Models with dynamical supersymmetry breaking are interesting because they may provide a solution to both the gauge hierarchy and the fine-tuning problems. However, because of strongly interacting dynamics, it is in general impossible to analyze them quantitatively. One of the few models with calculable dynamical supersymmetry breaking is a model with SU (5) gauge symmetry and two 10's and two 5 's as the matter content. We determine the ground state of this model, find the vaccum energy, reveal the symmetry breaking pattern and calculate the mass spectrum. The supertrace mass relation is exploited to verify the consistency of the calculated mass spectrum, and an accidental degeneracy is explained.

Gravitational Lensing Limits on Cold Dark Matter and Its Variants

view Abstract Citations (95) References (70) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Gravitational Lensing Limits on Cold Dark Matter and Its Variants Kochanek, Christopher S. Abstract Standard Ω0 = 1 cold dark matter (CDM) needs 0.27 < σ8 < 0.63 (2 σ) to fit the observed number of large separation lenses, and the constraint is nearly independent of H0 = 100 h km s-1 Mpc-1. This range is strongly inconsistent with the COBE estimate of 8 = (2.8±0:2)h. Tilting the primordial spectrum ∝ kn from n = 1 to 0.3 ≲ n ≲ 0.7, using an effective Hubble constant of 0.15 ≲ Γ = h ≲ 0.30, or reducing the matter density to 0.15 ≲ Ω0h ≲ 0.3 either with no cosmological constant (λ0 = 0) or in a flat universe with a cosmological constant (Ω0 + λ0 = 1), can bring the lensing estimate of σ8 into agreement with the COBE estimates. The models and values for σ8 consistent with both lensing and COBE match the estimates from the local number density of clusters and correlation functions. The conclusions are insensitive to systematic errors except for the assumption that cluster core radii are singular. If clusters with ρ ∝ (r2 + s2)-1 have core radii exceeding S = 15h-1σ23 kpc for a cluster with velocity dispersion σ = 103σ3 km s-1, then the estimates are invalid. There is, however, a fine-tuning problem in making the cluster core radii large enough to invalidate the estimates of σ8 while producing several lenses that do not have central or "odd images." The estimated completeness of the current samples of lenses larger than 5".0 is 20%, because neither quasar surveys nor lens surveys are optimized to find this class of lenses. Publication: The Astrophysical Journal Pub Date: November 1995 DOI: 10.1086/176417 arXiv: arXiv:astro-ph/9411082 Bibcode: 1995ApJ...453..545K Keywords: COSMOLOGY: GRAVITATIONAL LENSING; COSMOLOGY: THEORY; COSMOLOGY: DARK MATTER; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE; Astrophysics E-Print: 27 pages, uuencoded compressed postscript file including figures full text sources arXiv | ADS | data products SIMBAD (9) NED (8)

A fine tuning method for fuzzy logic rule bases

Abstract The problem of fine tuning the rule base of a fuzzy system is addressed in this paper. A method is proposed that treats the rule base of the fuzzy system as a multivariate function and performs parameter optimization to approach the desired rule base output with the given set of rules. The method is explained in detail and an application of it on two different rule bases is presented. This work is part of a research effort in robotic precision assembly using fuzzy logic.

Renormalization group flow for SU(2) Yang-Mills theory and gauge invariance

We study the formulation of the Wilson renormalization group (RG) method for a non-abelian gauge theory. We analyze the simple case of SU(2) and show that the local gauge symmetry can be implemented by suitable boundary conditions for the RG flow. Namely we require that the relevant couplings present in the physical effective action, i.e. the coefficients of the field monomials with dimension not larger than four, are fixed to satisfy the Slavnov-Taylor identities. The full action obtained from the RG equation should then satisfy the same identities. This procedure is similar to the one we used in QED. In this way we avoid the conspicuous fine tuning problem which arises if one gives instead the couplings of the bare lagrangian. To show the practical character of this formulation we deduce the perturbative expansion for the vertex functions in terms of the physical coupling g at the subtraction point μ and perform one-loop calculations. In particular we analyze to this order some ST identities and compute the nine bare couplings. We give a schematic proof of perturbative renormalizability.

Top condensation without fine-tuning

Quadratic divergencies which lead to the usual fine-tuning or hierarchy problem are discussed in top condensation models. As in the Standard Model a cancellation of quadratic divergencies is not possible without the boson contributions in the radiative corrections which are absent in lowest order of an 1 N c -expansion. To deal with the cancellation of quadratic divergencies we propose therefore an expansion in the flavor degrees of freedom. In leading order we find the remarkable result that quadratic divergencies automatically disappear.

One-loop analysis of the electroweak breaking in supersymmetric models and the fine-tuning problem

We examine the electroweak breaking mechanism in the minimal supersymmetric standard model (MSSM) using the complete one-loop effective potential V1. First, we study what is the region of the whole MSSM parameter space (i.e. M12, m0, μ, …) that leads to a successful SU(2) × U(1) breaking with an acceptable top-quark mass. In doing this it is observed that all the one-loop corrections to V1 (even the apparently small ones) must be taken into account in order to obtain reliable results. We find that the allowed region of parameters is considerably enhanced with respect to former “improved” tree-level results. Next, we study the fine-tuning problem associated with the high sensitivity of Mz to ht (the top Yukawa coupling). Again, we find that this fine-tuning, once the one-loop effects are considered, is appreciably smaller than in previous tree-level calculations. Finally, we explore the ambiguities and limitations of the ordinary criterion to estimate the degree of fine-tuning. As a result of all this, the upper bounds on the MSSM parameters, and hence on the supersymmetric masses, are substantially raised, thus increasing the consistency between supersymmetry and observation.

Quantum decay of a de Sitter universe and inflation without fine-tuning in 1+1 dimensions.

The problem of back reaction is investigated in a model of evolving de Sitter spacetime. It is shown in the leading semiclassical approximation to a dilaton gravity theory that a quantum correction gives rise to a decay of a de Sitter spacetime without encountering a curvature singularity. As an application this model may serve as a prototype of the inflationary scenario followed by a hot big bang free from the fine-tuning problem of a cosmological constant.

Effective Four-Fermion Interactions and Dynamical Breaking of Electroweak Symmetry11The project supported partially by the Grant LWTZ-1298 of Chinese Academy of Sciences and by National Natural Science Foundation of China.

The minimal dynamical breaking scheme of the electroweak group based on the Nambu-Jona-Lasinio mechanism is expounded in the bubble approximation for the case with one generation of fermions. The configurations of allowed composite Higgs and Goldstone bosons depend on the ratio between the two independent four-fermion coupling constants and can be simply read out from the four-fermion Lagrangian. The Higgs boson mass is restricted between the double mass of the lighter and the heavier flavor of the fermions. The implication of many-generation extension of the approach for the fine-tuning problem is conceived.