论文标题
QCD中的Mueller的偶极波函数：在双对数限制中的紧急KNO缩放
Mueller's dipole wave function in QCD: emergent KNO scaling in the double logarithm limit
论文作者
论文摘要
我们分析了双对数近似（DLA）中Mueller的QCD偶极波函数演化。使用复杂的分析方法，我们表明，波函数中偶极子的分布（Gluon多重性分布）渐近地满足了Koba-Nielsen-Olesen（KNO）缩放，并具有非平凡的缩放函数$ f（z）$，$ z = \ z = \ frac n {\ bar n} $。缩放函数在大$ z $处呈$ 2（2.55）^2ze^{ - \ frac { - \ frac {z} {0.3917}} $，而其增长为$ e^{ - \ frac { - \ frac {1} {2} {2} {2} {2} {2} \ ln^2 z} $。对$ f（z）$的傅立叶 - 拉普拉斯变换的详细分析允许执行逆傅立叶变换，并访问峰值周围的非质合体散装区域。如H1在HERA的HEA合作报道的大型$ q^2 $的H1合作报道，批量和渐近结果与DIS中测得的HADRONIC MULUVETICE非常吻合。包括$ f（z）$的数值表。值得注意的是，发现相同的缩放函数在喷气机演化中的双对数重新召集中出现。使用生成函数方法，我们说明为什么是这种情况。简要讨论了非批判性和超级可弥补理论中不存在KNO缩放率。我们还以KNO缩放极限讨论了纠缠熵的通用特征，并使用DIS和$ E^+E^ - $ nihilation中发射的多重性进行测量。
We analyze Mueller's QCD dipole wave function evolution in the double logarithm approximation (DLA). Using complex analytical methods, we show that the distribution of dipole in the wave function (gluon multiplicity distribution) asymptotically satisfies the Koba-Nielsen-Olesen (KNO) scaling, with a non-trivial scaling function $f(z)$ with $z=\frac n{\bar n}$. The scaling function decays exponentially as $2(2.55)^2ze^{-\frac{z}{0.3917}}$ at large $z$, while its growth is log-normal as $e^{-\frac{1}{2}\ln^2 z}$ for small-$z$. A detailed analysis of the Fourier-Laplace transform of $f(z)$, allows for performing the inverse Fourier transform, and access the non-asymptotic bulk-region around the peak. The bulk and asymptotic results are shown to be in good agreement with the measured hadronic multiplicities in DIS, as reported by the H1 collaboration at HERA in the region of large $Q^2$. A numerical tabulation of $f(z)$ is included. Remarkably, the same scaling function is found to emerge in the resummation of double logarithms in the evolution of jets. Using the generating function approach, we show why this is the case. The absence of KNO scaling in non-critical and super-renormalizable theories is briefly discussed. We also discuss the universal character of the entanglement entropy in the KNO scaling limit, and its measurement using the emitted multiplicities in DIS and $e^+e^-$ annihilation.
