We study the fluctuation theory analysis of multiple soft interactions that are used to design SIBYLL 2.1 and related cosmic ray event generators. We examine fluctuation stabilities of Lund string fragmentation involving quark-antiquark and diquark-antidiquark pairs. Using the primordial transverse momentum hadron-hadron pairs, we find that the resulting Gaussian distribution yields an ill-defined ensemble under fluctuation of the model parameters of parent quarks and diquarks. Further, we investigate the nature of multiple soft interactions through Pomeron-Reggeon fluctuations at various energy scales. We show that there are both stable and unstable regions under fluctuations of the Reggeon and Pomeron densities at all initial energy scales. We find that the optimal stability zone is achieved at the Reggeon and Pomeron densities as predicted by GRV model. For hadron-hadron collisions, the limiting Gaussian profile as a function of the impact parameters of soft interactions for proton-proton collisions corresponds to an indeterminate statistical basis. Subsequently, we add higher order corrections in the Regge trajectory of constituent hadrons that play an important role in determining the shape of a proton or meson profile function in the realm of minijet model. We also discuss the stability of accelerated nucleons with jerks and higher order contributions as well as soft profile functions at off-shell-conditions. In addition, we illustrate the wall of stability/ instability for multiple soft interactions by considering energy dependent soft contributions to scattering cross section as the model embedding. Qualitative discussions are provided at physical energy scales ranging from 1 GeV to 1800 GeV. This includes the analysis of CDF, P238, UA5 and ZEUS experiments.

我们研究了用于设计SIBYLL 2.1和相关宇宙射线事件生成器的多个软相互作用的涨落理论分析。我们研究了涉及夸克-反夸克和双夸克-反双夸克对的隆德弦碎裂的波动稳定性。使用原始横向动量强子-强子对，我们发现，在父夸克和双夸克模型参数波动的情况下，所得的高斯分布产生了不确定的整体。此外，我们研究了通过各种能级上的波美隆-雷根起伏产生的多个软相互作用的性质。我们显示在所有初始能级下，Reggeon和Pomeron密度的波动下都有稳定和不稳定的区域。我们发现最佳稳定区是在GRGE模型预测的Reggeon和Pomeron密度下实现的。对于强子-强子碰撞，作为质子-质子碰撞的软相互作用的冲击参数的函数的极限高斯分布对应于不确定的统计基础。随后，我们在强子的Regge轨迹中添加了更高阶的校正，这些校正在确定微型喷射模型领域中质子或介子轮廓函数的形状方面起着重要作用。我们还讨论了带有加速和高阶贡献的加速核子的稳定性，以及在脱壳条件下的软轮廓函数。此外，我们通过考虑对散射截面的能量相关软贡献作为模型嵌入来说明多个软相互作用的稳定性/不稳定性壁。定性讨论的物理能级为1 GeV到1800 GeV。这包括对CDF，P238，UA5和ZEUS实验的分析。