Bethe-Salpeter few-quark dynamics and the pion degree of freedom

The pionic interaction of baryon ($\mathrm{qqq}$) states is formulated in a Bethe-Salpeter (BS) model of harmonic confinement, characterized by a universal spring constant ($\tilde{\omega }=0.15\mathrm{}$ GeV) and the quark mass ($m_q=0.28\mathrm{}$ GeV) concerned, on lines similar to those developed recently for pionic couplings of meson ($q\overline{q}$) states, wherein the pionic degree of freedom is governed by the same BS dynamics as for other $q\overline{q}$ states, and not introduced by hand as an independent entity. The algebraic structures of the matrix elements for $\mathrm{NN}\pi$ and $\Delta N\pi$ couplings are strongly reminiscent of the quark-pair-creation model, as found recently for meson couplings ($\rho \pi \pi$, $\omega \rho \pi$). A Lorentz-invariant adaptation of the resulting pion-baryon form factors, on lines identical to those employed successfully to the meson couplings, leads to the parameter-free predictions ${\left(4\mathrm{}\pi \right)}^{-1\mathrm{}}{\left(G_{\mathrm{NN}\pi }\right)}^2=13.02\mathrm{}$ and $\Gamma (\Delta \to N\pi )=104.6\mathrm{}$ MeV, both within 10% of experiment. It is stressed that these pionic results are consistent with the one-pion-exchange-potential structure.