Abstract

\(z\)-Scaling of inclusive spectra as a manifestation of self-similarity and fractality of hadron interactions is illustrated. The scaling for negative particle production in \({\text{Au}} + {\text{Au}}\) collisions from BES-I program at RHIC is demonstrated. The scaling variable \(z\) depends on the momentum fractions of the colliding objects carried by the interacting constituents, and on the momentum fractions of the fragmenting objects in the scattered and recoil directions carried by the inclusive particle and its counterpart, respectively. Structures of the colliding objects and fragmentation processes in final state are expressed by fractal dimensions. Medium produced in the collisions is described by a specific heat. The scaling function \(\psi (z)\) reveals energy, angular, multiplicity, and flavor independence. It has a power behavior at high \(z\) (high \({{p}_{T}}\)). Based on the entropy principle and \(z\)-scaling, energy loss as a function of the collision energy, centrality and transverse momentum of inclusive particle is estimated. New conservation law including fractal dimensions is found. Quantization of fractal dimensions is discussed.

中文翻译：

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Tevatron、RHIC 和 LHC 强子和原子核碰撞的自相似性、分形性和熵原理

摘要

\(z\) - 包含光谱的缩放作为强子相互作用的自相似性和分形的表现被说明。展示了来自 RHIC 的 BES-I 程序的\({\text{Au}} + {\text{Au}}\)碰撞中负粒子产生的缩放。缩放变量\(z\)取决于相互作用成分携带的碰撞物体的动量分数，以及包含粒子及其对应物分别携带的散射和反冲方向上的碎片物体的动量分数。最终状态下碰撞物体的结构和破碎过程用分形维数表示。碰撞中产生的介质用比热来描述。标度函数\(\psi (z)\)揭示能量、角度、多样性和风味独立性。它在高\(z\)（高\({{p}_{T}}\)）时具有功率行为。基于熵原理和\(z\)-标度，估计作为碰撞能量、中心性和包含粒子的横向动量的函数的能量损失。发现了包括分形维数的新守恒定律。讨论了分形维数的量化。