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

## Abstract

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/submore »

- Authors:

- Publication Date:

- Research Org.:
- The Rockefeller University, New York, New York 10021

- OSTI Identifier:
- 7266774

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev., D; (United States)

- Additional Journal Information:
- Journal Volume: 14:3

- Country of Publication:
- United States

- Language:
- English

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

### Citation Formats

```
Caldi, D G, and Pagels, H.
```*A solution to the rho-. pi. puzzle: Spontaneously broken symmetries of the quark model*. United States: N. p., 1976.
Web. doi:10.1103/PhysRevD.14.809.

```
Caldi, D G, & Pagels, H.
```*A solution to the rho-. pi. puzzle: Spontaneously broken symmetries of the quark model*. United States. https://doi.org/10.1103/PhysRevD.14.809

```
Caldi, D G, and Pagels, H. Sun .
"A solution to the rho-. pi. puzzle: Spontaneously broken symmetries of the quark model". United States. https://doi.org/10.1103/PhysRevD.14.809.
```

```
@article{osti_7266774,
```

title = {A solution to the rho-. pi. puzzle: Spontaneously broken symmetries of the quark model},

author = {Caldi, D G and Pagels, H},

abstractNote = {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)},

doi = {10.1103/PhysRevD.14.809},

url = {https://www.osti.gov/biblio/7266774},
journal = {Phys. Rev., D; (United States)},

number = ,

volume = 14:3,

place = {United States},

year = {1976},

month = {8}

}