Large Spatial Dimensions Research Articles

Lepton flavor violation in extra dimension models

Models involving large extra spatial dimension(s) have interesting predictions on lepton flavor violating processes. We consider some five-dimensional (5D) models which are related to neutrino mass generation or address the fermion masses hierarchy problem. We study the signatures in low energy experiments that can discriminate the different models. The focus is on muon-electron conversion in nuclei $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ and $\ensuremath{\mu}\ensuremath{\rightarrow}3e$ processes and their $\ensuremath{\tau}$ counterparts. Their links with the active neutrino mass matrix are investigated. We show that in the models we discussed the branching ratio of $\ensuremath{\mu}\ensuremath{\rightarrow}e\ensuremath{\gamma}$ like rare process is much smaller than the ones of $\ensuremath{\mu}\ensuremath{\rightarrow}3e$ like processes. This is in sharp contrast to most of the traditional wisdom based on four-dimensional (4D) gauge models. Moreover, some rare tau decays are more promising than the rare muon decays.

String windings in the early universe

We study string dynamics in the early universe. Our motivation is the proposal ofBrandenberger and Vafa that string winding modes may play a key role in decompactifyingthree spatial dimensions. We model the universe as a homogeneous but anisotropicnine-torus filled with a gas of excited strings. We adopt initial conditions which fix thedilaton and the volume of the torus, but otherwise assume all states are equally likely. Westudy the evolution of the system both analytically and numerically to determine thelate-time behaviour. We find that, although dynamical evolution can indeed leadto three large spatial dimensions, such an outcome is not statistically favoured.

Moduli stabilization with the string Higgs effect

We review the notion of the Higgs effect in the context of string theory. We find that by including this effect in time dependent backgrounds, one is led to a natural mechanism for stabilizing moduli at points of enhanced gauge symmetry. We consider this mechanism for the case of the radion (size of the extra dimensions) and find that as decompactification of the large spatial dimensions takes place the radion will remain stabilized at the self-dual radius. We discuss how this mechanism can be incorporated into models of string cosmology and brane inflation to resolve some outstanding problems. We also address some issues regarding which string states should be included when constructing low energy actions in string cosmology.

Inflation and brane gases

We investigate a new way of realizing a period of cosmological inflation in the context of brane gas cosmology. It is argued that a gas of co-dimension one branes, out of thermal equilibrium with the rest of the matter, has an equation of state which can - after stabilization of the dilaton - lead to power-law inflation of the bulk. The most promising implementation of this mechanism might be in Type IIB superstring theory, with inflation of the three large spatial dimensions triggered by ``stabilized embedded 2-branes''. Possible applications and problems with this proposal are discussed.

Late-time dynamics of brane gas cosmology

Brane gas cosmology is a scenario inspired by string theory which proposes a simple resolution to the initial singularity problem and gives a dynamical explanation for the number of spatial dimensions of our universe. In this work we have studied analytically and numerically the late-time behaviour of these type of cosmologies taking a proper care of the annihilation of winding modes. This has help us to clarify and extend several aspects of their dynamics. We have found that the decay of winding states into non-winding states behaving like a gas of ordinary non-relativistic particles precludes the existence of a late expansion phase of the universe and obstructs the growth of three large spatial dimensions as we observe today. We propose a generic solution to this problem by considering the dynamics of a gas of non-static branes. We have also obtained a simple criterion on the initial conditions to ensure the small string coupling approximation along the whole dynamical evolution, and consequently, the consistency of an effective low-energy description. Finally, we have reexamined the general conditions for a loitering period in the evolution of the universe which could serve as a mechanism to resolve the {\sl brane problem} - a problem equivalent to the {\sl domain wall problem} in standard cosmology - and discussed the scaling properties of a self-interacting network of winding modes taking into account the effects of the dilaton dynamics.

Exact dynamical mean-field theory of the Falicov-Kimball model

The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions which provides an interesting benchmark for the physics of locally correlated systems. In this review, we develop the formalism for solving the Falicov-Kimball model from a path-integral perspective, and provide a number of expressions for single and two-particle properties. We examine many important theoretical results that show the absence of fermi-liquid features and provide a detailed description of the static and dynamic correlation functions and of transport properties. The parameter space is rich and one finds a variety of many-body features like metal-insulator transitions, classical valence fluctuating transitions, metamagnetic transitions, charge density wave order-disorder transitions, and phase separation. At the same time, a number of experimental systems have been discovered that show anomalies related to Falicov-Kimball physics [including YbInCu4, EuNi2(Si[1-x]Gex)2, NiI2 and TaxN].

B→Xs+missing energy in models with large extra dimensions

We study the neutral current flavour changing rare decay mode $B\to X_s +$ missing energy within the framework of theories with large extra spatial dimensions. The corresponding Standard Model signature is $B\to X_s + \nu \bar{\nu}$. But in theories with large extra dimensions, it is possible to have scalars and gravitons in the final state making it quite distinct from any other scenario where there are no gravitons and the scalars are far too heavier than the B-meson to be present as external particles. We give an estimate of the branching ratio for such processes for different values of the number of extra dimensions and the effective scale of the effective theory.

New exact solutions for polynomial oscillators in large dimensions

A new type of exact solvability is reported. The Schrodinger equation is considered in a very large spatial dimension D 1 and its central polynomial potential is allowed to depend on 'many' ( = 2q) coupling constants. In a search for its bound states possessing an exact and elementary wavefunction ψ (proportional to a harmonic-oscillator-like polynomial of a freely varying, i.e., not just small, degree N), the 'solvability conditions' are known to form a complicated nonlinear set which requires a purely numerical treatment at a generic choice of D, q and N. Assuming that D is large we discovered and demonstrate that this problem may be completely factorized and acquires an amazingly simple exact solution at all N and up to q = 5 at least.

Isotropization in brane gas cosmology

Brane Gas Cosmology (BGC) is an approach to unifying string theory and cosmology in which matter is described by a gas of strings and branes in a dilaton gravity background. The Universe is assumed to start out with all spatial dimensions compact and small. It has previously been shown that in this context, in the approximation of neglecting inhomogeneities and anisotropies, there is a dynamical mechanism which allows only three spatial dimensions to become large. However, previous studies do not lead to any conclusions concerning the isotropy or anisotropy of these three large spatial dimensions. Here, we generalize the equations of BGC to the anisotropic case, and find that isotropization is a natural consequence of the dynamics.

Landau-Gutzwiller quasiparticles

We define Landau quasi-particles within the Gutzwiller variational theory, and derive their dispersion relation for general multi-band Hubbard models in the limit of large spatial dimensions D. Thereby we reproduce our previous calculations which were based on a phenomenological effective single-particle Hamiltonian. For the one-band Hubbard model we calculate the first-order corrections in 1/D and find that the corrections to the quasi-particle dispersions are small in three dimensions. They may be largely absorbed in a rescaling of the total band width, unless the system is close to half band filling. Therefore, the Gutzwiller theory in the limit of large dimensions provides quasi-particle bands which are suitable for a comparison with real, three-dimensional Fermi liquids.

Searching for complex CA rules with GAs

AbstractAn important problem in the theory of cellular automata (CA) is the research of complex rules, the parameterization of the rule space, and the description of the CA dynamic behavior. In this article, the authors used evolutionary techniques in the search of CA with specific characteristics, in order to understand how their data are related to the previous findings in this sector. Using as fitness function, the variance of the input‐entropy, a genetic algorithm was built to search complex rules for multistate CA. The algorithm used is efficient and many complex rules have been found. Many of these rules present interesting characteristics. Gliders with large period and large spatial dimensions may be observed. The experiments performed show that complex rules have several λ values, which do not reside in a sharply defined region; on the contrary, these values are extended on very large regions of the λ parameter. The results provide also a view of the CA rule space. © 2003 Wiley Periodicals, Inc.

Limits on extra dimensions and new particle production in the exclusive photon and missing energy signature in pp collisions at square root [s]=1.8 TeV.

The exclusive gammaE(T) signal has a small standard model cross section and is thus a channel sensitive to new physics. This signature is predicted by models with a superlight gravitino or with large extra spatial dimensions. We search for such signals at the Collider Detector at Fermilab, using 87 pb(-1) of data at square root [s]=1.8 TeV, and extract 95% C.L. limits on these processes. A limit of 221 GeV is set on the scale |F|(1/2) in supersymmetric models. For 4, 6, and 8 extra dimensions, model-dependent limits on the fundamental mass scale M(D) of 0.55, 0.58, and 0.60 TeV, respectively, are found. We also specify a "pseudo-model-independent" method of comparing the results to theoretical predictions.

Cosmological string gas on orbifolds

It has long been known that strings wound around incontractible cycles can play a vital role in cosmology. In particular, in a spacetime with toroidal spatial hypersurfaces, the dynamics of the winding modes may help yield three large spatial dimensions. However, toroidal compactifications are phenomenologically unrealistic. In this paper we therefore take a first step toward extending these cosmological considerations to $D$-dimensional toroidal orbifolds. We use numerical simulation to study the timescales over which "pseudo-wound" strings unwind on these orbifolds with trivial fundamental group. We show that pseudo-wound strings can persist for many ``Hubble times'' in some of these spaces, suggesting that they may affect the dynamics in the same way as genuinely wound strings. We also outline some possible extensions that include higher-dimensional wrapped branes.

Reproduction of a given particle distribution by means of scanner

An analytical solution of the problem obtaining a given one-dimensional particle intensity distribution behind scanner has been demonstrated. The role is assessed of some side effects which one can compensate standing on the present results. The achieved results demonstrate the resources of dipole magnet with uniform field which competes with magnetic lenses of high order. The potential use is the effective uniform processing of large spatial dimension products.

Baryogenesis in theories with large extra spatial dimensions

We describe a simple and predictive scenario for baryogenesis in theories with large extra dimensions which resembles Affleck–Dine baryogenesis. The Affleck–Dine field is a complex scalar field carrying a U(1) χ charge which is dynamically broken after the end of inflation. This generates an excess of χ over χ ̄ , which then decays into Standard Model fermions to produce an excess of baryons over antibaryons. Our model is very constrained because the Affleck–Dine field has to be sufficiently flat during inflation. It is also a source for density fluctuations which can be tested in the coming satellite and balloon experiments.

Search for Large Extra Dimensions Using the DØ detector

We have searched for the effects of Kaluza Klein gravitons predicted in theories of large spatial extra dimensions (LED). Analyzing angular and invariant mass distributions of photon and electron pairs in 127 pb -1 of data, we find complete agreement with expectations from the Standard Model. There were no anomalous events found that are characteristic of virtual graviton exchange. We set lower limits on the compactification scale of large extra dimensions between 1.0 and 1.4 TeV for the number of extra dimensions between 2 and 7.

Spin-waves in itinerant ferromagnets

We introduce a novel approach for the investigation of spin-wave excitations in itinerant ferromagnets. Our theory is based on a variational treatment of general multi-band Hubbard models which describe elements and compounds of transition metals. The magnon dispersion is derived approximately as the energy of a variational spin-wave state in the limit of large spatial dimensions. A numerical evaluation of our results is feasible for general multi-band models. As a first application we consider a model with two degenerate orbitals per lattice site. From our results we can conclude that spin-wave excitations in strong itinerant ferromagnets are very similar to those in ferromagnetic spin systems.

Search for large extra dimensions in dielectron and diphoton production.

We report a search for effects of large extra spatial dimensions in pp collisions at a center-of-mass energy of 1.8 TeV with the D0 detector, using events containing a pair of electrons or photons. The data are in good agreement with the expected background and do not exhibit evidence for large extra dimensions. We set the most restrictive lower limits to date, at the 95% C.L. on the effective Planck scale between 1.0 and 1.4 TeV for several formalisms and numbers of extra dimensions.

Toy model for the mean-field theory of hard-sphere liquids

We investigate a toy model of liquid, based on simplified hypernetted chain equations in very large spatial dimension D. The model does not exhibit a phase transition, but several regimes of behavior when D-->infinity can be observed in different intervals of the density.

Phase separation and the segregation principle in the infinite-Uspinless Falicov-Kimball model

The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions contain both second-order phase transitions and first-order phase transitions (that involve phase separation or segregation) which are likely to illustrate the precursor physics behind the static charge-stripe ordering in cuprate systems. In addition, we find that the spinodal-decomposition temperature satisfies an approximate scaling law.