VMD, the WZW Lagrangian and ChPT:The Third Mixing Angle

Abstract

We show that the Hidden Local Symmetry Model, supplemented with well-known procedures for breaking flavor SU(3) and nonet symmetry, provides all the information contained in the standard Chiral Perturbation Theory (ChPT) Lagrangian L{sup (0)} + L{sup (1)}. This allows to rely on radiative decays of light mesons (VP{gamma} and P{gamma}{gamma}) in order to extract some numerical information of relevance to ChPT: a value for {Lambda}{sub 1} = 0.20 {+-} 0.04, a quark mass ratio of {approx_equal} 21.2 {+-} 2.4, and a negligible departure from the Gell-Mann--Okubo mass formula. The mixing angles are {theta}{sub 8} = {minus}20.40{degree} {+-} 0.96{degree} and {theta}{sub 0} = {minus}0.05{degree} {+-} 0.99{degree}. We also give the values of all decay constants. It is shown that the common mixing pattern with one mixing angle {theta}{sub P} is actually quite appropriate and algebraically related to the {eta}/{eta}{prime} mixing pattern presently preferred by the ChPT community. For instance the traditional {theta}{sub p} is functionally related to the ChPT {theta}{sub 8} and fulfills {theta}{sub P} {approx_equal} {theta}{sub 8}/2. The vanishing of {theta}{sub 0}, supported by all data on radiative decays, gives a novel relation between mixing angles and the violation of nonet symmetry in the pseudoscalar sector. Finally, it is shown that the interplay of nonet symmetry breaking through U(3) {r_arrow} SU(3) x U(1) satisfies all requirements of the physics of radiative decays without any need for additional glueballs.