Flavour symmetry

As already mentioned, the flavour symmetry SU 3)p of Gell-Mann and Neeman was very successful in providing a classification of the old (i.e. pre-charm) spectroscopy. The quantum numbers of each hadron were... 

Even in the absence of flavour symmetry, the quark model of hadrons correctly predicts the quantum numbers of the hadrons, the charm pseudoscalars D" = (cd),D = (c ),D+ = (cs), their vector counterparts D" " = (cd) etc. and the bottom pseudo-scalars B = (iwi),B = (1x1), B = (bs) etc. Detailed tables of heavy flavoiured hadrons are given in Chapter 13. 

Whereas the spatial part of the wave function requires detailed information about the interaction, the spin and flavour parts of the wave function can be worked out in a straightforward way if exact flavour symmetry is... 

In dynamical calculations, e.g. the quarkonium model, one does not impose exact flavour symmetry. However, attempts have been made to extend SU 3)f to more flavours. Details can be found in Lichtenberg (1978). 

Spectrum, the excitation patterns, i.e., the vertical aspects of the spectrum were quite well described in terms of the harmonic-oscillator model [4]. More meson-nucleon resonances have been identified meanwhile [5], all fitting quite well into the picture of the three-quark model with spin, radial, or orbital excitations [6]. These early baryons approximately obey SU(3)f flavour symmetry the wave function, including colour, spin, space, and flavour degrees of freedom, is antisymmetric under the exchange of any pair of quarks. The changes induced by the mass difference between the d and the u quarks or between the ordinary and the strange quarks can be treated as small corrections. 

Thus, by the end of 1977, five flavours of quark (u, d, s, c, b) were known to exist together with six flavours of lepton (e, p, t, Ve, Tp vj. Assuming that quarks and leptons are the fundamental constituents of matter, many of the strong and weak interactions of hadrons and the weak interactions of leptons can be explained. However, anticipating a symmetry in nature s building blocks, it was expected that a sixth quark would eventually reveal itself. This quark, labelled top (t), would be the 2/3 electronic charge partner to the b quark (see table). 

The thermal cycloaddition of two ethylenes is one of the textbook examples used in the illustration of the Woodward-Hoffmann rules of orbital symmetry control in concerted reactions. Therefore, the related potential energy surface can provide various types of information of chemical and theoretical interest. A first question is associated with the mechanistic question of whether this reaction proceeds via diradical or concerted pathways. Since this reaction is an example of a concerted thermally forbidden process, it can be expected that the flavoured path be the diradical one. However, it is important to have a detailed description of the structural and energetic features of these different pathways. A second question is associated... 

Now that we believe that quarks come in six flavours, SU(3) f cannot be an exact symmetry. It is somewhat ironic that a new SU(3) symmetry [517(3)cr] has now emerged as an exact ssunmetry of nature. 

The wave functions are often labelled with N, the number of quanta, with /, the total angular momentum and parity, and with the dimension of the SU(6) representation. The Hamiltonian (3.43) has, indeed, a symmetry of structure U(6) = SU(6) x U(l), where U(l) is associated with the number of quanta N [6]. In fact, SU(6) also denotes another symmetry combining spin and flavour. It becomes exact when one neglects hyperfine effects and takes the limit of equal quark masses m = m = m. We refer to the specialized literature [6] for these group-theoretical aspects of the harmonic oscillator. For our purpose, it is sufficient to know the following correspondence between SU(6) representations and permutation properties ... 

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