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Register a new userPossible $eta d$ bound state and its $s$-channel formation in the $gamma d to eta d$ reaction
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Authors
Takayasu Sekihara
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We theoretically investigate a possibility of an $eta ^{prime} d$ bound state and its formation in the $gamma d to eta d$ reaction. First, in the fixed center approximation to the Faddeev equations we obtain an $eta ^{prime} d$ bound state with a binding energy of 25 MeV and width of 19 MeV, where we take the $eta ^{prime} N$ interaction with a coupling to the $eta N$ channel from the linear $sigma$ model. Then, in order to investigate the feasibility from an experimental point of view, we calculate the cross section of the $gamma d to eta d$ reaction at the photon energy in the laboratory frame around 1.2 GeV. As a result, we find a clear peak structure with the strength $sim$ 0.2 nb/sr, corresponding to a signal of the $eta ^{prime} d$ bound state in case of backward $eta$ emission. This structure will be prominent because a background contribution coming from single-step $eta$ emission off a bound nucleon is highly suppressed. In addition, the signal can be seen even in case of forward $eta$ emission as a bump or dip, depending on the relative phase between the bound-state formation and the single-step background.
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The $eta$ mesic nucleus is considered to be one of the interesting exotic many body systems and has been studied since 1980s theoretically and experimentally. Recently, the formation of the $eta$ mesic nucleus in the fusion reactions of the light nuclei such as $d + d rightarrow (eta + alpha) rightarrow X$ has been proposed and the experiments have been performed by WASA-at-COSY. We develop a theoretical model to evaluate the formation rate of the $eta$ mesic nucleus in the fusion reactions and show the calculated results. We find that the $eta$ bound states could be observed in the reactions in cases with the strong attractive and small absorptive $eta$-nucleus interactions. We compare our results with existing data of the $d + d rightarrow eta + alpha$ and the $d + d rightarrow {^3 rm He} + N + pi$ reactions. We find that the analyses by our theoretical model with the existing data can provide new information on the $eta$-nucleus interaction.
The total cross section of the p d -> p d eta reaction has been measured at two energies near threshold by detecting the final proton and deuteron in a magneti spectrometer. The values are somewhat larger than expected on the basis of two simple theoretical estimates.
A model for the p d --> p d eta reaction published earlier, including the final state interaction (FSI) of all particles, is revisited to investigate the low energy data on this reaction. The three body problem of p-d-eta scattering in the final state is approximated in terms of pairwise interactions between the three particles in the final state. Apart from a comparison with some preliminary data, two new findings relevant to the near threshold data analysis are reported. The first one points toward the limitations of an FSI factor used conventionally to extract the eta-deuteron scattering length and infer subsequently on the existence of eta-mesic states. The second result emphasizes the role of the $p-d$ FSI and the strong Coulomb repulsion near threshold. Finally, a comparison of the above model calculation with low energy data, excludes very large eta-nucleon scattering lengths.
To investigate the interaction between the nucleon $N$ and nucleon resonance $N(1535)1/2^-$, the $eta d$ threshold structure, connected to the isoscalar $S$-wave $N$-$N(1535)1/2^-$ system, has been experimentally studied in the $gamma{d}${$to$}$pi^0eta{d}$ reaction at incident photon energies ranging from the reaction threshold to 1.15 GeV. A strong enhancement is observed near the $eta d$ threshold over the three-body phase-space contribution in the $eta d$ invariant-mass distribution. An analysis incorporating the known isovector resonance $mathcal{D}_{12}$ with a spin-parity of $2^+$ in the $pi^0d$ channel has revealed the existence of a narrow isoscalar resonance-like structure $mathcal{D}_{eta d}$ with $1^-$ in the $eta d$ system. The Breit-Wigner mass of $mathcal{D}_{eta d}$ is found to be $2.425^{-0.006}_{+0.003}$ GeV, located just close to the $eta d$ threshold, and the width is $0.034_{-0.003}^{+0.004}$ GeV. The $mathcal{D}_{eta d}$ would be a predicted isoscalar $1^-$ $eta NN$ bound state from the $eta NN$ and $pi NN$ coupled-channel calculation, or $eta d$ virtual state owing to strong $eta d$ attraction.
We consider the reaction g+d -> pi+d in a wide energy range around and above the eta-meson photoproduction threshold at backward CM angles of the outgoing pion. Our theoretical analysis is essentially motivated by the recent measurements of the CLAS Collaboration at Jefferson Lab, where this kinematical region of the reaction has been thoroughly studied for the first time and a cusps in the energy dependence of the differential cross section in the region of Eg = 600-800 MeV has been observed. Our preliminary and qualitative analysis, based on single- and double-scattering diagrams, shows that the observed structure can be explained by the contribution of the double-scattering diagram with intermediate production of the eta meson. The effect, to a considerable extent, is formed due to the contribution of N(1535) resonance to the amplitudes of subprocesses on the nucleons.
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