This study focuses on the presence of (multi)fractal structures in confined hadronic matter through the momentum distributions of mesons produced in proton-proton collisions between 23 GeV and 63 GeV. The analysis demonstrates that the $q$-exponential behaviour of the particle momentum distributions is consistent with fractal characteristics, exhibiting fractal structures in confined hadronic matter with features similar to those observed in the deconfined quark-gluon plasma (QGP) regime. Furthermore, the systematic analysis of meson production in hadronic collisions at energies below 1 TeV suggests that specific fractal parameters are universal, independently of confinement or deconfinement, while others may be influenced by the quark content of the produced meson. These results pave the way for further research exploring the implications of fractal structures on various physical distributions and offer insights into the nature of the phase transition between confined and deconfined regimes.

翻译：本研究聚焦于在23 GeV至63 GeV质子-质子碰撞中产生的介子动量分布所揭示的受限强子物质中的（多重）分形结构。分析表明，粒子动量分布的$q$-指数行为与分形特征一致，展现出受限强子物质中的分形结构，其特性类似于解禁闭夸克-胶子等离子体（QGP）区域中观测到的现象。此外，对能量低于1 TeV的强子碰撞中介子产生的系统分析表明，特定分形参数具有普适性，与禁闭或解禁闭状态无关，而其他参数可能受所产生介子的夸克成分影响。这些结果为进一步探索分形结构对各种物理分布的影响铺平了道路，并为理解禁闭与解禁闭区域之间相变的本质提供了见解。