vNRQCD的显式软规范不变式
Manifestly Soft Gauge Invariant Formulation of vNRQCD
摘要：
非相对论性QCD（NRQCD）中的齐次幂计数意味着同时存在软胶子和超软胶子。在速度重整化群（vNRQCD）的形式主义，我们表明，涉及软场与重势夸克相互作用的运营商可以放在一个明显的规范不变的形式，利用胶子和夸克积木，其中包含威尔逊线，并类似于软共线有效理论中使用的。这导致了几个简化，特别是显着减少的运营商的基础上，流线匹配和异常尺寸计算在subleading为了在速度膨胀的大小。此外，软鬼不再通过类似势的相互作用耦合到重夸克场，因此直到两个环才出现。此外，出现在静态势中的$α_s$中的每一阶的颜色结构仅是根据非阿贝尔指数化应该出现的那些。我们还讨论了如何零仓减法澄清的作用，$i\varepsilon$条款的重夸克传播极携带软动量。即使在我们的积木中软威尔逊线的方向的选择并不重要，仍然有一组有限的一致的选择，并且程函极点的预测形式确实影响了两个循环和更远的结果。
英文摘要：
Homogeneous power counting in Non-Relativistic QCD (NRQCD) implies the simultaneous existence of both soft and ultrasoft gluons. In the velocity renormalization group (vNRQCD) formalism we show that operators involving soft fields interacting with heavy potential quarks can be put in a manifestly gauge invariant form by utilizing gluon and quark building blocks which contain Wilson lines, and are analogous to those used in the soft collinear effective theory. This leads to several simplifications, in particular significantly reducing the size of the operator basis, which stream-lines matching and anomalous dimension calculations at subleading order in the velocity expansion. Also, soft ghosts no longer couple via potential like interactions to the heavy quark fields, and hence do not appear until two loops. Furthermore the the color structures that appear at each order in $α_s$ in the static potential are only those which should arise according to non-Abelian exponentiation. We also discuss how zero-bin subtractions clarify the role of $i\varepsilon$ terms in the heavy quark propagator poles carrying soft momenta. Even though the choice of the direction of the soft Wilson lines in our building blocks does not matter, there is still a limited set of consistent choices, and the predicted form of the eikonal poles does influence results at two-loops and beyond.
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