Micro-canonical pentaquark production in $\ee$ annihilations

The existence of pentaquarks, namely baryonic states made up of four quarks and one antiquark, became questionable, because the candidates, i.e. the $\Theta^+$ peak, are seen in certain reactions, i.e. p+p collisions, but not in others, i.e. $\ee$ annihilations. In this paper, we estimate the production of $\Theta ^{+}(1540)$ and $\Xi^{--} (1860)$ in $\ee$ annihilations at different energies using Fermi statistical model as originally proposed in its microcanonical form. The results is compared with that from pp collisions at SPS and RHIC energies. We find that, if pentaquark states exist, the production is highly possible in $\ee$ annihilations. For example, at LEP energy $\sqrt{s}$=91.2 GeV, both $\Theta ^{+}(1540)$ and $\Xi^{--} (1860)$ yield more than in pp collisions at SPS and RHIC energy.