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Q = t

where Q is the electric charge, t

Particle | Q | t | t_{3} |
Y |
---|---|---|---|---|

0 | 1/2 | 1/2 | -1 | |

e_{L} |
-1 | 1/2 | -1/2 | -1 |

e_{R} |
-1 | 0 | 0 | -2 |

u | 2/3 | 1/2 | 1/2 | 1/3 |

d | -1/3 | 1/2 | -1/2 | 1/3 |

s | -1/3 | 0 | 0 | -2/3 |

In strong interaction with SU(3) symmetry, the hypercharge for the quarks is generated by the

## Figure 03 Eightfold Way [view large image] |
## Figure 04 Mass Splitting [view large image] |

Another application of global gauge symmetry is to build mesons and baryons from quarks in strong interaction, where the wave functions for the quarks

---------- (20) |

Beginning with the fundamental representation in Eq.(20), all representations of SU(N) can be generated by taking the multiple (tensor) products. For example, the bound states of mesons can be constructed according to the following scheme:

---------- (21) |

Table 02 lists the relation between the meson wave functions and the quark pairs. The value within the brackets is the rest mass in Mev.

In these tables J is the total angular momentum quantum number. The mesons in the middle column belongs to J = 0, while those in the right column belongs to J = 1. In terms of the meson wave functions the octet in Eq.(21) can be re-written in the form of Eq.(22). Similarly, the baryon wave functions are related to the quark triplet as shown in Table 03 and Eq.(23).

This is clearly related to the Eightfold Way (Figure 03) originally proposed by Gell-Mann and Ne'eman in 1961.

Note: These elementary particles were referred to as resonances in the 1960s. Now they are considered as the excited states of hadrons with some of their constituent quarks boosted into higher energy levels. Most of them have a very short lifetime about 10

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