A Solution to the rho-pi Puzzle: Spontaneously Broken Symmetries of the Quark Model
Nov, 197564 pages
Published in:
- Phys.Rev.D 14 (1976) 809
Report number:
- COO-2232B-89
Citations per year
Abstract: (APS)
This article proposes a solution to the long-standing ρ−π puzzle: How can the ρ and π be members of a quark model U(6) 36 and the π be a Nambu-Goldstone boson satisfying partial conservation of the axial-vector current (PCAC)? Our solution to the puzzle requires a revision of conventional concepts regarding the vector mesons ρ, ω, K*, and φ. Just as the π is a Goldstone state, a collective excitation of the Nambu-Jona-Lasinio type, transforming as a member of the (3,¯3) + (¯3,3) representation of the chiral SU(3) × SU(3) group, so also the ρ transforms like (3,¯3) + (¯3,3) and is also a collective state, a "dormant" Goldstone boson that is a true Goldstone boson in the static chiral U(6) × U(6) limit. The static chiral U(6) × U(6) is to be spontaneously broken to static U(6) in the vacuum. Relativisitc effects provide for U(6) breaking and a massive ρ. This viewpoint has many consequences. Vector-meson dominance is a consequence of spontaneously broken chiral symmetry—the mechanism that couples the axial-vector current to the π couples the vector current to the ρ. The transition rate is calculated as γρ−1=fπmρ in rough agreement with experiment. This picture requires soft ρ's to decouple; but this requirement is not in conflict with any experimental features of the vector mesons. The chiral partner of the ρ is not the A1 but the B(1235). The experimental absence of the A1 is no longer a theoretical embarrassment in this scheme. As the analog of PCAC for the pion we establish a tensor-field identity for the ρ meson in which the ρ is interpreted as a dormant Goldstone state. The decays δ→η+π B→ω+π, ε→2π are estimated and are found to be in agreement with the observed rates. A static U(6) × U(6) generalization of the Σ model is presented with the π, ρ, σ, B in the (6,¯6) + (¯6,6) representation. The ρ emerges as a dormant Goldstone boson in this model. Symmetry breaking in the model leads to the remarkable relation mρ2−mπ2=mB2−mδ2, satisfied within 0.5%. Others' efforts towards an integration of PCAC with the quark model, particularly in the context of the Melosh transformation, are discussed.- QUARK
- SYMMETRY: U(6)
- MESON: MULTIPLET
- MULTIPLET: MESON
- PI
- RHO(765)
- FIELD THEORY: GOLDSTONE THEOREM
- PCAC model
- SYMMETRY: CHIRAL
- SYMMETRY: SU(3) X U(6)
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