发表机构
Ariel University（阿里埃勒大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究Mueller偶极子级联中快度窗口多重数的信息界，证明固定中间多重数时外侧窗口互信息低于高斯值，并给出其上界，揭示模型特性与实验数据的差异。
AI 中文摘要
在Mueller的无横向维度的偶极子级联中，每个在窗口内产生的偶极子计为一个粒子，三个连续快度窗口中的多重数是单个Gamma分布源的泊松计数。我们证明，在固定中间多重数的条件下，外侧两个窗口共享的信息少于其偏相关系数的高斯值$-\tfrac12\ln(1-\rho^2)$，该值仅由二阶矩决定。对于恒定分裂速率下具有共同宽度的窗口，该值不超过$\tfrac12\ln(4/3)$。高斯值通常不是互信息的上界，对于具有相同均值和方差但服从其他分布的源，信息量可能超过该值。当粒子迁移跨越窗口边界和探测损失对每个粒子独立于其他粒子和源作用时，计数的分布保持其形式，其二阶和三阶阶乘累积量检验其必要条件。在具有横向维度、前导对数精度和固定耦合的级联的蒙特卡洛模拟中，计数不是单个源的泊松计数，因此该界是不含横向维度的模型的结果。在不含横向维度的模型中，该分布还将一个窗口的归一化二阶阶乘累积量固定为$1/k$，其中$k$是初始偶极子数。由H1发表的深非弹性散射的均值和方差形成的该累积量的值远低于单个初始偶极子级联中每个窗口内产生的每个偶极子计为一个粒子的值1。被界定的量是计数多重数之间的经典条件互信息。
英文摘要
In Mueller's dipole cascade without transverse dimensions, with one counted particle for each dipole produced in a window, the multiplicities in three consecutive rapidity windows are Poisson counts of one Gamma-distributed source. We show that at fixed middle multiplicity the outer two share less information than the Gaussian value $-\tfrac12\ln(1-ρ^2)$ of their partial correlation, a value that second moments alone determine. For windows of one common width at a constant splitting rate this value never exceeds $\tfrac12\ln(4/3)$. The Gaussian value is not a bound on mutual information in general, and for a source of the same mean and variance with another law the information can exceed it. The law of the counts keeps its form under migration of particles across window edges and detection losses when both act on each particle independently of the others and of the source, and its factorial cumulants of second and third order test necessary conditions for it. In Monte Carlo simulations of the cascade with transverse dimensions at leading logarithmic accuracy and fixed coupling, the counts are not Poisson counts of one source, so the bound is a result of the model without them. In the model without transverse dimensions the law also fixes the normalized second factorial cumulant of one window at $1/k$, with $k$ the number of initial dipoles. The values of this cumulant formed from the mean and variance that H1 publishes for deep inelastic scattering lie far below the value one of a cascade from a single initial dipole with one counted particle for each dipole produced in a window. The quantity bounded is a classical conditional mutual information between counted multiplicities.
Comments16 pages, 2 figures; the programs that produce every computed number and both figures are in the ancillary files
