An Original Didactic of the Standard Model “The Particle’s Geometric Model” (Nucleons and K-Mesons)

This paper shows a didactic model (PGM), and not only, but representative of the Hadrons described in the Standard Model (SM). In this model, particles are represented by structures corresponding to geometric shapes of coupled quantum oscillators (IQuO). By the properties of IQuO one can define the electric charge and that of color of quarks. Showing the “aurea” (golden) triangular shape of all quarks, we manage to represent the geometric combinations of the nucleons, light mesons, and K-mesons. By the geometric shape of W-bosons, we represent the weak decay of pions and charged Kaons and neutral, highlighting in geometric terms the possibilities of decay in two and three pions of neutral Kaon and the transition to anti-Kaon. In conclusion, from this didactic representation, an in-depth and exhaustive phenomenology of hadrons emerges, which even manages to resolve some problematic aspects of the SM.

An Original Didactic about Standard Model (Geometric Model of Particle: The Quarks)

This work shows a didactic model representative of the quarks described in the Standard Model (SM). In the model, particles are represented by structures corresponding to geometric shapes of coupled quantum oscillators (GMP). From these didactic hypotheses emerges an in-depth phenomenology of particles (quarks) fully compatible with that of SM, showing, besides, that the number of possible quarks is six.

An Original Didactic about Standard Model: “The Particles’ Geometric Model” (Leptons and Bosons)

This work shows a didactic model representative (GPM) of the particles described in the Standard Model (SM). Particles are represented by geometric forms corresponding to geometric structures of coupled quantum oscillators. From the didactic hypotheses of the model emerges an in-depth phenomenology of particles that is fully compatible with that of SM. Thanks to this model, we can calculate “geometrically” the mass of Higgs’s Boson and the mass of the pair “muon and muonic neutrino”, and, by the geometric shapes of leptons and bosons, we can also solve crucial aspects of SM physics as the neutrinos’ oscillations and the intrinsic chirality of the neutrino and antineutrino.

A Novelty Solution to the Neutron Anomaly (An Anomalous Neutron or “Dark”?)

To explain the anomaly (τb ≠ τf) of the neutron lifetime τ in some experiments, in “bottle” τb and in “beam” τf, we resort to an anomalous form of the neutron na. This form belongs to one of two different states of the structure of the quark configurations making up the neutron (nucleon): first, an ordinary form Ψo, while the second is an “anomalous” form Ψa, difficult to detect and decay. If the ordinary configuration is present in everyone nuclear processes, to strong and weak interactions, and in diffusion processes, the anomalous form can emerge, in casual way and probabilistic, in some processes of fusion with production of neutrons and can be highlighted in some experiments as those in “bottle” and in “beam”, see the anomaly of the neutron lifetime. We show that the anomalous form Ψa can be highlighted in the coupling between a dipoles’ lattice of virtual bosons W and the neutron (nucleon) because the neutron into anomalous configuration does not decays. Finally, we interpret the anomalous neutron as a “dark” neutron, presenting, so, the dark matter as an anomalous form of hadron matter.

The Geometric Model of Particles (The Origin of Mass and the Electron Spin)

The geometrization process of physics could involve, in addition to space and time in General Relativity (GR), even elementary particles. Our starting point is the formulation of an original hypothesis about particles, compatible with the basic assumptions of the Standard Model (SM): a massive particle is a geometric structure of a set of elastically coupled quantum oscillators that propagates along a line of a non-massive base field (in impulse eigenstate). We show that the propagation equation of an oscillation associated with the geometric shape representing an electron propagates following Dirac’s wave equation. Thus, one gives a foundation to a geometric model of massive particles (GMP) which would explain the physical origin of the mass, spin, and the magnetic moment of the electron.

The Origin of the Color Charge into Quarks

Showing the origin of the mass in an additional coupling between field quantum oscillators, we formulate a hypothesis of a geometrical structure of the oscillators of “fields-particles”. In this way, we define the possible structure of quarks and hadrons (as the proton). This hypothesis is reasonable if one admits field oscillators composed by sub-oscillators at semi-quantum (IQuO) and in which a degree of internal freedom is definable. Using the IQuO model, we find the origin of the sign of electric charge in to particles and, in quarks, the isospin, the strangeness and colour charge. Finally, we formulate the structure of the gluons and the variation modality of the colour charge in quarks.

The Bare and Dressed Masses of Quarks in Pions via the of Quarks’ Geometric Model

In previous articles (Guido) we demonstrated that Quarks (u, d) are represented by golden geometric structures of coupled quantum oscillators. In this article we show the geometric structure of the pion triplet and, in particular, via the structure equation of neutral pion, we identify its decays and we solve the spin question in hadrons thanks also to introduction of algebraic operations [?, ⊕] on geometric structure. Moreover by means of the golden ratio between (u, d), we determine the values of bare masses of quarks (3.51 MeV for u-quark and 5.67 MeV for d-quark) and those ones bounded in a pion (53.31 MeV for u-quark and 85.26 MeV for d-quark). Finally, using algebraic operations [?, ⊕] we point out a new way to represent the processes of pions’ decay.

The Theoretical Value of Mass of the Light <i>η</i>-Meson via the Quarks’ Geometric Model

Highlighting a golden triangular form in u and d quarks (Quark Geometric Model), we build the geometric structures of light meson η and individualize its decays and spin. By the structure equations describing mesons, we determine a mathematic procedure to calculate the theoretical value of the mass of light mesons η.

The Theoretical Spectrum of Mass of the Light Mesons without Strangeness via the Quarks’ Geometric Model

Using the “Aureum Geometric Model” (AGM) of quarks, we formulate the structure equations describing mesons and, by a mathematic procedure, we calculate the theoretical spectrum of mass values of light mesons without strangeness.

Theoretical Spectrum of Mass of the Nucleons: New Aspects of the QM

In this paper, we show a new theoretical procedure for calculating the nucleonic mass values. We develop this procedure on the geometric representation of (u, d) quarks, these seen as golden structures of coupled quantum oscillators (Aureum Geometric Model or AGM). Using AGM, we also build the geometric structures of nucleons (p, n), determining their structure equations and spins. Thank AGM, coherent to QCD, new aspects of the Quantum Mechanics emerge, opening to anew descriptive paradigm in Particle Physics.

The Universe at Lattice-Fields

We formulate the idea of a Universe crossing different evolving phases where in each phase one can define a basic field at lattice structure (Uk) increasing in mass (Universe-lattice). The mass creation in Uk has a double consequence for the equivalence “mass-space”: Increasing gravity (with varying metric) and increasing space (expansion). We demonstrate that each phase is at variable metric beginning by open metric and to follow a flat metric and after closed. Then we define the lattice-field of intersection between two lattice fields of base into universe and we analyse the universe in the Nucleo-synthesis phase (intersection-lattice ) and in the that of recombination (intersection-lattice ). We show that the phase is built on the intersection of the lattices of the proton (Up) and electron (Ue) or . We show UH to be at variable metric (open in the past, flat in the present and closed in the future). Then, we explain some fundamental aspects of this universe UH: Hubble’s law by creating the mass-space in it, its age (13.82 million of Years) as time for reaching the flat metric phase and the value of critic density. In last we talk about dark universe lattice , having hadronic nature, and calculating its spatial step and its density in present phase of .

Variational Principle in an Expanding Universe

In this paper we complete the relativistic cosmological theory because we extend the variational principle including variations of metric induced by expansion of the space. We will show that the mass not only curves Space and Time but also generates them: we’ll speak of the principle of mass-space equivalence. Then the increasing mass generates variations of metric as also the space increasing or expansion. So, the dark component of the mass generates additional gravity around galaxies as well as additional space, which generates a pressure (dark energy) accelerating the galaxies in their move away. All this could explain the cosmic coincidence (Ωdm/Ωde ≈ 1). To talk about the increasing mass is equivalent to speak of mass creation in universe, causing the variation of the tensor (T) mass-energy tensor of all component fields. We conjecture that its variation is caused by mass-energy flow comes out from a physical system (Θ) composed by set of uncoupled quantum oscillators (structure of no-field) in vacuum state. All this allows formulating a variational principle which generates the cosmological equation with the (Λ) parameter and a tensor T* with variable mass density, where T*(T, Θ).

From the Dark Neutron to the Neutron Decay Anomaly and Lithium Cosmologic Problem

In the context of the geometric model of particles (PGM), we show two different forms of the structure of the quark positions making up the neutron: first, an ordinary form, while the second is a “dark” form (difficult to detect). By the “dark” form we attempt of explaining the anomaly of the neutron lifetime (τ) in its decay observed in two different experiments as that in “bottle” and “in beam” and expressed by discrepancy between the two lifetimes (τbottle ≠ τbeam). Using the structure equation of the dark neutron, we calculate its mass. In this framework, two problems can be resolved: the asymmetry between matter and antimatter and the abundance into universe of Lithium 7Li than the 6Li.