Manifestation of quark clusters in the emission of cumulative protons in the experiment on the fragmentation of carbon ions

The proton yields at an angle of $3.5^\circ$ have been measured in the FRAGM experiment on the fragmentation of carbon ions with the energies $T_0 = 0.6, 0.95$, and $2.0$ GeV/nucleon on a beryllium target at the heavy-ion accelerator complex TWAC (terawatt accumulator, Institute for Theoretical and Experimental Physics). The data are represented in the form of the dependences of the invariant cross section for proton yield on the cumulative variable $x$ in the range of $0.9 < x < 2.4$. This invariant cross section varies within six orders of magnitude. The proton spectra have been analyzed within the theoretical approach of the fragmentation of quark clusters with the fragmentation functions obtained in the quark-gluon string model. The probabilities of the existence of six- and nine-quark clusters in the carbon nuclei are estimated as $8$–$12$ and $0.2$–$0.6\%$, respectively. The results are compared to the estimated of quark effects obtained by other methods.