The maximum number of elementary particles in a super symmetric extension of the standard model

In a series of papers over the last few years El Naschie addressed the question of the minimum and maximum number of elementary particles which a mathematically consistent and a physically meaning full extended standard model should contain. El Naschie’s minimum is 62 particles namely 60 believed to have been already discovered in addition to one Higgs boson and one graviton which are theoretically needed but are not jet experimentally conformed. By contrast the maximum number of 69 particles is although consistent with many quantum field theories based models as well as a classical result by Dyson may not be the only possibility. In the present work we show that a larger number of 72 or even 84 particles are easily shown to be consistent with super string theory and super symmetry. Our work consists of two parts. The first part is a reappraisal of El Naschie’s results and the second is a derivation of the proposed possibility of an upper bound of 72 or 84 elementary particles.     

Light cone quantization, Heterotic strings and E–infinity derivation of the number of Higgs bosons

Using light cone quantization as well as a variety of super and Heterotic string theories in conjunction with E–infinity theory we show that while a minimum of one Higgs particle is absolutely necessary for a consistent standard model of elementary particles, the number could be as large as 12 particles and include one or more graviton.     

Different Higgs models and the number of Higgs particles

In this short paper we discuss some interesting Higgs models. It is concluded that the most likely scheme for the Higgs particles consists of five physical Higgs particles. These are two charged H⁺, H⁻ and three neutrals h⁰, H⁰, A⁰. Further more the most probably total number of elementary particles for each model is calculated [El Naschie MS. Experimental and theoretical arguments for the number of the mass of the Higgs particles. Chaos, Solitons & Fractals 2005;23:1091–8; El Naschie MS. Determining the mass of the Higgs and the electroweak bosons. Chaos, Solitons & Fractals 2005;24:899–905; El Naschie MS. On 366 kissing spheres in 10 dimensions, 528 P-Brane states in 11 dimensions and the 60 elementary particles of the standard model. Chaos, Solitons & Fractals 2005;24:447–57].     

Gravitational instanton in Hilbert space and the mass of high energy elementary particles

While the theory of relativity was formulated in real spacetime geometry, the exact formulation of quantum mechanics is in a mathematical construction called Hilbert space. For this reason transferring a solution of Einstein’s field equation to a quantum gravity Hilbert space is far of being a trivial problem.

On the other hand ^(∞) spacetime which is assumed to be real is applicable to both, relativity theory and quantum mechanics. Consequently, one may expect that a solution of Einstein’s equation could be interpreted more smoothly at the quantum resolution using the Cantorian ^(∞) theory.

In the present paper we will attempt to implement the above strategy to study the Eguchi–Hanson gravitational instanton solution and its interpretation by ‘t Hooft in the context of quantum gravity Hilbert space as an event and a possible solitonic “extended” particle. Subsequently we do not only reproduce the result of ‘t Hooft but also find the mass of a fundamental “exotic” symplictic-transfinite particle m1.8 MeV as well as the mass M_x and M (Planck) which are believed to determine the GUT and the total unification of all fundamental interactions respectively. This may be seen as a further confirmation to an argument which we put forward in various previous publications in favour of an alternative mass acquisition mechanism based on unification and duality considerations. Thus even in case that we never find the Higgs particle experimentally, the standard model would remain substantially intact as we can appeal to tunnelling and unification arguments to explain the mass. In fact a minority opinion at present is that finding the Higgs particle is not a final conclusive argument since one could ask further how the Higgs particle came to its mass which necessitates a second Higgs field. By contrast the present argument could be viewed as an ultimate theory based on the existence of a “super” force, beyond which nothing else exists.     

Periodic Solutions of the Abelian Higgs Model and Rigid Rotation of Vortices

The metric and potential energy on the reduced moduli space of selfdual vortices in the Abelian Higgs model on are computed in a certain limit, first identified by Bradlow. In this limit it is proved that the Higgs field is asymptotic to a standard holomorphic section. These results are then used to prove a theorem asserting the existence of time-periodic solutions of the Abelian Higgs model on which represent two vortices in rigid rotation about one another. The theorem answers affirmatively the question, raised by Jaffe and Taubes, of whether a balance between the inter-vortex attraction and the centrifugal repulsion provides for the existence of such solutions (as it does in the classical two body problem for point particles.) The starting point of the analysis is the adiabatic limit system, i.e. the Hamiltonian system defined by restricting the Abelian Higgs model to the moduli space of self-dual vortices. The Hamiltonian consists of a potential energy term and kinetic energy term which is given by the metric on the moduli space induced from . It is shown under two assumptions on the metric and potential energy that the adiabatic limit system admits periodic solutions of the required type. Periodic solutions to the full system are then obtained by an application of the implicit function theorem. Explicit examples where the assumptions on the adiabatic limit system hold are provided by the computations of the metric and potential in the Bradlow limit. Submitted: March 1998.     

Determining the number of Higgs particles starting from general relativity and various other field theories

The Riemann–Einstein tensor of general relativity as well as chiral and super-symmetry are utilized to develop various extended versions of the standard model of high energy physics.Based on these models, it is possible to predict that few new elementary particles conjectured to be the Higgs are likely to be found experimentally at an energy scale which is just above that of the electroweak. Connections to the massless states of different super-string theories as well as super-gravity are also discussed.     

On Pauli’s principles of “Zweiteilung und symmetrie verminderung” in Higgs physics and non-linear dynamics

Pauli’s principle of bi-division and symmetry reduction “Zweiteilung und symmetrie verminderung” is generalized to cover maximally symmetric spaces specified by Killing’s vector fields and its successive symmetry breaking to yield the particles of the standard model of high energy physics.An analogous picture borrowed from non-linear dynamics and complexity theory will be used to illustrate the conceptual aspect of the procedure from which one could infer, the existence not only of one, but several Higgs particles, possibly three neutral and two charged Higgs with masses not that far from the presently accessible electro-weak energy scale. A tree level estimation with one Higgs to approximate the mass was found to give m_H ≃ 162 Gev.     

Gauge anomalies,SU(N) irreducible representation and the number of elementary particles of a minimally extended standard model

By looking carefully at the adjoint representation of the SU(N) Lie group as well as the tensor representation of the same, relationships are found from which one can determine the number of Goldstone particles. Subsequently the number of elementary particles missing from the standard model are conjectured.     

Two-Higgs Doublet Model from Quasilocal Quark Interactions

Quark models with four-fermion interaction including derivatives of fields in the strong coupling regime are used to implement composite-Higgs extensions of the standard model. In this approach, the dynamical breaking of chiral symmetry occurs in two (or more) channels (near polycritical values for coupling constants), which gives rise to two (or more) composite Higgs doublets. Two types of models are built for which the flavor-changing neutral currents (FCNC) are naturally suppressed. In model I, the second Higgs doublet is regarded as a radial excitation of the first one. In model II, at low energies, the quasilocal Yukawa interaction with Higgs doublets reduces to a conventional local one where each Higgs doublet couples to a definite charge current and its vacuum expectation value brings the mass either to up- or to down-components of fermion doublets. For a special configuration of four-fermion coupling constants, the dynamical CP-violation in the Higgs sector appears as a result of complexity of the the vacuum expectation value (v.e.v.) for Higgs doublets. Bibliography: 32 titles.     

The standard model physical degrees of freedom interpretation of the electromagnetic fine structure coupling

The present short note gives for the first time a derivation of the inverse electromagnetic fine structure constant from the elementary particles content of the standard model plus graviton and the Higgs. It is the first derivation ever to interpret as the familiar N_f = (2)(48) = 96 Fermions and N_B = (2)(15) = 30 Bosons of the standard model plus the eleven dimensions D = 11 of super gravity spacetime . The exact theoretical value 137.082039325 and the accurate experimental results are also given clear mathematical derivation showing that all of the 137 and not only the 96 + 30 = 126 may be interpreted as physical particles so that in a sense elementary particles create and span spacetime.     

Massless Elementary Particles in a Quantum Theory over a Galois Field

We consider massless elementary particles in a quantum theory based on a Galois field (GFQT). We previously showed that the theory has a new symmetry between particles and antiparticles, which has no analogue in the standard approach. We now prove that the symmetry is compatible with all operators describing massless particles. Consequently, massless elementary particles can have only half-integer spin (in conventional units), and the existence of massless neutral elementary particles is incompatible with the spin–statistics theorem. In particular, this implies that the photon and the graviton in the GFQT can only be composite particles.     

Logunov's RTG in the Light of the Affine Connection Geometry

We study Logunov's theory of gravity from the standpoint of the affine connection geometry. Using the Lagrange–Hilbert variational method, we conclude that if a background metric can be introduced effectively, then the graviton mass must not be zero, but if the graviton mass is zero, then only the Christoffel connection is effective in the background metric.     

The elementary particles content of quantum spacetime via Feynman graphs and higher dimensional polytops

A fuzzy version of a great icosahedra-like platonic solid is used in conjunction with a Feynman diagram-polyhedron analogy to determine the number of elementary particles in the standard model of high energy physics which we define as a sub Yang–Mills model.     

Number of elementary particles using exceptional Lie symmetry groups hierarchy

This paper suggests several approaches to predict the number of elementary particles via a remarkable finite exceptional Lie symmetry groups hierarchy. This result confirms the earlier finding namely that nine elementary particles are still missing from the standard model.     

Supergravity and the number of fundamental particles in the standard model

Unification of the fundamental forces via supersymmetry is shown to yield valuable information about the number of particles and that of the Higgs particles which we could still discover experimentally within a reasonable distance from the electroweak energy scale.     

Motion of a massive particle in the vicinity of a singular sphere

In the relativistic theory of gravity, motion of a massive particle in the vicinity of the singularity of a static, spherically symmetric metric is studied. It is shown that the existence of the mass of the graviton leads to appearance of qualitatively new trajectories of massive particles. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 112, No. 2, pp. 337–352, August, 1997.     

λφ4model and Higgs mass in standard model calculated by Gaussian effective potential approach with a new regularization-renormalization method

Based on a new regularization-renormalization method, the λφ⁴ model used in standard model (SM) is studied both perturbatively and nonperturbatively by Gaussian effective potential (GEP). The invariant property of two mass scales is stressed and the existence of a (Landau) pole is emphasized. Then after coupling with theSU(2) ×U(1) gauge fields, the Higgs mass in standard model (SM) can be calculated to bem _H≈138 GeV. The critical temperature (T _c ) for restoration of symmetry of Higgs field, the critical energy scale (μ_max, the maximum energy scale under which the lower excitation sector of the GEP is valid) and the maximum energy scale (μ_max, at which the symmetry of the Higgs field is restored) in the SM areT _c ≈476 GeV, μ_c≈0.547 × 10¹⁵ and μ_max≈0.873 × 10¹⁵, respectively. Project supported in part by the National Natural Science Foundation of China.     

Hilbert space,the number of Higgs particles and the quantum two-slit experiment

Rigorous mathematical formulation of quantum mechanics requires the introduction of a Hilbert space. By contrast, the Cantorian E-infinity approach to quantum physics was developed largely without any direct reference to the afore mentioned mathematical spaces. In the present work we present a novel reinterpretation of basic ε^(∞) Cantorian spacetime relations in terms of the Hilbert space of quantum mechanics. In this way, we gain a better understanding of the physical and mathematical structure of quantum spacetime. In particular we show that the two-slit experiment required a definite topology which is consistent with a certain fuzzy Kähler manifold or more generally a Cantorian spacetime manifold. Finally by determining the Euler class of this manifold, we can estimate the most likely number of Higgs particles which may be discovered.