纵向重标度和高能有效作用
Longitudinal Rescaling and High-Energy Effective Actions
摘要：
在将纵坐标$x^{0,3}$重新标度为因子$λ$（取为零）的情况下，经典QCD作用量显著简化。这是高能极限，因为$λ$是$s^{-1/2}$阶，其中$s$是强子碰撞的质心能量平方。我们发现在一个循环的量子校正的重新标度的行动，特别是发现在这个行动中的$λ$的反常权力，为$λ$接近统一。该方法是对规范场的高动量分量的积分。这是一个威尔逊重整化过程，为了使锐动量截止规范不变，需要用到反项。在假设$λ$的对数很小的情况下，我们得到了量子作用量的结果，这对微扰理论的有效性是必不可少的。如果$λ$足够小（使得它的对数很大），则微扰重整化群分解。这是由于纵向色磁场的不可控波动。
英文摘要：
Under a rescaling of longitudinal coordinates $x^{0,3}$ by a factor $λ$ which is taken to zero, the classical QCD action simplifies dramatically. This is the high-energy limit, as $λ$ is of order $s^{-1/2}$, where $s$ is the center-of-mass energy squared of a hadronic collision. We find the quantum corrections to the rescaled action at one loop, in particular finding the anomalous powers of $λ$ in this action, for $λ$ close to unity. The method is an integration over high-momentum components of the gauge field. This is a Wilsonian renormalization procedure, and counterterms are needed to make the sharp-momentum cut-off gauge invariant. Our result for the quantum action is found, assuming that the logarithm of $λ$ is small, which is essential for the validity of perturbation theory. If $λ$ is sufficiently small (so that its logarithm is large), then the perturbative renormalization group breaks down. This is due to uncontrollable fluctuations of the longitudinal chromomagnetic field.
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