Photo-production of Bound States with Hidden Charms

Abstract

The photo-production of $J/Ψ$-$^3He$ bound state ($[^3He]_{J/Ψ}$) on a $^4He$ target has been investigated using the impulse approximation. The calculations have been performed using several $γ+N \rightarrow J/Ψ+N$ models based on the Pomeron-exchange and accounting for the pion-exchange mechanism at low energies. The $J/Ψ$ wavefunctions in $[^3He]_{J/Ψ}$ are generated from various $J/Ψ$-nucleus potentials which are constructed by either using a procedure based on the Pomeron-quark coupling mechanism or folding a $J/Ψ$-N potential ($v_{J/Ψ,N}$) into the nuclear densities. We consider $v_{J/Ψ,N}$ derived from the effective field theory approach, Lattice QCD, and Pomeron-quark coupling mechanism. The upper bound of the predicted total cross sections is about $0.1 - 0.3$ pico-barn. We also consider the possibility of photo-production of a six quark-$J/Ψ$ bound state ($[q^6]_{J/Ψ})$ on the $^3He$ target. The Compound Bag Model of $NN$ scattering and the quark cluster model of nuclei are used to estimate the $[q^6]$-N wavefunction in $^3He$ by imposing the condition that the calculated $^3He$ charge form factor must be consistent with what is predicted by the conventional nuclear model. The upper bound of the predicted total cross sections of $γ+ ^3He \rightarrow [q^6]_{J/Ψ} +N$ is about 2 - 4 pico-barn, depending on the model of $γ+N \rightarrow J/Ψ+N$ used in the calculations. Our results call for the need of precise measurements of $γ+p \rightarrow J/Ψ+p$ and also the $γ+^2H\rightarrow J/Ψ+n + p $ reactions near the threshold.