Classifying reported and missing resonances according to their P and C properties
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abstract
The Hubert space ℋ3q of the three quarks with one excited quark is decomposed into Lorentz group representations. It is shown that the quantum numbers of the reported and missing resonances fall apart and populate distinct representations that differ by their parity or/and charge conjugation properties. In this way, reported and missing resonances become distinguishable. For example, resonances from the full listing reported by the Particle Data Group are accommodated by Rarita-Schwinger (RS) type representations {k/2, k/2} ⊗ [{1/2, 0} ⊗ {0, 1/2}] with k = 1,3, and 5, the highest spin states being J = 3/2-, 7/2%2b, and 11/2%2b, respectively. In contrast to this, most of the missing resonances fall into the opposite parity RS fields of highest-spins 5/2-, 5/2%2b, and 9/2%2b, respectively. Rarita-Schwinger fields with physical resonances as lower-spin components can be treated as a whole without imposing auxiliary conditions on them. Such fields do not suffer the Velo-Zwanziger problem but propagate causally in the presence of electromagnetic fields. The pathologies associated with RS fields arise basically because of the attempt to use them to describe isolated spin-J = k %2b 1/2 states, rather than multispin-parity clusters. The positions of the observed RS clusters and their spacing are well explained trough the interplay between the rotational-like k/2 (k/2 %2b 1)-rule and a Balmer-like -1/(k%2b1)2-behavior.
