The Physics
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# Quantum Chromodynamics

## Discussion

### disorganized notes

Quantum chromodynamics (QCD)

The QCD story begins with pions — the force carriers between nucleons — their prediction and discovery. This is then followed by a "particle zoo" that begs for simplification — quarks and gluons are the answer. The strong force vs. the nuclear force a.k.a. the residual strong force.

Quarks are the matter particles. Gluons are the force particles. There are 6 known quarks with fanciful names. The names have no relation to the properties of the particles.

• up
• down
• charm
• strange
• top
• bottom

Quarks and gluons exist only in groups (in the "low" temperature realm below 1012 K).

• meson: quark-antiquark pair (qq)
• tetraquark: two quarks-two antiquarks (qqqq) or a meson "molecule" (qq qq)
• pentaquark: four quarks and one antiquark (qqqqq) or a hadron-meson "dimer" (qqq qq)

Ordinary matter is composed of up and down quarks.

• proton: up up down
• neutron: up down down

### color

The concept of charge was introduced to understand how electrostatic forces work. Electric charge comes in two types, identified as positive and negative because of the mathematical analogy between positive and negative numbers. Equal amounts of positive and negative charge give rise to neutral matter with an overall charge value of zero. Also, the rule of action, where opposite charges attract and like charges repel, agrees with the sign rules for multiplication if we assume that a negative force is attractive and a positive force is repulsive.

Product rule for signs (with the corresponding action)
signs +
+ +
(repulsion)

(attraction)

(attraction)
+
(repulsion)

Mass is the analog for charge in gravitation. The rule of action here is that like masses attract. Mass is always positive in sign, which the table above seems to say would give a repulsive force. This is why fancier versions of Newton's law of universal gravitation come with a minus sign out front.

 Fg = − Gm1m2 r̂ r2

For the strong force, the analog for charge is called color (or, according to the Department of Redundancy Department, color charge). Color is a property of quarks and gluons. Color comes in three types: red (r), green (g), and blue (b). Or in the case of antiquarks: antired (r), antigreen (g), and antiblue (b). Or in the case of gluons, certain combinations of the three colors and three anticolors. (More on that later.) The rule of action here is that different colors attract, except when they are very close. The interaction between particles with color is something like that of a spring. Extend it beyond its natural length and it wants to draw back. Compress is to less than its natural length and it wants to push out. The strong interaction is sometimes described as attractive with a repulsive core.

gravita­tion electro­magnetism strong interaction
fundamental quantity mass
(mass-energy)
charge
(electric charge)
color
(color charge)
types mass is mass, there are no "types" positive (+), negative (−) red (r), green (g), blue (b), antired (r), antigreen (g), antiblue (b)
rule of action always attractive opposites attract attractive with a repulsive core

### tubes of flux

Photons carry the electromagnetic force between particles with electric charge (electrons and protons, for example). The force can be visualized as a field that spreads out over three dimensional space, getting farther and farther apart. The electromagnetic field gets weaker with distance. Since space is, as far as we can tell, three-dimensional, the field strength is inversely proportional to distance.

 E ∝ 1 r2

Gluons carry the strong force between particles with color charge (quarks and other gluons). The force can also be visualized a field, but as one that does not spread out. Unlike photons, which basically ignore one another, gluons attract each other. The field lines that one would draw get pulled closer and closer together as distance increases forming a tube. The color field gets stronger with distance not weaker — until the tube breaks into smaller tubes. (It's complicated.)

Fcolor ~ r

### history

QCD people

Rutherford-style scattering experiments showed a three part structure for the proton.

George Zweig

Both mesons and baryons are constructed from a set of three fundamental particles called aces. The aces break up into an isospin doublet and singlet. Each ace carries baryon number ⅓ and is fractionally charged.

George Zweig, 1964

Murray Gell-Mann

A simpler and more elegant scheme can be constructed if we allow non-integral values for the charges. We can dispense entirely with the basic baryon b if we assign to the triplet t the following properties: spin ½, z = −⅓, and baryon number ⅓. We then refer to the members u, d−⅓, and s−⅓ of the triplet as "quarks" q and the members of the anti-triplet as anti-quarks q. Baryons can now be constructed from quarks by using the combinations (qqq), (qqqqq), etc., while mesons are made out of (qq), (qqqq), etc.

Murray Gell-Mann, 1964

Murray Gell-Mann

In 1963, when I assigned the name "quark" to the fundamental constituents of the nucleon, I had the sound first, without the spelling, which could have been "kwork." Then, in one of my occasional perusals of Finnegans Wake, by James Joyce, I came across the word "quark" in the phrase "Three quarks for Muster Mark." Since "quark" (meaning, for one thing, the cry of a gull) was clearly intended to rhyme with "Mark," as well as "bark" and other such words, I had to find an excuse to pronounce it as "kwork." But the book represents the dreams of a publican named Humphrey Chimpden Earwicker. Words in the text are typically drawn from several sources at once, like the "portmanteau words" in Through the Looking Glass. From time to time, phrases occur in the book that are partially determined by calls for drinks at the bar. I argued, therefore, that perhaps one of the multiple sources of the cry "Three quarks for Muster Mark" might be "Three quarts for Mister Mark," in which case the pronunciation "kwork" would not be totally unjustified. In any case, the number three fitted perfectly the way quarks occur in nature.

James Joyce. Finnegans Wake. Book 2, Episode 4, Page 383

Three quarks for Muster Mark!
Sure he hasn't got much of a bark
And sure any he has it's all beside the mark.
But O, Wreneagle Almighty, wouldn't un be a sky of a lark
To see that old buzzard whooping about for uns shirt in the dark
And he hunting round for uns speckled trousers around by Palmerstown Park?

Hohohoho, moulty Mark!
You're the rummest old rooster ever flopped out of a Noah's ark
And you think you're cock of the wark.
Fowls, up! Tristy's the spry young spark
That'll tread her and wed her and bed her and red her
Without ever winking the tail of a feather
And that's how that chap's going to make his money and mark!

Overhoved, shrillgleescreaming. That song sang seaswans. The winging ones. Seahawk, seagull, curlew and plover, kestrel and capercallzie. All the birds of the sea they trolled out rightbold when they smacked the big kuss of Trustan with Usolde.

Timeline

1. James Chadwick and E.S. Bieler conclude that some strong force holds the nucleus together.
2. Condon, Gamow, Gurney, alpha emission is due to quantum tunneling
3. Hideki Yukawa combines relativity and quantum theory to describe nuclear interactions by an exchange of new particles (mesons called "pions") between protons and neutrons. From the size of the nucleus, Yukawa concludes that the mass of the conjectured particles (mesons) is about 200 electron masses. This is the beginning of the meson theory of nuclear forces. (1933–1934)
4. Hideki Yukawa presents a theory of strong interactions and predicts mesons
5. Seth Neddermeyer, Carl Anderson, J.C. Street, and E.C. Stevenson discover muons using cloud chamber measurements of cosmic rays
6. A particle of 200 electron masses is discovered in cosmic rays. While at first physicists thought it was Yukawa's pion, it was later discovered to be a muon.
7. Physicists realize that the cosmic ray particle thought to be Yukawa's meson is instead a "muon," the first particle of the second generation of matter particles to be found. This discovery was completely unexpected — I.I. Rabi comments "who ordered that?" The term "lepton" is introduced to describe objects that do not interact too strongly (electrons and muons are both leptons).
8. Cecil Powell, C.M.G. Lattes, and G.P.S. Occhialini discover the pi meson by studying cosmic ray tracks
9. A meson that does interact strongly is found in cosmic rays, and is determined to be the pion.
10. Enrico Fermi and C.N. Yang suggest that a pion is a composite structure of a nucleon and an anti-nucleon. This idea of composite particles is quite radical.
11. Discovery of K+ via its decay.
12. The neutral pion is discovered.
13. Two new types of particles are discovered in cosmic rays. They are discovered by looking a V-like tracks and reconstructing the electrically-neutral object that must have decayed to produce the two charged objects that left the tracks. The particles were named the lambda0 and the K0.
14. Martin Deutsch discovers positronium
15. Discovery of particle called delta: there were four similar particles (∆++, ∆+, ∆0, and ∆.)
16. The beginning of a "particle explosion" — a true proliferation of particles.
17. Scattering of electrons off nuclei reveals a charge density distribution inside protons, and even neutrons. Description of this electromagnetic structure of protons and neutrons suggests some kind of internal structure to these objects, though they are still regarded as fundamental particles.
18. The concept of strangeness is introduced by by Gell-Mann and Nishijima to explain why some exotic particles seemed to decay too slowly. (They decay via the weak interaction, described in the next section of this book.)
19. C.N. Yang and Robert Mills develop a new class of theories called "gauge theories." Although not realized at the time, this type of theory now forms the basis of the standard model.
20. Murray Gell-Mann and Yuval Ne'eman discover the Eightfold Way patterns — SU(3) group. Jeffery Goldstone considers the breaking of global phase symmetry. As the number of known particles keep increasing, a mathematical classification scheme to organize the particles (the group SU(3)) helps physicists recognize patterns of particle types.
21. The first three quarks are proposed by Gell-Mann and Zweig (up, down, and strange). The notion of color charge is proposed by Greenberg. A fourth quantum number dubbed "charm" was proposed by Bjorken and Glashow to counterbalance the "strangeness" carried by the strange quark.
22. Nambu and and Han describe the SU(3) symmetry for quarks. It later came to be called color symmetry.
23. Richard Taylor, Jerome Friedman, and Henry Kendall used Stanford University's linear electron accelerator to probe this fuzzball by shooting electrons at protons. Some of the electrons scattered quite strongly, revealing that the proton was not simply a uniform smear of matter. Later that year, theoretical analysis by James Bjorken suggested that this scattering could result from point-like constituents within the proton.
24. High-Energy Inelastic e-p Scattering at 6° and 10° & Observed Behavior of Highly Inelastic Electron-Proton Scattering
25. Sheldon Glashow, John Iliopoulos, and Luciano Maiani propose the charm quark
26. Burton Richter and Samuel Ting discover the psi meson implying the existence of the charm quark. Evidence for a fourth quark is found in November of 1974. Two experiments (one at BNL the other at SLAC) simultaneously announced the discovery of a meson with a mass of about 3.1 GeV/c2. Called the J meson by BNL and the ψ meson by SLAC it was later determined to be a combination of charm and anticharm quarks. Since neither group had priority on the discovery, the meson is now called J/ψ. Like many particles discovered in the 20th century, it was also given a whimsical name, charmonium.
27. The names top and bottom were introduced by Haim Harari to match the names of the first generation of quarks (up and down).
28. Unexpected discovery of the bottom quark. The bottom quark was discovered in 1977 by the Fermilab E288 experiment team led by Leon M. Lederman, when collisions produced bottomonium.
29. Mass of the top quark finally determined. The top quark is more massive than many atoms and it is so unstable that is does not live long enough to combine with other quarks to form a hadron.

18 quarks + 18 antiquarks

All 36 quarks
first generation second generation third generation
up
family
red up red charm red top quarks
blue up blue charm blue top
green up green charm green top
down
family
red down red strange red bottom
blue down blue strange blue bottom
green down green strange green bottom
up
family
anti­red anti­up anti­red anti­charm anti­red anti­top anti­quarks
anti­blue anti­up anti­blue anti­charm anti­blue anti­top
anti­green anti­up anti­green anti­charm anti­green anti­top
down
family
anti­red anti­down anti­red anti­strange anti­red anti­bottom
anti­blue anti­down anti­blue anti­strange anti­blue anti­bottom
anti­green anti­down anti­green anti­strange anti­green anti­bottom

There should be 9 gluons, but there ain't. Effectively, gluons behave like the color-anticolor pairs shown in this table.

Effective gluon color-anticolor pairs
red green blue
anti­red rr gr br
anti­green rg gg bg
anti­blue rb gb bb

Because of the way real QCD works, as opposed to how introductory textbook physics explains it, the actual gluons exist as weird superpositions of the effective gluons.

There are 8 gluons. You really can't put them in table form. It's more like a list. Here's one way to list them. It's kind of a "textbook" order that looks nice (and sort of makes better sense).

 rb + br √2
 −i(rb − br) √2

 rg + gr √2
 −i(rg − gr) √2

 gb + bg √2
 −i(gb − bg) √2

 rr − bb √2
 rr + bb − 2gg √6

Here's another way to list them. This is the way Murray Gell-Mann originally ordered them because of reasons that I don't understand.

 rb + br √2
 −i(rb − br) √2
 rr − bb √2
 rg + gr √2

 −i(rg − gr) √2
 gb + bg √2
 −i(gb − bg) √2
 rr + bb − 2gg √6

The order corresponds to what are now known as the Gell-Mann matrices. Quarks go by columns. Antiquarks by rows. The color sequence is red-blue-green instead of red-green-blue, for some odd reason. See if you can convince yourself that the list above and the list below are the same thing. If matrices aren't your thing, this might be hard to do.

 λ1 = ⎛⎜⎜⎝ 0 +1 0 ⎞⎟⎟⎠ +1 0 0 0 0 0
 λ2 = ⎛⎜⎜⎝ 0 −i 0 ⎞⎟⎟⎠ +i 0 0 0 0 0
 λ3 = ⎛⎜⎜⎝ +1 0 0 ⎞⎟⎟⎠ 0 −1 0 0 0 0
 λ4 = ⎛⎜⎜⎝ 0 0 +1 ⎞⎟⎟⎠ 0 0 0 +1 0 0

 λ5 = ⎛⎜⎜⎝ 0 0 −i ⎞⎟⎟⎠ 0 0 0 +i 0 0
 λ6 = ⎛⎜⎜⎝ 0 0 0 ⎞⎟⎟⎠ 0 0 +1 0 +1 0
 λ7 = ⎛⎜⎜⎝ 0 0 0 ⎞⎟⎟⎠ 0 0 −i 0 +i 0
 λ8 = 1 √3

+1 0 0

0 +1 0
0 0 −2