Photo-production of Bound States with Hidden Charms

Abstract

The photo-production of $J/\hat{I}¨$-${}^{3}He$ bound state (${[}^{3}He{]}_{J/\hat{I}¨}$) on a ${}^{4}He$ target has been investigated using the impulse approximation. The calculations have been performed using several ${\hat{I}}^3+N\to J/\hat{I}¨+N$ models based on the Pomeron-exchange and accounting for the pion-exchange mechanism at low energies. The $J/\hat{I}¨$ wavefunctions in ${[}^{3}He{]}_{J/\hat{I}¨}$ are generated from various $J/\hat{I}¨$-nucleus potentials which are constructed by either using a procedure based on the Pomeron-quark coupling mechanism or folding a $J/\hat{I}¨$-N potential ($v_{J/\hat{I}¨,N}$) into the nuclear densities. We consider $v_{J/\hat{I}¨,N}$ 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-$J/\hat{I}¨$ bound state ($[q^6{]}_{J/\hat{I}¨})$ on the ${}^{3}He$ 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 ${}^{3}He$ by imposing the condition that the calculated ${}^{3}He$ 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 ${\hat{I}}^3{+}^{3}He\to [q^6{]}_{J/\hat{I}¨}+N$ is about 2 - 4 pico-barn, depending on the model of ${\hat{I}}^3+N\to J/\hat{I}¨+N$ used in the calculations. Our results call for the need of precise measurements of ${\hat{I}}^3+p\to J/\hat{I}¨+p$ and also the ${\hat{I}}^3{+}^{2}H\to J/\hat{I}¨+n+p$ reactions near the threshold.

23 pages, 11 figures