Hadronic cross-section fluctuations and proton coherent diffractive dissociation on helium

The differential cross-section of inelastic coherent diffractive dissociation off nuclei $p~+~^4$He $\rightarrow X ~+ ~^4$He is expressed in terms of the relative cumulants of the cross-section distribution $P_N(\sigma)$. The theoretical 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 the value $r=7.1 \pm 0.75$ which we extracted from the FNAL data. These are the only $A>2$ data of this kind. The comparison provides the first confirmation of the cross-section fluctuation approach to the description of the absolute value of the inelastic diffraction cross-section off nuclei. It provides also a new constraint on the first 4 cumulants of the cross-section distribution.