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Quark Soup

Quark Soup. U C T. d S b. Elementary Particles?? (circa 1960) p  (pions), l, r, w, y, h K  , , etc proton neutron D 0 S + X 0 L, L c, L b, Etc www-pnp.physics.ox.ac.uk/~huffman/.

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Quark Soup

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  1. Quark Soup U C T d S b Elementary Particles?? (circa 1960) p(pions), l, r, w, y, h K, , etc proton neutron D0 S+ X0 L, Lc, Lb, Etc www-pnp.physics.ox.ac.uk/~huffman/

  2. Long before the discovery of quantum mechanics, the Periodic table of the Elements gave chemists a testable model with enough predictive power to search for the missing ones. Result: Discovery of Ge and Ga (among others)

  3. Examples of Similarities among ‘elementary’ particles Total Spin 1/2: p+ n  938, 939 (all masses in MeV) 0  1116 + 0 -  1189,1192, 1197 0 -  1315, 1321 D++, D+, D0, D-  1231, 1235, 1234, 1235(?) Total Spin 0: 0  139, 134 (all masses in MeV) 0  547 K K0LK0S 494, 497 ’ 0  958 D D0 1869, 1864 c0  2980 These similarities are what has led to the quark model of particle bound states.

  4. Meson Baryon Quarks: up charm top down strange bottom Quark Model Botany lessons: Hadrons: Everything that is a bound state of the quarks which are spin 1/2 (Fermions). Held together by the strong nuclear force. Hadrons split into two sub-classes: Mesons: bound quark- antiquark pairs. Bosons; none are stable; copiously produced in interactions involving nuclear particles. Baryons: bound groups of 3 quarks or 3 antiquarks. Fermions; proton is stable; neutron is almost stable; copiously produced in interactions involving nuclear particles. Conservation of Baryon number  conservation of quark number

  5. Leptons:electron muon tau ne nmnt  neutrinos More Botany lessons: Each individual Lepton number is conserved exactly in all interactions electron number, muon number, and tau number are all conserved. (But New Discovery of Neutrino oscillations at SNO!) You will learn about this later in the course. Leptons do not form any stable bound states with themselves, only with hadrons (in atoms). Since Leptons also do not interact with the strong nuclear force, we will not discuss them much further in this part of the course.

  6. The Hadrons - composite structures The Leptons - ‘elementary’ What does ‘elementary’ mean? ANS: an exact geometric point in space. Are the quarks and leptons black holes? ANS: Beats me! The Fermions of the Standard Model

  7. What Makes a Theory “Good”? Any theory … not just a theory of matter and Energy.

  8. Falsifiable!

  9. The only Example There is also a complete octet where L = 1 but you will never see it. JP = 1/2+ Baryon Octet: S 0 -1 -2 Notes: U+D-S = 3 for all Baryon states. Quark compositions are NOT the same as quark wave functions I3 0 -1 1 1/2 -1/2

  10. 0 -1 -2 -1 -1/2 The only Example JP = 3/2+ Baryon Decuplet: S -3 I3 0 1 -3/2 3/2 1/2

  11. S 1 0 -1 0 -1 1 1/2 -1/2 Examples Pseudoscalars JP = 0- Meson Nonets: Vector Mesons JP = 1- Q = 1 Q = 0 Q = -1 I3

  12. Much Ado about Isospin(apologies for revealing my bias) Talk about ad hoc! First we make ‘upness’ and ‘downness’ and then proceed to make this Isospin quantum number, the ‘z’ component of which is really just 1/2 times up-ness or down-ness. Legitimate question: Is this useful at all? Why is there no uuu or ddd state in the spin 1/2 Baryon chart? Before we get much deeper into Isospin though, it would be a good idea to divert somewhat and revision on spin 1/2 particles and introduce the Special Unitary group in Two dimensions (the infamous SU(2)).

  13. 1 +1 1 0 +1/2 +1/2 1 0 0 +1/2 -1/2 1/2 1/2 1 -1/2 +1/2 1/2 - 1/2 - 1 -1/2 -1/2 1 3/2 +3/2 3/2 1/2 +1 +1/2 1 +1/2 + 1/2 +1 -1/2 1/3 2/3 3/2 1/2 0 +1/2 2/3 -1/3 -1/2 -1/2 0 -1/2 2/3 1/3 3/2 -1 +1/2 1/3 -2/3 -3/2 -1 -1/2 1 Clebsch-Gordan Coefficients J J M M m1 m2 m1 m2 . . . . Notation: 1/2 x 1/2 coefficient 1 x 1/2 Note: A square-root sign is to be understood over every coefficient, e.g., for -8/15, read -(8/15).

  14. J J M M m1 m2 m1 m2 . . . . Notation: 5/2 +5/2 5/2 3/2 +3/2 +1 1 +3/2 +3/2 +3/2 0 2/5 3/5 5/2 3/2 1/2 +1/2 +1 3/5 -2/5 +1/2 +1/2 +1/2 +3/2 -1 1/10 2/5 1/2 +1/2 0 3/5 1/15 -1/3 5/2 3/2 1/2 -1/2 +1 3/10 -8/15 1/6 -1/2 -1/2 -1/2 +1/2 -1 3/10 8/15 1/6 -1/2 0 3/5 -1/15 -1/3 5/2 3/2 -3/2 +1 1/10 -2/5 1/2 -3/2 -3/2 -1/2 -1 3/5 2/5 5/2 -3/2 0 2/5 -3/5 -5/2 -3/2 -1 1 coefficient Clebsch-Gordan Coefficients 3/2 x 1 Note: A square-root sign is to be understood over every coefficient, e.g., for -8/15, read -(8/15).

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