Using a gauged flavor SU(3)-invariant hadronic Lagrangian, we calculate the cross sections for the strangeness-exchange reactions $YY\leftrightarrow N\Xi$ ($Y=\Lambda ,\Sigma$) in the Born approximation. These cross sections are then used in the relativistic Vlasov-Uehling-Uhlenbeck transport model to study $\Xi$ production in $\mathrm{Ar}+\mathrm{KCl}$ collisions at incident energy of 1.76A GeV and impact parameter $b=3.5$ fm. We find that including the contributions of hyperon-hyperon scattering channels strongly enhances the yield of $\Xi$, leading to the abundance ratio ${\Xi }^{-}/(\Lambda +{\Sigma }^0)=3.38\times {10}^{-3}$, which is essentially consistent with the recently measured value of $(5.6\pm {1.2}_{-1.7}^{+1.8})\times {10}^{-3}$ by the HADES Collaboration at GSI.

• Received 5 April 2012

DOI:https://doi.org/10.1103/PhysRevC.85.064902