A possible minimal gauge–Higgs unification

A possible minimal model of the gauge–Higgs unification based on the higher dimensional spacetime M ⁴⊗(S ¹/Z ₂) and the bulk gauge symmetry SU(3) _C ⊗SU(3) _W ⊗U(1) _X is constructed in some detail. We argue that the Weinberg angle and the electromagnetic current can be correctly identified if one introduces the extra U(1) _X above and a bulk scalar triplet. The VEV of this scalar as well as the orbifold boundary conditions will break the bulk gauge symmetry down to that of the standard model. A new neutral zero-mode gauge boson Z′ exists that gains mass via this VEV. We propose a simple fermion content that is free from all the anomalies when the extra brane-localized chiral fermions are taken into account as well. The issues on recovering a standard model chiral-fermion spectrum with the masses and flavor mixing are also discussed, where we need to introduce the two other brane scalars which also contribute to the Z′ mass in the similar way as the scalar triplet. The neutrinos can get small masses via a type I seesaw mechanism. In this model, the mass of the Z′ boson and the compactification scale are very constrained being, respectively, given in the ranges: 2.7 TeV<m _Z′<13.6 TeV and 40 TeV<1/R<200 TeV.     

Exceptional Point of the Neutral Heavy Higgs System H2–H3

We study the singularity of the surface that represents the masses of the isolated doublet of heavy, neutral Higgs bosons, H ₂–H ₃, in a toy model based on the MSSM with CP violation, in parameter space. These two heavy, neutral Higgs bosons are coherent and, for large values of the masses, nearly degenerate. In this scenario, mixing between the mass eigenstates of the H ₂–H ₃ system could be very large and exact degeneracy is possible. As function of the Lagrangian parameters, the physical mass of the doublet has an algebraic branch point of rank one at the exceptional point where the two masses are equal. The real and imaginary parts of the masses in the doublet have branch cuts that start at the same branch point but extend in opposite directions in parameter space. Associated with this branch point, the propagator of the mixing doublet of neutral heavy Higgs bosons has a double pole in the complex s-plane of the energy squared. We computed the mass surface of the isolated doublet of H ₂–H ₃ bosons as function of the Lagrangian parameters in the neighbourhood of the exceptional point in a toy model of the system H ₂–H ₃. We also computed the trajectories of the poles of the transition matrix for values of the Lagrangian parameters close to the exceptional point and explained the characteristic change of identity seen in these trajectories in the s-plane as a manifestation of the topology of the two-sheeted mass surfaces in the space of Lagrangian parameters.     

Maximal lensing: mass constraints on point lens configurations

We set constraints and an upper bound on the masses required for a configuration of n point lenses to produce the maximum of 5n − 5 images of a distant source. We show how this result can be used to detect and constrain the mass of planets or brown dwarfs in multiple-star systems.     

Nuclear compressibility and its effect on nuclear binding energies from the study of muonic atoms

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr ₀. It is observed from the behaviour ofr ₀ that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr ₀ is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E _exp−E _cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.     

Moments and Distributions of Trajectories in Slow Random Monads

Given a finite set B (basin) with n>1 elements, which we call points, and a map M:B→B, we call such pairs (B,M) monads. Here we study a class of random monads, where the values of M(⋅) are independently distributed in B as follows: for all a,b∈B the probability of M(a)=a is s and the probability of M(a)=b, where a≠b, is (1−s)/(n−1). Here s is a parameter, 0≤s≤1. We fix a point ⊙∈B and consider the sequence M ^t (⊙), t=0,1,2,… . A point is called visited if it coincides with at least one term of this sequence. A visited point is called recurrent if it appears in this sequence at least twice; if a visited point appears in this sequence only once, it is called transient. We denote by Vis _n , Rec _n and Tra _n the numbers of visited, recurrent and transient points respectively. We prove that, when n tends to infinity, Vis _n and Tra _n converge in law to geometric distributions and Rec _n converges in law to a distribution concentrated at its lowest value, which is one. Now about moments. The case s=1 is trivial, so let 0≤s<1. For any natural number k there is a number such that the k-th moments of Vis _n , Rec _n and Tra _n do not exceed this number for all n. About Vis _n : for any natural k the k-th moment of Vis _n is an increasing function of n. So it has a limit when n→∞ and for all n it is less than this limit. About Rec _n : for any k the k-th moment of Rec _n tends to one when n tends to infinity. About Tra _n : for any k the k-th moment of Tra _n has a limit when n tends to infinity.     

On the masses of elementary particles

We make an attempt to describe the spectrum of masses of elementary particles, as it comes out empirically in six distinct scales. We argue for some rather well defined mass scales, like the electron mass; we elaborate on the assumption that there is a minimum mass associated to any electric charge. Another natural mass scale is Λ = Λ _QCD coming arbitrarily at quantizing a classically conformal SU(3) _c theory. Indeed, some scales of masses will cover also masses of composite particles or mass differences. We extend some plausible arguments for other scales, as binding or self-energy effects of the microscopic forces, plus some speculative uses, here and there, of gravitation. We also consider briefly exotics like supersymmetry and extra dimensions in relation to the mass scale problem, including some mathematical arguments (e.g. triality), which might throw light on the three-generation problem. We also address briefly the issues of dark matter and dark energy.     

The structure of the Yang–Mills spectrum for arbitrary simple gauge algebras

The mass spectrum of pure Yang–Mills theory in 3+1 dimensions is discussed for an arbitrary simple gauge algebra within a quasigluon picture. The general structure of the low-lying gluelump and two-quasigluon glueball spectrum is shown to be common to all algebras, while the lightest C=− three-quasigluon glueballs only exist when the gauge algebra is A _r≥2, that is, in particular, \mathfraksu(N 3 3)\mathfrak{su}(N\geq3). Higher-lying C=− glueballs are shown to exist only for the A _r≥2, D_odd−r≥4 and E₆ gauge algebras. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis and a funnel form; it appears to be gauge-algebra dependent when at least three sources are considered. As a main result, the present framework’s predictions are shown to be consistent with available lattice data in the particular case of an \mathfraksu(N)\mathfrak{su}(N) gauge algebra within ’t Hooft’s large-N limit.     

Improvement of the Applicability, Efficiency, andPrecision of the Penning Trap Mass Spectrometer ISOLTRAP

With the Penning trap mass spectrometer ISOLTRAP, close to 200 nuclides have already been investigated and their masses determined with a typical relative precision of δm/m=10⁻⁷. Recently, ISOLTRAP's beam preparation system was replaced by an RFQ ion beam cooler and buncher. The principle and the characteristics of this new beam preparation system will be presented. It is planned to use ions of various carbon clusters C⁺ _n (n>1) as reference ions for mass measurements. Apart from negligible molecular binding energies, these clusters have masses that are exact multiples of the unified atomic mass unit. This will allow ISOLTRAP to carry out absolute mass measurements as well as to investigate possible mass-dependent systematic errors. The results of tests of the production, transport, and trapping of such carbon clusters will be presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Global strings in extra dimensions: The full map of solutions,matter trapping,and the hierarchy problem

We consider (d ₀ + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d ₀ dimensions, endowed with a warp factor e ^2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l _c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough distances l _c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane, where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading to matter particle mass spectra that seem promising from the standpoint of hierarchy problems. The text was submitted by the authors in English.     

Pseudoscalar meson masses in unitarized chiral perturbation theory

This contribution summarizes the work explained in arXiv:hep-ph/0608290 where we perform a non-perturbative chiral study of the masses of the lightest pseudoscalar mesons. The pseudoscalar self-energies are calculated by the evaluation of the scalar self-energy loops with full S-wave meson-meson amplitudes taken from Unitary Chiral Perturbation Theory (UCHPT). These amplitudes, among other features, contain the lightest nonet of scalar resonances σ, f ₀(980), a ₀(980) and κ. The self-energy loops are regularized by a proper subtraction of the infinities within a dispersion relation formulation of the amplitudes. Values for the bare masses of pions and kaons and the η ₈ mass are obtained. We then match to the self-energies from standard Chiral Perturbation Theory (CHPT) to O(p ⁴) and resum higher orders from our calculated scalar self-energies. The dependence of the self-energies on the quark masses allows a determination of the ratio of the strange-quark mass over the mean of the lightest-quark masses, m _s/ , in terms of the O(p ⁴) CHPT low-energy constant combinations 2L ^r ₈ - L ^r ₅ and 2L ^r ₆ - L ^r ₄. In this way, we give a range for the values of these low-energy counterterms and for 3L ₇ + L ^r ₈, once the η-meson mass is invoked. The low-energy constants are further constraint by performing a fit to the recent MILC lattice data on the pseudoscalar masses, and m _s/ = 25.6±2.5 results. This value is consistent with 24.4±1.5 from CHPT and phenomenology and more marginally with the value 27.4±0.5 obtained from pure perturbative chiral extrapolations of the MILC lattice data to physical values of the lightest-quark masses.     

Hadron spectrum and infrared-finite behavior of QCD running coupling

We study the behavior of the QCD effective coupling α _s in the low-energy region by exploiting the conventional meson spectrum within a relativistic quantum-field model based on analytical confinement of quarks and gluons. The spectra of quark-antiquark and two-gluon bound states are defined by using a master equation similar to the ladder Bethe-Salpeter equation. A new, independent and specific infrared-finite behavior of QCD coupling is found below energy scale ∼1 GeV. Particularly, an infrared-fixed point is extracted at α _s (0) ≅ 0.757 for confinement scale Λ = 345 MeV. We provide a new analytic estimate of the lowest-state glueball mass. As applications, we also estimate masses of some intermediate and heavy mesons as well as the weak-decay constants of light mesons. By introducing only a minimal set of parameters (the quark masses m _f and Λ) we obtain results in reasonable agreement with recent experimental data in a wide range of energy scale ∼0.1–10 GeV. We demonstrate that global properties of some low-energy phenomena may be explained reasonably in the framework of a simple relativistic quantum-field model if one guesses correct symmetry structure of the quark-gluon interaction in the confinement region and uses simple forms of propagators in the hadronisation regime. The model may serve a reasonable framework to describe simultaneously different sectors in low-energy particle physics.     

Persistence of the Feigenbaum Attractor in One-Parameter Families

Consider a map ψ₀ of class C ^r for large r of a manifold of dimension n greater than or equal to 2 having a Feigenbaum attractor. We prove that any such ψ₀ is a point of a local codimension-one manifold of C ^r transformations also exhibiting Feigenbaum attractors. In particular, the attractor persists when perturbing a one-parameter family transversal to that manifold at ψ₀. We also construct such a transversal family for any given ψ₀, and apply this construction to prove a conjecture by J. Palis stating that a map exhibiting a Feigenbaum attractor can be perturbed to obtain homoclinic tangencies. Received: 4 August 1998 / Accepted: 11 May 1999     

Rigorous Scaling Law for the Heat Current in Disordered Harmonic Chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T ₁ and T _n . Let E J _n be the steady-state energy current across the chain, averaged over the masses. We prove that E J _n ~ (T ₁ − T _n )n ^−3/2 in the limit n → ∞, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.     

The ideal polymer chain near planar hard wall beyond the Dirichlet boundary conditions

We present a new ab initio approach to describe the statistical behavior of long ideal polymer chains near a plane hard wall. Forbidding the solid half-space to the polymer explicitly (by the use of Mayer functions) without any other requirement, we derive and solve an exact integral equation for the partition function G _D(r,r′, N) of the ideal chain consisting of N bonds with the ends fixed at the points r and r′ . The expression for G(r,r′, s) is found to be the sum of the commonly accepted Dirichlet result G _D(r,r′, N) = G ₀(r,r′, N) - G ₀(r,r”, N) , where r” is the mirror image of r′ , and a correction. Even though the correction is small for long chains, it provides a non-zero value of the monomer density at the very wall for finite chains, which is consistent with the pressure balance through the depletion layer (so-called wall or contact theorem). A significant correction to the density profile (of magnitude 1/is obtained away from the wall within one coil radius. Implications of the presented approach for other polymer-colloid problems are discussed.     

Nuclear matter properties in relativistic mean-field model with σ- ω coupling

The σ-ω coupling is introduced phenomenologically in the linear σ-ω model to study the nuclear matter properties. It is shown that not only the effective nucleon mass M^* but also the effective σ meson mass m _σ ^* and the effective ω meson mass m _ω ^* are nucleon-density-dependent. When the model parameters are fitted to the nuclear saturation point, with the nuclear radius constant r ₀ = 1.14 fm and volume energy a ₁ = 16.0 MeV, as well as to the effective nucleon mass M ^* = 0.85M, the model yields m _σ ^* = 1.09m _σ and m _ω ^* = 0.90m _ω at the saturation point, and the nuclear incompressibility K ₀ = 501 MeV. The lowest value of K₀ given by this model by adjusting the model parameters is around 227 MeV. Received: 23 March 2001 / Accepted: 8 June 2001     

Laser spectroscopy and mass measurements on alkali isotopes

Isotope shifts, spins, hyperfine structures and masses have been measured for the series of the alkali isotopes including the nuclei far from stability. The method of laser spectroscopy and its combinations with rf excitation are described. Some results are discussed, namely the first observation of the red doublet D₁-D₂ of francium, and the study of shell effects and changes of shape with mass and δ〈r ²〉 measurements for Rb and Na isotopes.     

Embedding of non-simple Lie groups,coupling constant relations and non-uniqueness of models of unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU _L (2) ⇔ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU _L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU _L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin²ϑ=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons likeE ₆, while addition of extra charged fermion singlets can reduce the value of sin² ϑ to 1/4. We point out that at the present time the models of grand unification are far from unique.     

Generic Diffeomorphisms with Superexponential Growth of Number of Periodic Orbits

Let M be a smooth compact manifold of dimension at least 2 and Diff ^r (M) be the space of C ^r smooth diffeomorphisms of M. Associate to each diffeomorphism f;isin; Diff ^r (M) the sequence P _n (f) of the number of isolated periodic points for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms Diff ^r (M) such for a Baire generic diffeomorphism f∈N the number of periodic points P _n f grows with a period n faster than any following sequence of numbers {a _n } _{n ∈ Z +} along a subsequence, i.e. P _n (f)>a _ni for some n _i →∞ with i→∞. In the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth of the number of periodic points is a Newhouse domain. A proof of the man result is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of that theorem is also presented. Received: 27 January 1999 / Accepted: 23 November 1999     

Static charged spheres with anisotropic pressure in general relativity

We report a generalization of our earlier formalism [Pramana, 54, 663 (1998)] to obtain exact solutions of Einstein-Maxwell’s equations for static spheres filled with a charged fluid having anisotropic pressure and of null conductivity. Defining new variables: w=(4π/3)(ρ+ε)r ², u=4πξr ², v _r=4πp _r r ², v _⊥=4πp _⊥ r ²[ρ, ξ(=−(1/2)F ₁₄ F ¹⁴), p _r, p _⊥ being respectively the energy densities of matter and electrostatic fields, radial and transverse fluid pressures whereas ε denotes the eigenvalue of the conformal Weyl tensor and interpreted as the energy density of the free gravitational field], we have recast Einstein’s field equations into a form easy to integrate. Since the system is underdetermined we make the following assumptions to solve the field equations (i) u=v _r=(a ²/2κ)r ⁿ⁺², v _⊥=k ₁ v _r, w=k ₂ v _r; a ², n(>0), k ₁, k ₂ being constants with κ=((k ₁+2)/3+k ₂) and (ii) w+u=(b ²/2)r ⁿ⁺², u=v _r, v _⊥−v _r=k, with b and k as constants. In both cases the field equations are integrated completely. The first solution is regular in the metric as well as physical variables for all values of n>0. Even though the second solution contains terms like k/r ² since Q(0)=0 it is argued that the pressure anisotropy, caused by the electric flux near the centre, can be made to vanish reducing it to the generalized Cooperstock-de la Cruz solution given in [14]. The interior solutions are shown to match with the exterior Reissner-Nordstrom solution over a fixed boundary. Dedicated to Prof. F A E Pirani.