By Simon R. Swindell
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Extra resources for [(Sequence Data Analysis Guidebook: Pt. 3 )] [Author: Simon R. Swindell] [Apr-1997]
With d = −c/4, this is the Gell-Mann–Okubo mass formula that was used by Gell-Mann 1964 to order the baryon resonances into a decuplet and to predict the mass of the Ω− . 101) is good within a few per cent for the baryons but does not work well for the mesons. 52 CHAPTER 3. 4: Baryon multiplets of SU (3). 5: Meson multiplets of SU (3). (a) Octet of pseudoscalar mesons with J π = 0− ; (b) octet of vector mesons with J π = 1− Chapter 4 Quarks In Chap. 3 it was shown how the observed strongly interacting particles can be grouped into multiplets according to the relevant symmetry group.
Multiplets. To determine the isospin T (defined via the eigenvalue T (T + 1) of the operator T 2 , which is just the Casimir operator of SU (2)) of a multiplet, we make use of the similarity of the group SU (2) and the group of spatial rotations in three dimensions, SO(3), whose generators are the angular momentum operators; both groups have the same algebra. A well known example for an SO(3) symmetry is the hydrogen atom. There the spectrum consists of 2L + 1 dimensional multiplets labeled by the eigenvalues of the Casimir operator L2 ; the states in each multiplet are labeled by L3 .
The conservation of the total electric charge of a closed system can be deduced from the electric neutrality of macroscopic matter. This yields very stringent tests for the conservation of charge with time. Furthermore, in all known reactions charge is also conserved; for example, in the β-decay of the neutron one finds for the relative change of charge: ∆q/q ≤ 10−23 . Particles and resonance states that decay ultimately into protons are called baryons. These particles all have half-integer spins and masses higher than that of the nucleon.