Implementation in Physics

In particle physics, a generation or family is a division of the elementary particles.

• Between generations, particles differ by their flavour quantum number and mass, but their electric and strong interactions are identical.
• There are three generations according to the Standard Model of particle physics. Each generation contains two types of leptons and two types of quarks. The two leptons may be classified into one with electric charge −1 (electron-like) and neutral (neutrino); the two quarks may be classified into one with charge −1⁄3 (down-type) and one with charge +2⁄3 (up-type).

The basic features of quark–lepton generation or families, such as their masses and mixings etc., can be described by some of the proposed family symmetries.

Those particles with half-integer spins, are known as fermions, while those particles with integer spins, such as 0, 1, 2, are known as bosons.

• The two families of particles obey different rules and broadly have different roles in the world around us. A key distinction between the two families is that fermions obey the Pauli exclusion principle: that is, there cannot be two identical fermions simultaneously having the same quantum numbers (meaning, roughly, having the same position, velocity and spin direction). Fermions obey the rules of Fermi–Dirac statistics.
• In contrast, bosons obey the rules of Bose–Einstein statistics and have no such restriction, so they may “bunch together” in identical states. Also, composite particles can have spins different from their component particles.

For example, a helium-4 atom in the ground state has spin 0 and behaves like a boson, even though the quarks and electrons which make it up are all fermions. (Wikipedia)

Quantum field theory is any theory that describes a quantized field.

• QED, or Quantum Electrodynamics, is the quantum theory of the electromagnetic field, a so-called Abelian field (referencing an internal mathematical symmetry of the theory.)
• Electroweak theory is a generalization of QED, unifying it with the weak nuclear force in the form of a Yang-Mills field theory (aka. a non-Abelian field theory).
• QCD, or Quantum Chromodynamics, is another example of a non-Abelian field theory, but one with very different asymptotic behavior than electroweak theory.
• The Standard Model of particle physics is the combination of electroweak theory and QCD in the form of a unified theory obeying a complex set of symmetries.

This theory describes all the known fields and all the known interactions other than gravity. (Quora)

Feynman diagram of the fusion of two (2) electroweak vector bosons to the scalar Higgs boson, which is a prominent process of the generation of Higgs bosons at particle accelerators. (The symbol q means a quark particle, W and Z are the vector bosons of the electroweak interaction. H° is the Higgs boson.) (Wikipedia)

There are three (3) generations of quarks (up/down, strange/charm, and top/bottom), along with three (3) generations of leptons (electron, muon, and tau). All of these particles have been observed experimentally, and we don’t seem to have seen anything new along these lines. A priori, this doesn’t eliminate the possibility of a fourth generation, but the physicists I’ve spoken to do not think additional generations are likely. (StackExchange)

In particle physics, a vector boson is a boson whose spin equals one. Vector bosons that are also elementary particles are gauge bosons, the force carriers of fundamental interactions. Some composite particles are vector bosons, for instance any vector meson (quark and antiquark).

In the SM interactions are determined by a gauge quantum field theory containing the internal symmetries of the unitary group product SU(3)C × SU(2)L × U(1)Y [?].

• TheSU(3)C symmetry corresponds to the strong interaction (C index marks colour charge, see section 1.1.4 )
• The product SU(2)L × U(1)Y is responsible for the electroweak interaction (indices L and Y correspond to the left-handed interaction of weak currents and hypercharge, respectively, see section 1.1.2). (The Standard Model - pdf)

The Higgs boson field (often referred to as the God particle) is a scalar field with two neutral and two electrically charged components that form a complex doublet of the weak isospin SU(2) symmetry.

• Its “Mexican hat-shaped” potential leads it to take a nonzero value everywhere (including otherwise empty space), which breaks the weak isospin symmetry of the electroweak interaction and, via the Higgs mechanism, gives mass to many particles. (Wikipedia)
• Despite its success at explaining the universe, the Standard Model does have limits. For example, the Higgs boson gives mass to quarks, charged leptons (like electrons), and the W and Z bosons. However, we do not yet know whether the Higgs boson also gives mass to neutrinos – ghostly particles that interact very rarely with other matter in the universe.

Also, physicists understand that about 95 percent of the universe is not made of ordinary matter as we know it. Instead, much of the universe consists of dark matter and dark energy that do not fit into the Standard Model.

So now I will attempt to show the minor hexagons are significant. This is not easy as they are linked to the nature of prime numbers, and nothing is easy about the nature of prime numbers. But I begin with this assumption: if the hexagons participate in the Universe in any way other than haphazardly, they must be demonstrably congruent to something organized. That is, if I can show they are organized (not random) in relation to some other thing, then primes and the thing are linked. (Hexspin)

The Standard Model presently recognizes seventeen distinct particles (twelve fermions and five bosons). As a consequence of flavor and color combinations and antimatter, the fermions and bosons are known to have 48 and 13 variations, respectively. Among the 61 elementary particles embraced by the Standard Model number electrons and other leptons, quarks, and the fundamental bosons. (Wikipedia)

The Standard Model of Particle Physics, describes for us all know fundamental interaction in nature till date, with the exception of Gravity (work on this front is going on). Here is a summary of the fundamental content of the standard model

• There are three families of particle, the Quarks, the Leptons and the Gauge Bosons. The Quarks in groups of three forms the composite particles such as the Protons, along with the electron this forms ordinary matter.
• The Gauge Bosons are the ones those are responsible for interactions. The Quarks interact among themselves by the exchange of a Gluon these are responsible for the strong nuclear force.
• The newly discovered Higgs Boson interacts with all the Quarks and the first group of Leptons (electron, muon and tau) providing them with their mass. The neutrinos which are the other Leptons originally were thought to have zero mass, but recent discoveries argue that this is not the case.
• The Weak bosons interact with both Leptons and Quarks, these are responsible for the Weak nuclear forces. The exchange of photon is responsible for the Electromagnetic Force.

They interact, they transfer energy and momentum and angular momentum; excitations are created and destroyed. Every excitation that’s possible has a reverse excitation. (Quora)

The Standard Model explains three of the four fundamental forces that govern the universe: electromagnetism, the strong force, and the weak force.

• Electromagnetism is carried by photons and involves the interaction of electric fields and magnetic fields.
• The strong force, which is carried by gluons, binds together atomic nuclei to make them stable.
• The weak force, carried by W and Z bosons, causes nuclear reactions that have powered our Sun and other stars for billions of years.

The fourth fundamental force is gravity, which is not adequately explained by the Standard Model.

Elementary particles are classified according to their spin. Fermions are one of the two fundamental classes of particles, the other being bosons. Fermions have half-integer spin while bosons have integer spin.

• Bosons are characterized by Bose–Einstein statistics and all have integer spins. Bosons may be either elementary, like photons and gluons, or composite, like mesons.
• The Higgs boson is postulated by the electroweak theory primarily to explain the origin of particle masses. In a process known as the “Higgs mechanism”, the Higgs boson and the other gauge bosons in the Standard Model acquire mass via spontaneous symmetry breaking of the SU(2) gauge symmetry.
• The Minimal Supersymmetric Standard Model (MSSM) predicts several Higgs bosons. On 4 July 2012, the discovery of a new particle with a mass between 125 and 127 GeV/c2 was announced; physicists suspected that it was the Higgs boson. Since then, the particle has been shown to behave, interact, and decay in many of the ways predicted for Higgs particles by the Standard Model, as well as having even parity and zero spin, two fundamental attributes of a Higgs boson.
• This also means it is the first elementary scalar particle discovered in nature. Elementary bosons responsible for the four fundamental forces of nature are called force particles (gauge bosons). Strong interaction is mediated by the gluon, weak interaction is mediated by the W and Z bosons.

According to the Standard Model there are five (5) elementary bosons:

• One (1) scalar boson (spin = 0) Higgs boson – the particle that contributes to the phenomenon of mass via the Higgs mechanism
• Four (4) vector bosons (spin = 1) that act as force carriers.

These four are the gauge bosons:

• γ Photon – the force carrier of the electromagnetic field
• g Gluons (eight (8) different types) – force carriers that mediate the strong force
• Z Neutral weak boson – the force carrier that mediates the weak force
• W± Charged weak bosons (two (2)types) – force carriers that mediate the weak force

A second order tensor boson (spin = 2) called the graviton (G) has been hypothesised as the force carrier for gravity, but so far all attempts to incorporate gravity into the Standard Model have failed.

The diagram shows the elementary particles of the Standard Model (the Higgs boson, the three generations of quarks and leptons, and the gauge bosons), including their names, masses, spins, charges, chiralities, and interactions with the strong, weak and electromagnetic forces. It also depicts the crucial role of the Higgs boson in Electroweak Symmetry Breaking, and shows how the properties of the various particles differ in the (high-energy) symmetric phase (top) and the (low-energy) broken-symmetry phase (bottom). (Wikipedia)

Theories that lie beyond the Standard Model include various extensions of the standard model through supersymmetry, such as the Minimal Supersymmetric Standard Model (MSSM) and Next-to-Minimal Supersymmetric Standard Model (NMSSM), and entirely novel explanations, such as string theory, M-theory, and extra dimensions. As these theories tend to reproduce the entirety of current phenomena, the question of which theory is the right one, or at least the “best step” towards a Theory of Everything, can only be settled via experiments, and is one of the most active areas of research in both theoretical and experimental physics.

The organization of the book is as follows. In Chapter 1, we give a brief introduction of the standard model for the elementary particles to describe their structures and interactions. This is followed by Chapter 2 with a description of Fermi theory of weak interactions and its limitation. Preparation for the under-standing of electroweak gauge theory is done in Chapter 3, which covers symmetry, symmetry breaking and the gauge theory. Glashow-Weinberg-Salam (GWS) theory of electroweak interactions is covered in Chapter 4. In Chapter 5, quantum chromodynamics (QCD), i.e. the theory of strong interactions, is discussed briefly.

After these chapters, we will come to the description of physics beyond the standard model. In Chapter 6, we discuss a current hot topic, neutrino physics, i.e. neutrino masses and neutrino ocsillations. Then, in Chapter 7, we deal with supersymmetric theories as the typical example of physics beyond the standard model. We further attempt to discuss other representative topics in the physics beyond the standard model; precision tests of electroweak radiative corrections and new physics search through these analyses in Chapter 8 and flavor physics and CP violation, which are also sensitive to the presence of new physics, in Chapter 9. Each chapter is accompanied by a few problems, hoping that solving them will be of some help in the understanding of the main text. The topics we chose depend on our preference. (The physics of the standard model and beyond - pdf)