A solution to the rho-. pi. puzzle: Spontaneously broken symmetries of the quark model

Journal Article · Sun Aug 01 00:00:00 EDT 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.14.809· OSTI ID:7266774

Caldi, D G; Pagels, H

This article proposes a solution to the long-standing rho-..pi.. puzzle: How can the rho and ..pi.. be members of a quark model U(6) 36 and the ..pi.. 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 rho, ..omega.., K*, and phi. Just as the ..pi.. 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) x SU(3) group, so also the rho 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) x U(6) limit. The static chiral U(6) x U(6) is to be spontaneously broken to static U(6) in the vacuum. Relativisitc effects provide for U(6) breaking and a massive rho. 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 ..pi.. couples the vector current to the rho. The transition rate is calculated as ..gamma../sub rho/ /sup -1/ = f/sub pi//m/sub rho/ in rough agreement with experiment. This picture requires soft rho's to decouple. The chiral partner of the rho is not the A/sub 1/ but the B (1235). The experimental absence of the A/sub 1/ 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 rho meson in which the rho is interpreted as a dormant Goldstone state. The decays delta ..-->.. eta + ..pi.., B ..-->.. ..omega.. + ..pi.., epsilon ..-->.. 2..pi.. are estimated and are found to be in agreement with the observed rates. A static U(6) x U(6) generalization of the ..sigma.. model is presented with the ..pi.., rho, sigma, B in the (6, 6) + (6, 6) representation. The rho emerges as a dormant Goldstone boson in this model. (AIP)

• Research Organization: The Rockefeller University, New York, New York 10021
• OSTI ID: 7266774
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 14:3; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645303* -- High Energy Physics-- Particle Invariance Principles & Symmetries-- Applications to Strong Interactions-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
CHIRAL SYMMETRY
COMPOSITE MODELS
ELEMENTARY PARTICLES
GOLDSTONE BOSONS
HADRONS
LIE GROUPS
MATHEMATICAL MODELS
MELOSH TRANSFORMATION
MESON RESONANCES
MESONS
PARTICLE MODELS
PARTICLE PROPERTIES
PCAC THEORY
PIONS
POSTULATED PARTICLES
PSEUDOSCALAR MESONS
QUARK MODEL
RESONANCE PARTICLES
RHO-765 RESONANCES
SU GROUPS
SU-3 GROUPS
SYMMETRY
SYMMETRY BREAKING
SYMMETRY GROUPS
U GROUPS
U-6 GROUPS
VECTOR MESONS