Theory of mesonic and dibaryonic excitations in the πNN system: Derivation of πNN scattering equations

A πNN theory, incorporating mesonic and dibaryonic excitation mechanisms, is introduced to give a unified description of NN and πd reactions. The mesonic mechanism is built into the theory by extending the conventional meson theory of nuclear force to include the isobar Δ excitation. The dibaryonic excitation at short distance is introduced according to current understanding of six-quark dynamics. The theory is free of the nucleon mass renormalization problem and is therefore tractable in practice. The model Hamiltonian consists of (a) $V_{\mathrm{BB}}$ for two-baryon interactions between NN, NΔ, and ΔΔ states; (b) $h_{\pi \mathrm{N}\mathit{\leftrightarrows }\mathit{\Delta }}$ for Δ excitation; (c) $v_{\pi \mathrm{N}}$ for πN two-body interaction in nonresonant channels; (d) $F_{\pi \mathrm{NN}\mathit{\leftrightarrows }\mathrm{NN}}$ for nonresonant pion production; and (e) $H_{D\leftrightarrows \mathrm{BB}}$ for the formation of a dibaryon state D. Dynamical equations for NN and πd scattering are derived by making the assumption that all NN and πd processes can be described in a subspace spanned by NN, NΔ, ΔΔ, πNN, and the dibaryon state D. The resulting scattering theory satisfies the essential two-body (NN) and three-body (πNN) unitarity relations. The projection technique is applied to cast the theory into a form such that all NN and πd reaction transition matrix elements can be calculated by solving, separately, a two-body integral equation and a Faddeev-type three-body equation. Both can be solved by well-established numerical methods. This makes the calculation based on the most sophisticated meson theory of nuclear force possible. Explicit formalisms have also been developed for exploring the question of the excitation of a dibaryon resonance during NN and πd scattering from the point of view of six-quark dynamics. The numerical results obtained from the theory are presented in a separate paper.