Chiral dynamics and heavy quark symmetry in a solvable toy field-theoretic model

We study a solvable QCD-like toy theory, a generalization of the Nambu-Jona-Lasinio model, which implements chiral symmetries of light quarks and heavy quark symmetry. The chiral symmetric and chiral broken phases can be dynamically tuned. This implies a parity-doubled heavy-light meson system, corresponding to a ($0^{-}$, $1^{-}$) multiplet and a ($0^{+}$, $1^{+}$) heavy spin multiplet. Consequently the mass difference of the two multiplets is given by a Goldberger-Treiman relation and $g_A$ is found to be small. The Isgur-Wise function $\xi \mathrm{}\left(w\right)\mathrm{}$, the decay constant $f_B$ and other observables are studied.