Probing the existence of η\etad and η3\eta^3He with a few-body approach

We investigate the possible $\eta$-deuteron and $\eta-^3$He bound states with the $\eta NN$ and $\eta NNN$ few body method. In order to solve the three body and four body Schr\"odinger equations, we apply the Gaussian expansion method. The realistic AV8' $NN$ potential together with an extra 3N three body force which reproduce the binding energies of deuteron, $^3$H and $^3$He, are used. We construct the relations between the complex Gaussian-type energy-independent $\eta N$ interactions and the $\eta N$ scattering lengths $a$. The relations between the binding energies in $\eta$d and $\eta^3$He, and the scattering lengths are then obtained. We find that to have a bound $\eta$d nucleus, the real $\eta N$ scattering length should exceed at least 1.35 fm. As for the $\eta^3$He system, the bound state exists when the real $a>0.75\sim0.8$ fm if we neglect the imaginary part of the $\eta N$ interaction. After solving the full four body complex Schr\"odinger equation, we find the imaginary $\eta N$ potential causes the system more unbound. Thus, we give the relations between the bound or unbound scenarios of the $\eta^3$He system and the complex $\eta N$ scattering lengths.Comment: 7 pages, 11 figure

Estimation of Υ\Upsilon(1S) production in ep process near threshold

The near-threshold photo-productions of heavy quarkonia are important ways to test the QCD-inspired models and to constrain the gluon distribution of nucleon in the large x region. Investigating the various models, we choose a photon-gluon fusion model and a pomeron exchange model for J/$\Psi$ photo-production near threshold, emphasising on the explanation of the recent experimental measurement by GlueX at JLab. We find that these two models are not only valid in a wide range of the center-of-mass energy of $\gamma$ and proton, but also can be generalized to describe the $\Upsilon$(1S) photo-production. Using these two models, we predict the electro-production cross-sections of $\Upsilon$(1S) at EicC to be 48 fb to 85 fb at the center-of-mass energy of 16.75 GeV.Comment: 5 pages, 4 figure