Di-Ω(ΩΩ)Jπ=0+production cross section calculation

Abstract

Cross sections of $\mathrm{baryon}+\mathrm{baryon}\ensuremath{\rightarrow}(\ensuremath{\Omega}\ensuremath{\Omega}{)}_{{J}^{\ensuremath{\pi}}{=0}^{+}}+X$ are studied using an effective Hamiltonian method. For low energy region, the \ensuremath{\gamma} production process dominates; its cross sections are of order of $0.3--1.6 \ensuremath{\mu}\mathrm{b}$ for ${p}_{\ensuremath{\Omega}}=100--400 \mathrm{MeV}.$ There are also some strong interaction processes for forming di-$\ensuremath{\Omega}$ such as $\ensuremath{\Omega}+\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Omega}}(\ensuremath{\Omega}\ensuremath{\Omega}{)}_{{0}^{+}}+\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}},\ensuremath{\varphi})$ and $\ensuremath{\Omega}+\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Xi}}(\ensuremath{\Omega}\ensuremath{\Omega}{)}_{{0}^{+}}{+K(K}^{\ensuremath{\star}}).$ But these processes only make contributions in the high momentum region, because their threshold energies are around (or greater than) 1 GeV. The cross sections for the pseudoscalar meson production processes are about $2.0--4.5 \ensuremath{\mu}\mathrm{b},$ and for the vector meson production processes the cross sections are one order larger than those of the pseudoscalar meson production cases. Besides the above processes, a two-step process is also discussed, in which the first step is $\ensuremath{\Omega}+\stackrel{\ensuremath{\rightarrow}}{N}(N\ensuremath{\Omega}{)}_{{J}^{\ensuremath{\pi}}{=2}^{+}}+\ensuremath{\pi}$ (or $\ensuremath{\gamma})$ and the second step is $\ensuremath{\Omega}+(N\ensuremath{\Omega}{)}_{{2}^{+}}\ensuremath{\rightarrow}(\ensuremath{\Omega}\ensuremath{\Omega}{)}_{{0}^{+}}+N.$ The result shows that the cross sections are quite large for both steps. It seems that some two-step processes might also be important.