The Role of Δ(1232) in Two-Pion Exchange Three-Nucleon Potential

Abstract

In this paper we have studied the two-pion exchange three-nucleon potential (2πE−3NP ) using an approximate SU (2) × SU (2) chiral symmetry of the strong interaction. The off-shell pion-nucleon scattering amplitudes obtained from the Weinberg Lagrangian are supplemented with contributions from the well-known σ-term and the ∆(1232) exchange. It is the role of the ∆-resonance in 2πE − 3NP , which we have investigated in detail in the framework of the Lagrangian field theory. The ∆-contribution is quite appreciable and, more significantly, it is dependent on a parameter Z which is arbitrary but has the empirical bounds |Z| ≤ 1/2. We find that the ∆-contribution to the important parameters of the 2πE − 3NP depends on the choice of a value for Z, although the correction to the binding energy of triton is not expected to be very sensitive to the variation of Z within its bounds.

Dynamics of low-energy nuclear forces for electromagnetic and weak reactions with the deuteron in the Nambu-Jona-Lasinio model of light nuclei

“…In order to fit the experimental value of the cross section we should set Z = 0.473. This agrees with the experimental bound |Z| ≤ 1/2 [18]. At Z = 1/2 the contribution of the ∆(1232) resonance to the amplitude of the M1-capture is defined only by the nucleon tensor current.…”

“…In order to fit the experimental value of the cross section we should set Z = 0.473. This agrees with the experimental bound |Z| ≤ 1/2 [18]. At Z = 1/2 that is favoured theoretically [15] we get the cross section σ(np → Dγ)(T n ) = 325.5 mb agreeing with the experimental value with accuracy better than 3%.…”

“…In the low-energy limit the effective local four-nucleon interaction Eq. (1.17) vanishes due to the reduction 18) where N(x) is an operator of the neutron or the proton interpolating field. Such a vanishing of the one-pion exchange contribution to the NN potential is well-known in the EFT approach [11,12] and the PMA [26].…”

On the ΔΔ component of the deuteron in the Nambu-Jona-Lasinio model of light nuclei

“…The fields ∆ a µ (x) obey the subsidiary constraints: [7][8][9]. The Green function of the free ∆-field is determined by…”

“…From theoretical point of view Z = 1/2 is preferred [7]. Phenomenological studies give only the bound |Z| ≤ 1/2 [9]. The value of the coupling constant g πN∆ relative to the coupling constant g πNN is g πN∆ = 2 g πNN [10].…”