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Chapter 32 Lecture Notes Physics 2424 - Strauss

Formulas: mc2 ≈ hc/2πd 1. INTRODUCTION What are the most fundamental and what are the most fundamental that make up the ? For a brick house, the fundamental building blocks (particles) are bricks and the fundamental , or glue, is the mortar that holds the bricks together. With these two elements, bricks and mortar, any variety of brick house can be built.

In 1930, the answer to the question of what are the most fundamental particles and forces in the universe would have been the , the , and the for the particles, and gravity, and electromagnetism for the forces. The answer was pretty easy. Then things started to happen. The , a massless produced in , was proposed in 1930 (although not discovered until 1956). In 1937 a particle very much like the electron, but much heavier, now called a was discovered. Then in the 1950’s and 1960’s as particle accelerators were constructed many new particles were discovered. These particles had similarities to the neutron and proton but were also different. Just like the periodic table demonstrates some underlying structure to , many people thought that this proliferation of similar particles demonstrated that there was some underlying structure. This has led to an understanding of nature called the of Elementary Particles and Fields. 2. PARTICLES We now know that there are two main classes of truly elementary (fundamental) particles, called and . There are six leptons and six quarks and they are classified as being in pairs.

Leptons (six of them) Quarks (six of them) − e−   µ  τ −  u c  t  ←+23e             ν  ν ν        ←− e  µ  τ d s b 13e

The names for the six leptons are the electron, the , the muon, the , the , and the . The six quarks are the up, down, charm, strange, top, and bottom quarks. The have no electric . The other three leptons all have an of Ðe, where e is the charge of the proton. The electrical charge of the up, the charm, and the

1 top is +(2/3)e. The electrical charge of the down, the strange, and the are Ð(1/3)e. 2.1 Leptons Leptons are themselves fundamental. The electron is a lepton, so it is a fundamental particle. Leptons are not easily bound together. They are bound together loosely in an where the electron is attracted to the nucleus. Even then they are very weakly bound compared to the particles bound in the nucleus. Other than in the atom, they are usually found free, not bound to any other particle. Cosmic rays which continually bombard us on earth, are mostly µ. 2.2 Quarks Quarks on the other hand are always tightly bound together. In fact, a single free quark, (a quark existing by itself), has never been seen. They are either bound together in groups of three’s or in a quark and an antiquark.

We have been introduced to antiparticles when we talked about the . Every particle above has an antiparticle. Antiparticles have the same as particles and opposite charge. There is mostly matter (particles) in the universe and very little anti-matter (antiparticles). We have some ideas why that may be, but we need to study it further. When first discovered, we thought there were 3 kinds of quarks so the name “quark” was used because it was a nonsense word in James Joyce’s novel, Finnegan’s Wake. The sentence in the novel says, “Three quarks for Muster Mark” -James Joyce Finnegan’s Wake. . (We now know there are six kinds of quarks and not just three kinds).

Any particle made of quarks is called a . There are two classes of . Those made of three quarks (or three antiquarks) are called (which means “heavy”). The neutron and the proton are baryons and made of the three quarks shown below. Those made of a quark and an antiquark are called .

2.2.1 BARYONS (GROUPS OF 3) We get the charge of the proton and neutron by adding up the charges of their constituent quarks.

p (uud) The electric charge is q = (2/3) + (2/3) + (-1/3) = 1 n (udd) The electric charge is q = (2/3) + (-1/3) + (-1/3) = 0

Almost every property of neutron and proton can be explained as a of 3 quarks. Everyday matter consists almost entirely of , and up and down quarks, since and are made of up and down quarks, and are made of neutrons, protons and electrons.

2 Virtually all the other particles made of quarks are unstable and decay in about 10-6 to 10-23 seconds. In fact, any combination of three quarks can be combined to form a particle. Most of these have been created and seen in collisions or in particle accelerators.

For instance, a particle called the lambda (Λ) particle is made up of a uds combination and has an electric charge of 0 (2/3-1/3-1/3).

Another made of three quarks is called the omega-minus. (Ω-) and is made up of three strange quarks (sss), with an electric charge of -1. Any combination of three antiquarks will produce an anti-baryon. For instance, an is made up of an two antiup quarks and one antidown quark with an electric charge of -1!

2.2.2 MESONS (QUARK AND ANTIQUARK) The second major category of hadrons are called mesons (“medium weight”). These are made up of one quark and one antiquark Some mesons include:

π+ (ud) (pi plus, with a charge of 2/3 + 1/3 = 1) π- (ud) (pi minus, with a charge of -2/3 - 1/3 = -1) π0 (uu) (pi nought, with a charge of +2/3 - 2/3 = 0) K+ (us) (K plus with a charge 2/3 + 1/3 = 1)

Any sets of quarks and antiquarks combined will make a particle. 3. INTERACTIONS Particles interact via forces. It is also these forces which bind the particles together. In fact, particles are classified as leptons, quarks, or whatever based on the type of interactions in which they participate.

Particles don’t necessary have mass, but they do interact. For instance, neutrinos and have no mass, but are particles. (Of course, we also know that all particles are waves, too).

When we talked about earlier in the semester, we talked about electric fields. One model of a would consist of particles interacting in space. This is Yukawa’s idea discussed in the textbook. Remember, these are only models. We can think of an interaction between two particles as taking place because a third particle is exchanged, or transferred, between the first two particles. The forces of nature consist of “force” particles being exchanged between “matter” particles. The leptons and quarks are “matter” particles.

3 We say that if two particle with an electric charge are repelled from (or attracted to) each other, that is because they “exchanged,” or transferred, a between them which changed their respective momentums. The photon is called the “carrier” of the electromagnetic force, because any two particles with electric charge will interact when they exchange a photon.

Electron

Photon

Another Electron

There are four major forces in nature: gravity, electromagnetism, the weak nuclear force, and the strong nuclear force. In the last 20 years, the weak nuclear force and electromagnetic force have been shown to be different manifestations of the same force, so in some sense, there are only three unique forces of nature. We list the electromagnetic force separately from the weak force, but we know that at very high energies, they combine into a single unified force. The following paragraphs will list the force, the particle which carries the force, and then the property of the particle which allows it to interact via that force. For instance for the electromagnetic force, the photon is the carrier, and any particle with electric charge interacts via the electromagnetic force.

Electromagnetic (photons -- electric charge) Anything with an electric charge interacts via a photon. (Would a neutron? No. A proton? Yes. A quark? A neutrino?)

Gravity: ( - (not yet discovered) -- mass/energy) Anything with mass (or energy) interacts via . Even photons, with no mass but energy, have been shown to bend around stars because of the star’s gravitational attraction. Gravity is very weak and not important in most interactions in the world. All particles interact via gravity.

Strong Nuclear Force: ( -- 8 different kinds -- The charge is the strong charge.) There is only one kind of electric charge which is either plus or minus. However, there are three kinds of strong nuclear charge. We need to name them. We could call them kind 1 positive, kind 1 negative, etc. Instead, we call them colors and anticolors. This has nothing to do with actual color as we know it. It is a label (because there are 3 primary colors and 3 types of strong nuclear force). For a particle to interact via the strong nuclear force, it must have a

4 strong . Only quarks and gluons have a strong color charge. So only quarks and gluons interact via the strong nuclear force. Also, things made of quarks and gluons interact via the strong force. (This is due to something like van-der Waals force which binds together even though they may be electrically neutral). So all Hadrons interact via the strong nuclear force.

There is a very interesting thing about gluons. They can interact with themselves because they carry color themselves. (This is in contrast to photons which can not interact with themselves because they do not carry electric charge themselves). Actually, gluons tend to carry both a color and an anticolor. Then, when a is exchanged from one quark to another, it carries color from one quark to the other, and they each change their color. So the color of an individual quark is constantly changing. In reality it is impossible to tell the color of any quark or gluon at any moment. All we know is that the baryon itself is colorless, which means made up of one green, one blue, and one red quark, or that the has one color and the same anticolor.

Weak Nuclear Force: (Intermediate Vector , three kinds W+, W-, and Z0 - the charge has no name but is sometimes called the weak charge). All particles we know of interact via the weak nuclear force. Neutrinos only interact via the weak nuclear force and are produced naturally in nature during all radioactive beta decays.

The weak nuclear force is a very short ranged force because the Intermediate Vector Bosons that mediate the force are so massive. In most cases, there isn’t enough energy to create the particle which mediates this force, so we can only create it quantum mechanically using Heisenberg’s .

∆E∆t ≈ h/2π mc2(d/c) = h/2π mc2 = hc/2πd d = h/2πmc

If m is very large, then the distance the force acts d, is very small.

So here is a chart listing properties of the fundamental forces.

Particles Relative Force Charge Carrier(s) Affected Strength Range Gravity Mass/Energy Graviton All 10-38 ∞(1/r2) Weak Nuclear “Weak” IVB (3) All 10-1 <10-18 m Electromagnetic Electric Charge Photon (1) Charged 10-2 ∞(1/r2) Strong Nuclear “Color”-3 kinds Gluons (8) Quarks/Hadrons 1 ≈10-15 m

5 4. THE FUTURE What is there still to explore about elementary particles and forces? 1. The Standard Model predicts a particle called the Higgs should be found. This would help us understand why other particles have the specific mass that they do. 2. Are quarks and leptons made of still more fundamental objects? The search for smaller components of the quarks and leptons, or compositeness, is continuing? 3. Are there more undiscoverd particles? One theory called “” predicts that there are many more very exotic undiscovered particles. 4. What about Grand Unified Theories? We believe that all forces are really manifestations of some more fundamental force. We have already seen that electricity and magnetism, which used to be thought of as two separate forces are really different manifestations of the same force. (We have seen that moving electric charges produces magnetic fields, and changing magnetic fluxes produce electric fields). We also know now that the electromagnetic and weak nuclear forces have been shown to be manifestations of the same force. At very high energies, they are indistinguishable, and we call the force the electro-weak force. There is an effort to unify the strong nuclear force with this force. The unification of these three forces into one theory is called a “Grand Unified Theory” (GUT). Eventually gravity should also be unified into a single theory of forces. 5. EXPERIMENTS How do we determine what the fundamental forces and particles are? How do we know how anything is put together? What about a car? There are three ways we know how something is put together.

1. Have someone tell us 2. Take it Apart (or look inside of it) 3. Put it together

5.1 Take It Apart - Look Inside Probe inside of it. Recall Rutherford’s experiment to study the atom. Also recall the De Broglie wavelength, λ=h/p. If I want to probe something very small, I need a very small wavelength (λ). I get that from a very large (p). So I accelerate electrons or protons to large speeds and smash them into an object. That is one of the experiments leading to the discovery of the quark.

6 5.2 Put It Together How do we put it together? To create matter, we need the stuff that matter is made of. Since, matter is a form of energy (E = mc2), I can create matter from energy. If I collide two beams together, one with antiparticles and one with particles, they will annihilate each other and will create the same amount of energy as the sum of their total energies (kinetic energy plus mass energy of both particles). This energy can change into mass.

1) Here is a particle and an antiparticle

2) They collide to make energy (could be a photon)

3) The energy produces any particle and its antiparticle (as long as the sum of the of the particle and antiparticle is less than the energy we started with). Any extra energy goes into kinetic energy of the particles.

4) If this particle and antiparticle are quarks, as the separate, the strong nuclear force acts like a rubber band which stretches,

5) Eventually the rubber band breaks and from the energy stored in the rubber band, we create another quark and antiquark. This is called hadronization because we are producing hadrons.

6) This process can continue to create a lot of hadrons.

So in our detector, we see a whole lot hadrons if we started out with one quark and one antiquark.

7 Problem: In the reaction π- + p → n + π0 the proton was initially at rest. The final kinetic energies of the neutron and the are 0.4 MeV and 2.9 MeV, respectively. Determine the initial kinetic energy of the π-. (Rest energies in MeV are π- = 139.6; π0 =135.0; p = 938.3; n=939.6)

6. COSMOLOGY High energy is related to the early universe because as we accelerate particles to very high energies, we probe what the universe was like during the first few minutes of the . During that time the universe was very small, very hot, and very dense, just like the high energy collisions which are produced in the laboratory.

Big Bang 10-43s10-35s 10-10s 10-6s 3 min 700,000 years 15 billion years

1032K 1027K 1013K 1010K 3000 K 3 K 1019GeV 1014GeV 1GeV 1 MeV 0.3 eV 3×10-4 eV

GUTs Quarks and Hadrons Nuclei Atoms, Stars, and Leptons Form Form Galaxies form

To go from temperature to energy use, ENERGY ≈ kT ≈ 10-4 eV/K where k is Boltzman’s constant which is 1.4 × 10-23 J/K.

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