We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations. This paper pro- vides the first demonstration that such calculations can be performed through the algebraic evaluation of the path integral for the class of effective field theories that are (i) constructed using a non-trivial one-to-many mode decomposition of the UV theory, and (ii) valid for non-relativistic kinematics. We discuss the interplay between operators that appear at intermediate steps and the constraints imposed by the residual Lorentz symmetry that is encoded as reparameterization invariance within the effective description. The tools presented here provide a systematic approach for computing corrections to higher order in the heavy mass expansion; precision applications include predictions for experimental data and connections to theoretical tests via lattice QCD. A set of pedagogical appendices comprehensively reviews modern approaches to performing functional calculations algebraically, and derives contributions from a term with open covariant derivatives for the first time.

中文翻译：

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重夸克有效理论的泛函方法

我们使用泛函方法来计算重夸克有效理论中的单环效应。协变导数展开技术有助于有效提取匹配系数和重整化群演化方程。本文首次证明了此类计算可以通过对有效场论类的路径积分进行代数评估来执行，这些场论是 (i) 使用 UV 的非平凡一对多模式分解构建的理论，以及 (ii) 对非相对论运动学有效。我们讨论了出现在中间步骤的算子与剩余洛伦兹对称性所施加的约束之间的相互作用，该约束在有效描述中被编码为重新参数化不变性。这里介绍的工具提供了一种系统方法，用于计算重质量膨胀中更高阶的修正；精密应用包括对实验数据的预测以及通过晶格 QCD 与理论测试的联系。一组教学附录全面回顾了代数执行函数计算的现代方法，并首次从具有开放协变导数的术语中得出贡献。