Solution to the rho-π puzzle: spontaneously broken symmetries of the quark model

A solution is offered to the rho-π puzzle, which is the problem of understanding how the rho and π can be members of the same quark model U(6) 36 and yet the π be a Nambu-Goldstone boson satisfying PCAC. The solution is to consider the vector mesons to be collective states like the π, ''dormant'' Goldstone bosons which are true Goldstone states in the static chiral U(6) x U(6) limit. These dormant Goldstone vector mesons transform like (3, anti 3) + (anti 3, 3) of chiral SU(3) x Su(3). This solution is abstracted from a static U(6) x U(6) generalization of the Σ-model in which π, rho, sigma, B fields are in a (6, anti 6) + (anti 6, 6) representation. Relativistic symmetry breaking leads to the experimentally verified relation m2/sub rho/-m2/sub π/ m2/sub B/-m2/sub delta/. The solution has many consequences. The chiral partner of the rho is not the experimentally absent A1 but the well established B(1235). Vector meson dominance is seen as a consequence of spontaneously broken chiral symmetry so that the mechanism that couples the axial current to the π also couples the vector current to the rho. The transition rate is calculated to be γ-1/sub rho/ app