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Flavour SU(3)

Flavour SU(3). Origin of SU(3) Why a simple extension of SU(2) is not enough Extending the Graphical method of finding states Application to Baryon and Meson spectrum. Fundamental SU(3) Representation. Fundamental SU(2) Representation. Y. I 3. +2/3. 1. 1/2. -1/2. I 3. 1. 0.

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Flavour SU(3)

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  1. Flavour SU(3) • Origin of SU(3) • Why a simple extension of SU(2) is not enough • Extending the Graphical method of finding states • Application to Baryon and Meson spectrum

  2. Fundamental SU(3) Representation Fundamental SU(2) Representation Y I3 +2/3 1 1/2 -1/2 I3 1 0 1/2 -1/3 0 -2/3 -1/2 -1 Fundamentally Different….see?

  3. Unlike SU(2), antiquarks can’t fit on the graph the same way as quarks Y Y Quarks Antiquarks +2/3 +2/3 1/2 -1/2 I3 1 0 -1/3 -1/2 I3 1 0 1/2 -1/3 -2/3 -2/3

  4. Use Same Graphical method to combine quark- antiquark pairs into mesons Y Y Quarks Antiquarks +2/3 +2/3 1/2 -1/2 I3 1 0 -1/3 -1/2 I3 1 0 1/2 -1/3 -2/3 -2/3

  5. Use Same Graphical method to combine quark- antiquark pairs into mesons Y +1 Caveat: only one of the states at S=I3=0 is fully antisymetric. -1/2 I3 1 0 1/2 -1

  6. Baryon Woes • We have one decplet, two Octets, and one singlet 10s  8ms  8ma  1a. • The decuplet is fully symmetric • The first octet is symmetric in the interchange of the first two quarks. • The second octet is symmetric in the interchange of the second two quarks (therefore antisymmetric in the interchange of the first two quarks). • The singlet is fully antisymmetric in the interchange of any two quarks. • BUT: Nature only has 10s  8s!WHY????

  7. Baryon Woes: The Wave Function • Not a problem in Mesons….a quark and an antiquark are fundamentally distinguishable particles. We have to pay attention to the form of the baryon wave function (antisymmetric, fermion): • Y = y(space)(flavour)(spin)(colour) • (colour) is always antisymmetric • This is related to the fact that no hadron is observed to have any net ‘colour’ charge. • So y(space)(flavour)(spin)  symmetric • Assume, for the moment, that there is no orbital angular momentum between the quarks in the baryon. (l = 0) • Then y(space) will be symmetric.

  8. Baryon Woes: The Wave Function • Y = y(space)(flavour)(spin)(colour) • y(space)l=0symmetric. • So we need (flavour)(spin) to be symmetric also. • Look at (spin) • Combine 3 spin 1/2 objects using SU(2)…the group that correctly handles spins. • 222 = 4s2ms2ma • 4s is symmetric, 2ms is symmetric in the exchange quarks 1 2, 2ma is antisymmetric in the exchange of quarks 1  2. • Combine with 10s  8ms  8ma  1a • (10s  8ms  8ma  1a) (4s2ms2ma)  Keep symmetric ones • (10s 4s) and two (8  2) combinations survive.

  9. Hadrons Are Looking Up! • We can understand/predict a whole bunch of stuff! • Why the Baryons cluster like they do. • IF the strong force is a ‘colour SU(3)c’ group • Why the l=0 Decuplet MUST have j=3/2 spin. • Why the l=0 Octets MUST have j=1/2 spin. • Predicts structure of l0 states as well. (many not found yet). • Can get mass splittings and magnetic moments! • Why the Mesons only form Octets + singlets. • The symmetry we must invoke for more quarks: • SU(4) for Charm…up to SU(6) to get to top quarks. • But this makes NO sense because even SU(4) is broken beyond all recognition.

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