Faddeev-type calculation ofηdthreshold scattering

Abstract

The scattering length for the η-meson collision with deuteron is calculated on the basis of rigorous few-body equations (AGS) for various ηN input. The results obtained strongly support the existence of a resonance or quasi-bound state close to the ηd threshold.PACS numbers: 25.80.-e, 21.45.+v, 25.10.+s The production of η mesons and their collisions with nuclei have been studied experimentally and theoretically with increasing interest during the last years. To a large extent this is motivated by the fundamental questions of charge-symmetry breaking and the break-down of the Okubo-Zweig-Iizuka rule. Another relevant question concerns the possible formation of η-nucleus quasi-bound states.In many respects the η-meson is similar to the π 0 -meson despite it's being four times heavier. Both are neutral and spinless, they have almost the same lifetime, ∼ 10 −18 sec, and are the only mesons which have a high probability of pure radiative decay, that is, their quarks can annihilate into on-shell photons. However, when being involved in nuclear reactions they behave rather differently. The S 11 -resonance N * (1535), for instance, is formed in both πN and ηN systems, but at different collision energies,Thus, due to the large mass of the η-meson (547.45 MeV), this resonance is very close to the ηN-threshold. Furthermore it is very broad, with Γ ≈ 150 MeV, covering the whole low energy ηN region. As a result the interaction of nucleons with η-mesons in this region, 1 where the S-wave interaction dominates, is much stronger than with pions.After its creation the N * (1535)-resonance decays into ηN and πN channels with equally high probabilities [1]which indicates that the ηN and πN interactions are to be treated by a coupled channel analysis. The resulting ηN interaction, obtained in this way, turned out to be attractive [2]. This raises the question whether the attraction is strong enough to support η-nucleus quasi-bound states. Let us recall in this context that, because of their short lifetime, η-mesons can only be observed in final states of certain nuclear reactions. Within nuclei they are considered to undergo multiple absorption and production processes via the S 11 resonance, with a final transition into pions. Such quasi-bound states therefore would be of considerable interest for studying η-meson properties in more detail.For the calculation of these states various model treatments were employed, among them the optical potential method [3][4][5][6], the Green's function method [7], and the modified multiple scattering theory [8]. Calculations, based on the exact Alt-Grassberger-Sandhas (AGS) equations [9], for the ηd system were also made in Ref. [10] in early nineties.The predictions concerning the possibility of η-mesic nucleus formation are very diverse. One obvious reason for such a diversity is the poor knowledge of the ηN forces. Another reason comes from the differences among the employed approximations some of which might be detrimental in view of the resonant character of the ηN dynamics and...

ηN scattering lengths favour ηd and ηα states

“…Since the η-mesic bound states and resonances are basically low energy phenomena, it seems justified to use the FRA for calculations of the present work. In [21], the authors mention that though the use of FRA for η 3 He and η 4 He systems seems justified, it is questionable for the case of ηd scattering and investigate the shortcoming due to the neglect of excitations of the nuclear ground state in η-deuteron calculations. Within their model, they find that the FRA results differ from those evaluated using the rigorous Alt-Grassberger-Sandhas (AGS) equations in the case of the strong ηN interaction (Re a ηN > 0.5 fm), while for small values of Re a ηN , the FRA is reasonably good.…”

“…This state led to a remarkable enhancement of the ηd elastic cross section. In some other Faddeev-type calculations [20,21] of ηd scattering, a resonance at low energies was predicted.…”

“…In order to check the validity of the above FRA approach for the ηd case (where it is known to have limitations [21]), we evaluate time delay using a model [42] which obtains the ηd elastic scattering amplitude using a relativistic version of the Faddeev equations described in [43]. The ηd amplitude in [42] is parametrized using the effective range formula:…”

“…This t-matrix is subsequently used to evaluate the time delay in η-light nucleus scattering. Since the applicability of the FRA for the ηd case is limited (it was shown in [21] that FRA agrees with the Faddeev calculations for real part of the scattering lengths less than 0.5 fm only), we use a parameterization of the η d t-matrix using relativistic Faddeev equations and present the results of this calculation in Sec. 4.…”

Production of η and η′ mesons on nucleons and nuclei

“…Since there are only three particles in the ηnp system, the final state interaction is then theoretically much more tractable and the Alt-Grassberger-Sandhas equations have been resolved for various ηN inputs [287]. Taking a ηN = 0.25 + 0.16i, 0.55 + 0.30i, and 0.98 + 0.37i fm, this group found η-deuteron scattering lengths of a ηd = 0.73 + 0.56i, 1.64 + 2.99i, and −4.69 + 1.59i fm, respectively.…”