We study the manifestation of the $Delta^{++}-Delta^-$ component of the deuteron wave function in the exclusive reaction $bar p d to pi^- pi^- Delta^{++}$. Due to the large binding energy the internal motion in the $Delta-Delta$ system is relativistic. We take this into account within the light-cone (LC) wave function formalism and, indeed, found large differences between calculations based on the LC and non-relativistic (NR) wave functions. We demonstrate, that the consistent LC treatment of the $Delta-Delta$ system plays the key role in the separation of the signal and background. Within the LC approach, the characteristic shape of the momentum distribution of the $Delta-Delta$ bound system predicted by the meson-exchange model is well visible on the background of usual annihilations at beam momenta between 10 and 15 GeV/c.
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