Recent advances in physics and astronomy --- our current

understanding of the Universe

Lecture 2: Toward a unified theory, Interactions of elementary particles

April 9th, 2003

How we see different-sized objects

What is the world made of•Different things in this world share the same characteristics.

•Nature is made from a few fundamental building blocks.

•The Greek thinker Empedocles (not the commonly acknowledged Aristotle!) first classified the fundamental elements as fire, air, earth, and water.

The ancient Chinese believed that the five basic components of the physical universe were earth, wood, metal, fire, and water. And in India, the Samkhya-karikas by Ishvarakrsna (c. 3rd century AD) proclaims the five gross elements to be space, air, fire, water, and earth.

How small can we go, atoms?In 1990, people believe that atom is the fundamental component of everything.

Soon however, it is realized that atoms can be categorize into groups that shared similar chemical properties. ====> atoms were made up of simpler building blocks.

Atoms are made of nuclei and electrons.

Can the division go further? What are electron and nucleus made of?

Nucleus and nuclei decay

                                              

Atoms are made of nuclei and electrons. There are many different nuclei existing in nature. Some of them have a very peculiar property: they decay and become another element.

A lump of uranium-238 will decay at a constant rate such that in 4,460,000,000 years -- give or take a few days -- half the uranium will be gone. But there is no way to tell when a specific uranium atom will decay; it could decay five minutes from now, or in ten billion years.

Classification of decay particles are helium nuclei (2 p, 2 n):

particles are speedy electrons:                                                     radiation is a high-energy photon:  

These three forms of radiation can be distinguished by a magnetic field since

•the positively-charged alpha particles curve in one direction, •the negatively-charged beta particles curve in the opposite direction, •and the electrically-neutral gamma radiation doesn't curve at all.

How do we know which is which?

Electrons and quarks•Electron shows no sign of being able to be divided further. Nucleus, with the study of nuclear decay, we know they consist of protons and neutrons. •Protons and neutrons are much heavier than electrons. They are not fundamental particles. Instead, we believe they consist of quarks, which, according to our current theory, are as fundamental as electrons.

•Unlike electron, “seen” regularly in modern experiments, free quarks can not be “seen”---- they are always bounded in nuclei and we can only infer their existence from experiments.

Scales of an atom

•It is possible that our current theory is not complete and quarks and electrons are not fundamental after all, and will turn out to be made up of other, more fundamental particles.

•How small can a quark or electron be? We don't know exactly the answers are; they are definitely smaller than 10-18 meters,

The Standard Model•6 quarks.

•6 leptons.

All matter can be “cooked” by quarks and leptons.

• Force carrier particles

Fermions

BosonsAll interactions (strong, weak, EM), except gravity are carried through these intermediate bosons.

The almost impartial God: Anti-matter

We know their existence because when a matter particle and antimatter particle meet, they annihilate into pure energy!

For every type of matter particle we've found, there also exists a corresponding antimatter particle, or antiparticle.

Antiparticles have the same mass as their corresponding matter particles, but opposite charges and spins.

Flavor of quarks

The idea of quark is proposed by Murray Gell-Mann and George Zweig in 1964. After 18 year, in 1995, the top quark (the last one) is confirmed experimentally at Fermi-Lab.

Hadrons, baryons and mesons

                                                              

Quarks are social animals. No single “free” quarks are observed in Nature. Instead, they either come in group of three, in which case, a baryon is formed; or come in a pair of quark and anti-quark pair, in which case, a meson is formed.

Baryon Meson

All combinations of three quarks (or anti-quarks) and quark-anti quark pairs are possible and detectable in Nature.

Leptons As the case for quarks, there are six leptons: e, , and corresponding neutrinos e , and .

Lepton decays

Leptons of higher generations () can decay to lower generations(). The decay must conserve lepton number of each generation.

e + e +

_

Initial state: lepton number = +1

e lepton number = 0

Final state:

lepton number () =1,

e lepton number e-1, e+1 _

NeutrinosNuclear decays. Missing energy of nuclei decays: the energy of

radiated electrons is not single valued, rather, the spectrum is continuous.

Maybe a sign of violation of energy conservation?

Wolfgang Pauli proposed in 1930 that there must be a second particles alongside with the emitted electron. This particle must be very light and neutral, so that it is very hard to detect.

Later, Enrico Fermi named it neutrino when he developed the nuclear decay theory.

Today we know that neutrinos are very light and they only participate in Weak Interaction and Gravitation.

Properties of quarks and leptons

I

II

III

Properties of intermediate bosons

The four interactions

It seems that all phenomena in nature can be well described by these four interactions.

Force as exchange of particles

Heisenberg’s Uncertainty Principle and Virtual particle

In 1927, Werner Heisenberg determined that it is impossible to measure both a particle's position and its momentum exactly. The more precisely we determine one, the less we know about the other. Similarly we can not measure both the particle energy and time precisely, which means if a particle only exist a very short period of time, it could have a very large energy. Such a particle is called a virtual particle.

: the Planck's constant , called "h-bar," equals 1.05 x 10-34 joule-seconds, or 6.58 x 10-22 MeV-seconds.

EM Interaction

Electricity

Magnetism

Apart from Gravitation, the electromagnetic force is the other interaction we can feel at macroscopic scale (for example, friction). It causes like-charged things to repel and oppositely-charged things to attract. The force is mediated by a photon.

Neutral atoms stick one to another through Residual E-M interaction.

Strong Interaction

• What binds the nucleus together?

• Why no “free” quarks exist in nature?

As EM interaction is operating on electric charges, the manifestation of strong interaction requires an altogether different kind of charge, called “color” charge. Only quarks and gluons (which mediate strong force) have color charges.

The strong force, as indicated by its name, is very strong. This leads to the nomenclature of the intermediate boson as “gluons”.

Color Charge

When two quarks are close to one another, they exchange gluons and create a very strong color force field that binds the quarks together. The force field gets stronger as the quarks get further apart. Quarks constantly change their color charges as they exchange gluons with other quarks.

Each flavor of quark (u,d,s,c,t,u) can have three color charges: red, green and blue. Anti-quarks have anti-colors. When quarks are combined to form nucleon and other particles, the total color charge must be neutral.

Color charges of quark and gluons

Unlike photons, which is charge neutral as the force carrier of EM interaction, gluons can have color charges. Indeed, 6 of 8 gluons carry colors which allow quarks to change their colors. The other two gluons are colorless.

Color charge conservation

The color charge, like the electron charge, is a conserved quantity. When quarks interact and change their color identities by exchanging gluons, they must obey this conservation law.

Quark Confinement

The fact that there is no observation of “free” quarks in nature is sometimes referred to as “quark confinement”. This is because gluons, the strong force carrier particles, gets stronger as the separation between two quarks gets larger.

When the energy contained in the gluons field becomes so large, a quark-anti quark pair will appear and new particles are formed--quite similar to breaking a rubber band.

Residual Strong Force

We now know quarks are “confined” within baryons (such as proton and neutron) or meson (such as pions). But what holds various nuclei together?

As the case for atoms, where electrons and nuclei from different atoms interact with each other and hold atoms together, the exchange of gluons between quarks of different nuclei serves to hold nuclei together.

The fundamental strong interaction The effective residual nuclear force

Weak Interaction—charged currentWeak interaction is responsible for change of flavors --- particle can only transmute from one generation to another through Weak interaction.

Charged current always involve leptons changing to corresponding neutrinos and vice versa. The force carrier particles are W+ and W-.

Weak Interaction – the neutral current and the unification of ElectroWeak

Interaction

The neutral weak current (via exchanging of Z0 meson) is very similar to the EM current (via exchanging of photon). This leads to the unification of electromagnetic force and weak force.

Spontaneous Symmetry Breaking

If EM and Weak interaction are the same thing, how can we explain the fact that the W+/- and Z0 are (too) massive while the photons are massless?

Answer: Maybe originally the W+/- and Z0 bosons are massless, exactly the same as the photon. They however, acquire their mass by interacting with another boson, called the “Higg’s” boson, which is replete in the vaccum.

The fact that the “vaccum” orresponds to a condensation of Higg’s bosons is referred as spontaneous symmetry breaking.

Comparison of the four interactionsThe four fundamental interactions are similar to each other. For example, they all involve exchange of force-mediate particles. However, their strength are very different from each other.

As an example, we compare the strength and range of the four fundamental forces between two protons. For this matter, we consider the potential energy associated with each force acting between two protons. This energy is characterized by both the strength of the interaction and the range over which the interaction takes place. In each case the strength is determined by a coupling constant, and the range is characterized by the mass of the exchanged particle. The potential energy, U, between two protons a distance r apart is written as

C: the coupling constant

R: the range of the force

Comparison of the four interactions (2)

Interaction Gravity Weak EM Strong (by residual exchange particle)

Exchange particle

Graviton Z0, (W+/-) Photon Pion

Mass (eV) 0 91*109 0 135x106

Coupling constant (Jm)

1.87x10-64 3.22x10-31 2.31x10-28 2.5x10-27

Range (m) Infinity 2x10-18 Infinity 1.5x10-15

Summary of the four fundamental interactions

                                                                                                                                     

Running coupling constant

The coupling constant of different interactions are energy dependent. At larger energies (shorter distances), the strong interaction becomes milder, while the electro and weak interaction become stronger.

GUT: Grand Unify Theory propose that Strong, EM and Weak interaction become unified when E>1016 GeV.

Asymptotic Freedom

Gluons have color charges lead to the phenomenon of asymptotic freedom.

Beyond Standard Model-Supersymmetry

Every fundamental matter particle should have a massive "shadow" force carrier particle, and every force carrier should have a massive "shadow" matter particle. This relationship between matter particles and force carriers is called supersymmetry. For example, for every type of quark there may be a type of particle called a "squark."

Beyond Standard Model-string theory

String Theory: one of the recent proposals of modern physics, suggests that in a world with three ordinary dimensions and some additional very "small" dimensions, particles are strings and membranes.

Project ideas

• Feynmann Diagrams: a picturesque description of interactions.

• The extra dimensions: Can we detect them?

----- verify 1/r2 law of gravitation at small scale.

• Higg’s mechanism: How various particles gain their mass?

• Symmetries and symmetry breakings: Local gauge theory and its importance in constructing various interactions.

• Renormalization.

References

Websites:

•http://particleadventure.org (courtesy for many cartons used here)

• http://pdg.lbl.gov

• http://www.cpepweb.org/

Books

• Particle physics in the cosmos

• Atomic building blocks of Matter

• Particle physics, the new view of the Universe