Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau-Pomeranchuk-Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, $A\to \infty$, as assumed in previous studies. Due to the correlative nature of the twist-four matrix elements under consideration, it is actually the off-forward parton distributions that appear naturally in this decomposition, rather than the ordinary diagonal distributions probed in deeply-inelastic scattering. However, we argue that the difference between these two distribution classes is small in certain kinematic regimes. In these regions, the twist-four nuclear parton matrix elements are evaluated numerically and compared to the factorized form for different nuclear sizes within a schematic model of the two-nucleon correlation function. The nuclear size dependence is found to be $A^{4/3}$ in the limit of large $A$, as expected. We find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. The deviation can be more than a factor of 2, however, for small gluon momentum fractions, where the gluon distribution is very large.
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机译：大原子核内的多个parton散射通常涉及较高扭曲的核parton矩阵元素。由于Landau-Pomeranchuk-Migdal干涉效应，多重散射引起的胶子致辐射不仅取决于直接的Parton矩阵元素，而且取决于动量交叉的元素。我们显示，在以前的研究中假设，在非常大的核（$ A \到\ infty $）的极限内，两种类型的扭曲四核parton矩阵元素都可以近似分解为扭曲二核子矩阵元素的乘积。由于所考虑的扭曲四矩阵元素的相关性质，实际上是在分解过程中自然出现的偏偏parton分布，而不是在深非弹性散射中探测到的普通对角线分布。但是，我们认为，在某些运动状态下，这两种分配类别之间的差异很小。在这些区域中，对四旋核Parton矩阵元素进行了数值评估，并与两核子相关函数的示意图模型中不同核尺寸的因式分解形式进行了比较。如预期的那样，在大的A $的极限中，发现核尺寸依赖性为A ^ {4/3} $。我们发现，当胶子场携带的动量分数适中时，因式分解是相当好的。但是，对于胶子分布非常大的小胶子动量分数，偏差可能大于2倍。
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