A self-affne analysis of charged-particle multiplicity distribution (protons + pions) in $\pi^{−}$ –AgBr interaction at 350 GeV/c is performed according to the two-dimensional factorial moment methodology using the concept of Hurst exponent in $X_{\cos \theta^{-}} $X_{\phi}$ phase space. Comparing with the results obtained from self-similar analysis, the self affine analysis shows a better power-law behaviour. Corresponding results are compared with shower multiplicity distribution (pions). Multifractal behaviour is observed for both types of distributions.

The multiplicity fluctuations of the produced pions were studied using scaled variance method in ¹⁶O–AgBr interactions at 2.1 AGeV, ²⁴Mg–AgBr interactions at 4.5 AGeV, ¹²C–AgBr interactions at 4.5 AGeV, ¹⁶O–AgBr interactions at 60 AGeV and ³²S–AgBr interactions at 200 AGeV at two different binning conditions. In the first binning condition, the rapidity interval was varied in steps of one centring about the central rapidity until it reached 14. In the second case, the rapidity interval was increased in steps of 1.6 up to 14.4. Multiplicity distributions and their scaled variances were presented as a function of the dependence on the rapidity width for both the binning conditions. Multiplicity fluctuations were found to increase with the increase of rapidity interval and later found to saturate at larger rapidity window for all the interactions and in both the binning conditions. Multiplicity fluctuations were found to increase with the energy of the projectile beam. The values of the scaled variances were found to be greater than one in all the cases in both the binning conditions indicating the presence of correlation during the multiparticle production process in high-energy nucleus–nucleus interactions. Experimental results were compared with the results obtained from the Monte Carlo simulated events for all the interactions. The Monte Carlo simulated data showed very small values of scaled variance suggesting very small fluctuations for the simulated events. Experimental results obtained from ¹⁶O–AgBr interactions at 60 AGeV and ³²S–AgBr interactions at 200 AGeV were compared with the events generated by Lund Monte Carlo code (FRITIOF model). FRITIOF model failed to explain the multiplicity fluctuations of pions emitted from ¹⁶O–AgBr interactions at 60 AGeV for both the binning conditions. However, the experimental data agreed well with the FRITIOF model for ³²S–AgBr interactions at 200 AGeV.