Dynamical models of the excitations of nucleon resonances

Abstract

The development of a dynamical model for investigating the nucleon resonances using the reactions of meson production from πN , γN , N (e, e ′ ), and N (ν, l ) reactions is reviewed. The results for the ∆ (1232) state are summarized and discussed. The progress in investigating higher mass nucleon resonances is reported.N (ν, l π)N reactions.The main challenge of developing dynamical reaction models of meson production reactions in the higher mass N * region can be seen in Fig.1. We see that two-pion photo-production cross sections shown in the left-hand-side become larger than the one-pion photo-production as the γp invariant mass exceeds W ∼ 1.4 GeV. In the right-hand-side, KY ( K + Λ, K + Σ 0 , K 0 Σ + ), ηp, and ωp production cross sections are a factor of about 10 weaker than the dominant π + π − p production. From the unitarity condition, we have for any single meson production processwhere ρ α denotes an appropriate phase space factor for the channel α. The large two-pion production cross sections seen in Fig.1 indicate that the second term in the right-hand-side of Eq.(1) is significant and hence the single meson production reactions above the ∆ region must be influenced strongly by the coupling with the two-pion channels. Similarly, the two-pion production γN → ππN is also influenced by the transition to two-body M B channelClearly, a sound dynamical reaction model must be able to describe the two pion production and to account for the above unitarity conditions. Such a model has been developed by using the unitary transformation method in Ref.[8] and applied to investigate πN elastic scattering[10], γN → πN reactions[11] πN → ηN reactions[12], and πN → ππN reactions[13]. In this article, we will also review these results. This article is organized as follows. In section 2, we explain the unitary transformation method developed in Ref.[31] using a simple model. The constructed model Hamiltonian for investigating N * states is given in section 3. The multi-channel multi-resonance reaction model developed in Refs.[4,8] for calculating the mesonbaryon reaction amplitudes is presented in section 4. In section 5, we give formula for defining the N -N * transition form factors and calculating the cross sections of pion production from πN , γN , N (e, e ′ ), and N (ν, l ) reactions. The results in the ∆ (1232) region and in the higher mass N * region are reviewed in section 6. A summary and discussions of future developments are given in section 7. Unitary Transformation MethodThe unitary transformation method was essentially based on the same idea of the Foldy-Wouthuysenth transformation developed in the study of electromagnetic interactions. It was first developed in 1950's by Fukuda, Sawada and Taketani [32], and independently by Okubo[33]. This approach, called the FST-Okubo method, has been very useful in investigating nuclear electromagnetic currents [34,35] and relativistic descriptions of nuclear interactions [36,37,38]. The advantage of this approach is that the resulting effective Hamiltonian is energy...

Semirelativistic approximation to the γ*N→N(1520) and γ*NRamalho1 2017Phys. Rev. D192120View full textAdd to dashboardCite

“…Overall, we conclude that we have a good description of the valence quark content of the N (1520) and N (1525) systems, since we describe very well the large Q 2 data. Estimates of the valence quark contributions to the form factors can by performed using dynamical coupledchannel reaction models like the DMT [15,57], and the EBAC/Argonne-Osaka model [18,19,56]. Those models take into account the meson and photon coupling with the baryon cores and can be used to estimate the effect of the bare core, when the meson cloud effects are removed, or the effect of the meson cloud, when the bare core effect is subtracted [18][19][20].…”

“…The model A may be useful in the future to compare with lattice QCD simulations with large pion masses (small meson cloud effects) and other estimates of the baryon core effects as the ones performed by the EBAC/Argonne-Osaka model [18,19,56] In future works one may also use the difference between our estimate of the bare core and a parametrization of the data to extract the contributions of the meson cloud.…”

“…The closeness between the model A and the A 1/2 data for small Q 2 may be interpreted as a coincidence due to the results observed for the form factors (the model cannot describe simultaneously the form factors F * 1 , F * 2 in the region Q 2 < 2 GeV 2 ). As for large Q 2 the closeness between model and data is expectable due to the predicted falloff of the meson cloud contributions, and also due to the smaller impact of F * 2The model A may be useful in the future to compare with lattice QCD simulations with large pion masses (small meson cloud effects) and other estimates of the baryon core effects as the ones performed by the EBAC/Argonne-Osaka model [18,19,56] In future works one may also use the difference between our estimate of the bare core and a parametrization of the data to extract the contributions of the meson cloud.In Fig. 5, we compare the high Q 2 model (model B) directly with the data.…”

“…At low Q 2 , the agreement is not so good, since the meson cloud contributions are expected to be important and even dominant in some transitions [1,2,[18][19][20][21].…”

Nucleon resonances within a dynamical coupled-channels model ofπNandγNreactions

“…1, of phenomenological Lagrangian. Within the unitary transformation method [15,[35][36][37] used in the derivation, those potentials are energy independent and free of singularities. In Appendix B, we list the Lagrangian used in our derivations.…”