Multitude of classical solutions in the hidden gauge model of pions and vector mesons

We consider the hidden gauge model of pions and vector mesons, where we construct static, spherically symmetric finite-energy solutions of the field equations in the topological sectors $B=0\mathrm{}$ (vacuum sector) and $B=1\mathrm{}$ (baryon sector). We investigate the effects of the anomaly and of higher-order Skyrme terms on the classical solutions, by varying the respective coupling strengths. For nonvanishing values of the coupling strengths, finite sets of solutions exist: pairs of branches of solutions appear spontaneously at critical values of these coupling strengths. When these couplings are decreased to zero, the pairs of solutions form infinite sequences, one for each topological sector studied. Their common limit is the sphaleron, present also in the Weinberg-Salam model. We investigate the stability of the classical solutions and find that only the lowest branch of solutions in each sector is classically stable. With each higher set of solutions one further unstable mode appears. We interpret the lowest solutions in the vacuum sector as diquonium states.