## Saturday, 26 January 2008

### Grand Unification Theory

Grand Unification Theory

Arip Nurahman
Department of Physics
Faculty of Sciences and Mathematics, Indonesia University of Education

and

Follower Open Course Ware at Massachusetts Institute of Technology
Cambridge, USA
Department of Physics
http://web.mit.edu/physics/
http://ocw.mit.edu/OcwWeb/Physics/index.htm
&
Aeronautics and Astronautics Engineering
http://web.mit.edu/aeroastro/www/
http://ocw.mit.edu/OcwWeb/Aeronautics-and-Astronautics/index.htm

The Ball-of-Light Particle Model
Introduction, The Picture Puzzle Analogy, Old Intro, More, Summary of the Grand Unification Theory -- "The Ball-of-Light Particle Model", Highlights of information in this Grand Unification, Ball Lightning, Examples of Balls of Light, Balls-of-Light from cracking rock,
Forces
Induction of forces, The Strong Force,

The "Poynting Vector",

Balls-of-Light
Decay Modes, Induction off of a Ball-of-Light's Pole, Induction off of a Ball-of-Light's Pole, The Towers of M16, SS433 (A decaying ball-of-light), The explosion (decay) of small elementary particles, A Large Ball-of-Light Inducing a Small Ball-of-Light, Example: The Artificial Decay of the Lithium Nucleus, Gravitational Induction of an Electromagnetic Wave on a Ball-of-Light,

Gravity

Experiments
Experiments with Balls-of-Light, Example: A Scientist who makes Spherical Sparks,

Problems
What are the problems with the Ball-of-Light Particle Model?,

 Book 1 Book 2 Book 3 Book 4 Book 5 Book 6

Abstract

For years, humanity has always wondered “why are we here?”. Through the creation of God or the Big Bang to the Primordial Soup, either way, humanity was always look for answers. Each culture prior to the scientific age identified a “Creator or God” responsible for the existence of the heavens and the earth. Since the induction of “modern thought”, contemporary explanation concludes the universe was created from a big bang that happened approximately 13.7 billion years ago. From which the expansion and the cooling down resulted in us, a mixture of carbon and gases, with a combination of electric static.

Introduction

A Grand Unified Theory, (GUT), is a model in particle physics in which at high energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry and thus one unified coupling constant. In contrast, the experimentally verified Standard Model of particle physics is based on three independent interactions, symmetries and coupling constants.

Models that do not unify all interactions using one simple Lie group as the gauge symmetry, but do so using semisimple groups, can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well.

Unifying gravity with the other three interactions would provide a theory of everything (TOE), rather than a GUT. Nevertheless, GUTs are often seen as an intermediate step towards a TOE.

The new particles predicted by models of grand unification cannot be observed directly at particle colliders because their masses are expected to be of the order of the so-called GUT scale, which is predicted to be just a few orders of magnitude below the Planck scale and thus far beyond the reach of currently foreseen collision experiments. Instead, effects of grand unification might be detected through indirect observations such as proton decay, electric dipole moments of elementary particles, or the properties of neutrinos. Some grand unified theories predict the existence of magnetic monopoles.

GUT refers to any of several very similar unified field theories or models in physics that predicts that at extremely high energies (above 1014 GeV), the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field.

Thus far, physicists have been able to merge electromagnetism and the weak nuclear force into the electroweak force, and work is being done to merge electroweak and quantum chromodynamics into a QCD-electroweak interaction sometimes called the electrostrong force. Beyond grand unification, there is also speculation that it may be possible to merge gravity with the other three gauge symmetries into a theory of everything.

## History

Historically, the first true GUT which was based on the simple Lie group SU(5), was proposed by Howard Georgi and Sheldon Glashow in 1974. The Georgi–Glashow model was preceded by the Semisimple Lie algebra Pati–Salam model by Abdus Salam and Jogesh Pati,[3] who pioneered the idea to unify gauge interactions.

The acronym GUT was first coined in 1978 by CERN researchers John Ellis, Andrzej Buras, Mary K. Gaillard, and Dimitri Nanopoulos, however in the final version of their paper they opted for the less anatomical GUM (Grand Unification Mass). Nanopoulos later that year was the first to use the acronym in a paper.

## Motivation

There is a general aesthetic among high energy physicists that the more symmetrical a theory is, the more "beautiful" and "elegant" it is. According to this aesthetic, the Standard Model gauge group, which is the direct product of three groups (modulo some finite group), is "ugly". Also, reasoning in analogy with the 19th-century unification of electricity with magnetism into electromagnetism, and especially the success of the electroweak theory, which utilizes the idea of spontaneous symmetry breaking to unify electromagnetism with the weak interaction, people wondered if it might be possible to unify all three groups in a similar manner. Physicists feel that three independent gauge coupling constants and a huge number of Yukawa coupling coefficients require far too many free parameters, and that these coupling constants ought to be explained by a theory with fewer free parameters.

A gauge theory where the gauge group is a simple group only has one gauge coupling constant, and since the fermions are now grouped together in larger representations, there are fewer Yukawa coupling coefficients as well. In addition, the chiral fermion fields of the Standard Model unify into three generations of two irreducible representations ($10\oplus \bar{5}$) in SU(5), and three generations of an irreducible representation (16) in SO(10). This is a significant observation, as a generic combination of chiral fermions which are free of gauge anomalies will not be unified in a representation of some larger Lie group without adding additional matter fields. SO(10) also predicts a right-handed neutrino.

GUT theory specifically predicts relations among the fermion masses, such as between the electron and the down quark, the muon and the strange quark, and the tau lepton and the bottom quark for SU(5) and SO(10). Some of these mass relations hold approximately, but most don't. See Georgi-Jarlskog mass relation. If we look at the renormalization group running of the three-gauge couplings have been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU(5)/SO(10) GUTs, which are precisely the GUT groups which lead to a simple fermion unification.

This is a significant result, as other Lie groups lead to different normalizations. However, if the supersymmetric extension MSSM is used instead of the Standard Model, the match becomes much more accurate. It is commonly believed that this matching is unlikely to be a coincidence. Also, most model builders simply assume SUSY because it solves the hierarchy problem—i.e., it stabilizes the electroweak Higgs mass against radiative corrections. And the Majorana mass of the right-handed neutrino SO(10) theories with its mass set to the gauge unification scale is examined, values for the left-handed neutrino masses (see neutrino oscillation) are produced via the seesaw mechanism. These values are 10–100 times smaller than the GUT scale, but still relatively close.

(For a more elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.)

## Proposed theories

Several such theories have been proposed, but none is currently universally accepted. An even more ambitious theory that includes all fundamental forces, including gravitation, is termed a theory of everything. Some common mainstream GUT models are:

 minimal left-right model — SU(3)C × SU(2)L × SU(2)R × U(1)B-L Georgi–Glashow model — SU(5) SO(10) Flipped SU(5) — SU(5) × U(1) Pati-Salam model — SU(4) × SU(2) × SU(2) Flipped SO(10) — SO(10) × U(1) Trinification — SU(3) × SU(3) × SU(3) SU(6) E6 331 model chiral color
Not quite GUTs:

Note:

These models refer to Lie algebras not to Lie groups. The Lie group could be [SU(4)×SU(2)×SU(2)]/Z2, just to take a random example.

The most promising candidate is SO(10). (Minimal) SO(10) does not contain any exotic fermions (i.e. additional fermions besides the Standard Model fermions and the right-handed neutrino), and it unifies each generation into a single irreducible representation. A number of other GUT models are based upon subgroups of SO(10). They are the minimal left-right model, SU(5), flipped SU(5) and the Pati-Salam model. The GUT group E6 contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E6 models comes from E8 × E8 heterotic string theory.

GUT models generically predict the existence of topological defects such as monopoles, cosmic strings, domain walls, and others. But none have been observed. Their absence is known as the monopole problem in cosmology. Most GUT models also predict proton decay, although not the Pati-Salam model; current experiments still haven't detected proton decay. This experimental limit on the proton's lifetime pretty much rules out minimal SU(5).

## Ingredients

A GUT model basically consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a Yang-Mills action for that connection given by an invariant symmetric bilinear form over its Lie algebra (which is specified by a coupling constant for each factor), a Higgs sector consisting of a number of scalar fields taking on values within real/complex representations of the Lie group and chiral Weyl fermions taking on values within a complex rep of the Lie group. The Lie group contains the Standard Model group and the Higgs fields acquire VEVs leading to a spontaneous symmetry breaking to the Standard Model. The Weyl fermions represent matter.

## Current status

As of today, there is still no hard evidence that nature is described by a Grand Unified Theory. Moreover, since the Higgs particle has not yet been observed, the smaller electroweak unification is still pending. The discovery of neutrino oscillations indicates that the Standard Model is incomplete and has led to renewed interest toward certain GUT such as SO(10). One of the few possible experimental tests of certain GUT is proton decay and also fermion masses. There are a few more special tests for supersymmetric GUT.

The gauge coupling strengths of QCD, the weak interaction and hypercharge seem to meet at a common length scale called the GUT scale and equal approximately to 1016 GeV, which is slightly suggestive. This interesting numerical observation is called the gauge coupling unification, and it works particularly well if one assumes the existence of superpartners of the Standard Model particles. Still it is possible to achieve the same by postulating, for instance, that ordinary (non supersymmetric) SO(10) models break with an intermediate gauge scale, such as the one of Pati-Salam group.

## Origin of name

The coining of the widely-used acronym GUT has been attributed to a paper published in 1978 by Texas A&M University theorist Dimitri Nanopoulos
(previously at Harvard University).