标题： QCD高能下Koba-Nielsen-Olesen标度的普遍性与纠缠 显示英文标题

标题： Universality of Koba-Nielsen-Olesen scaling in QCD at high energy and entanglement

摘要： 使用穆勒的偶极子形式主义来研究QCD中的深度非弹性散射，我们推导并求解了在高能强子过程中产生的粒子多重性的生成函数的演化方程。 多重性的解满足科巴-尼尔森-奥利森（KNO）标度，与最近重新分析的HERA（DESY）的H1实验数据以及LEP（CERN）的强子$Z$衰变的老ALEPH数据有很好的一致性。 相同的KNO标度函数也适用于电子-正电子湮灭中喷注的强子多重性。 这种一致性是{\it 先验}令人困惑的，因为在穆勒的偶极子演化中，考虑的是波函数中的虚偶极子，而在电子-正电子湮灭中，描述的是真实粒子的截面。 我们解释了这种相似性的起源，并指出了这两个过程之间的特定对偶性。 最后，我们从QCD中慢度和快速自由度之间量子纠缠的角度解释了我们的结果，并推导了电子-正电子湮灭产生强子喷注的相关纠缠熵。 显示英文摘要

摘要： Using Mueller's dipole formalism for deep inelastic scattering in QCD, we formulate and solve the evolution for the generating function for the multiplicities of the produced particles, in hadronic processes at high energy. The solution for the multiplicities satisfies Koba-Nielsen-Olesen (KNO) scaling, with good agreement with the recently re-analyzed data from the H1 experiment at HERA (DESY), and the old ALEPH data for hadronic $Z$ decay at LEP (CERN). The same scaling function with KNO scaling, carries to the hadronic multiplicities from jets in electron-positron annihilation. This agreement is {\it a priori} puzzling, since in Mueller's dipole evolution, one accounts for virtual dipoles in a wave function, whereas in electron-positron annihilation, one describes cross-sections of real particles. We explain the origin of this similarity, pointing at a particular duality between the two processes. Finally, we interpret our results from the point of view of quantum entanglement between slow and fast degrees of freedom in QCD, and derive the entanglement entropy pertinent to electron-positron annihilation into hadronic jets.