SU(3) Ladder Operators

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Combining uds Quarks to form Baryons Have already seen that constructing Baryon states is a fairly tedious process when we derived the proton wave-function. Concentrate on multiplet structure rather than deriving all the wave-functions. Everything we do here is relevant to the treatment of colour • First combine two quarks: Yields a symmetric sextet and anti-symmetric triplet: Same “pattern” as the anti-quark representation SYMMETRIC ANTI-SYMMETRIC Prof. M.A. Thomson Michaelmas 2011 236 •Now add the third quark: •Best considered in two parts, building on the sextet and triplet. Again concentrate on the multiplet structure (for the wave-functions refer to the discussion of proton wave-function). Building on the sextet: Symmetric Decuplet Mixed Symmetry Octet Prof. M.A. Thomson Michaelmas 2011 237
Building on the triplet: •Just as in the case of uds mesons we are combining obtain an octet and a singlet and again Mixed Symmetry Octet • Can verify the wave-function is a singlet by using ladder operators, e.g. Totally Anti-symmetric Singlet Very Important for following discussion of COLOUR In summary, the combination of three uds quarks decomposes into Prof. M.A. Thomson Michaelmas 2011 238 Baryon Decuplet The baryon states (L=0) are: • the spin 3/2 decuplet of symmetric flavour and symmetric spin wave-functions BARYON DECUPLET (L=0, S=3/2, J=3/2, P= +1 ) Mass in MeV (1232) (1318) (1384) (1672) If <strong>SU</strong>(3) flavour were an exact symmetry all masses would be the same (broken symmetry) Prof. M.A. Thomson Michaelmas 2011 239
Page 1 and 2: Particle Physics Michaelmas Term 20
Page 3 and 4: • In general the symmetry operati
Page 5 and 6: Properties of Isopin • Isospin ha
Page 7 and 8: Derive the states from From the 6
Page 9 and 10: combine mixed symmetry spin and mix
Page 11 and 12: SU(3) Flavour Extend these ideas t
Page 13 and 14: Quarks and anti-quarks in SU(3) Fla
Page 15: It is easy to check that is a singl
Page 19: Appendix: the SU(2) anti-quark repr

SU(3) Ladder Operators

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