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The differential cross-section of inelastic coherent diffractive dissociationoff nuclei $p~+~^4$He $\rightarrow X ~+ ~^4$He is expressed in terms of therelative cumulants of the cross-section distribution $P_N(\sigma)$. Thetheoretical result for the ratio$r=\Bigg(\frac{d\sigma_{diff}}{dt}\Bigg)^{pHe}_{t=0} \Bigg/\Bigg(\frac{d\sigma_{diff}}{dt}\Bigg)^{pp}_{t=0}=6.8 \div 7.6$ is close to thevalue $r=7.1 \pm 0.75$ which we extracted from the FNAL data. These are theonly $A>2$ data of this kind. The comparison provides the first confirmation ofthe cross-section fluctuation approach to the description of the absolute valueof the inelastic diffraction cross-section off nuclei. It provides also a newconstraint on the first 4 cumulants of the cross-section distribution.Comment: 10 pages, revte

Color fluctuations in hadrons and proton coherent diffractive dissociation on helium