Magnetic Moments of ${\mathrm{\Delta }}^{++}$ and ${\mathrm{\Omega }}^{-}$ from QCD Sum Rules

QCD sum rules for the magnetic moments of ${\mathrm{\Delta }}^{++}$ and ${\mathrm{\Omega }}^{-}$ are derived using the external field method. They are analyzed by a Monte-Carlo based procedure, using realistic estimates of the QCD input parameters. The results are consistent with the measured values, despite relatively large errors that can be attributed mostly to the poorly-known vacuum susceptibility $\chi$. It is shown that a 30% level accuracy can be achieved in the derived sum rules, provided the QCD input parameters are improved to the 10% level.