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

Abstract

The pionic interaction of baryon (qqq) states is formulated in a Bethe-Salpeter (BS) model of harmonic confinement, characterized by a universal spring constant (ω=0.15 GeV) and the quark mass (m_q=0.28 GeV) concerned, on lines similar to those developed recently for pionic couplings of meson (qq̅) states, wherein the pionic degree of freedom is governed by the same BS dynamics as for other qq̅ states, and not introduced by hand as an independent entity. The algebraic structures of the matrix elements for NNπ and ΔNπ couplings are strongly reminiscent of the quark-pair-creation model, as found recently for meson couplings (ρππ, ωρπ). 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 (4π)^-1(G_NNπ)² = 13.02 and Γ(Δ→Nπ) = 104.6 MeV, both within 10% of experiment. It is stressed that these pionic results are consistent with the one-pion-exchange-potential structure.