标题： 在壳重整化方案中质量标量对引力势的修正 显示英文标题

标题： Massive Scalar Corrections to Gravitational Potentials in the On-Shell Renormalization Scheme

摘要： 我们通过求解有效爱因斯坦场方程，计算由非最小耦合的宏观标量引起的在闵可夫斯基空间中由静态点质量产生的两个引力势的一环修正。 我们首先获得一个明显横向的引力子自能，并通过进行泡图的重求和，导出一般协变规范下的相应重整化引力子传播子。 对于一类包括朗道规范在内的规范，重整化引力子传播子在物理极限下与树级传播子成正比。 这一事实使我们能够采用物理重整化方案，使得重整化的牛顿常数$G$取实验测得的值。 对引力势的修正结果在解析表达式和长距离行为方面与真空极化对库仑势的修正具有相似结构。 通过将我们的结果与引力滑动测量进行比较，我们建立了对非最小耦合的约束：$|\xi| \lesssim 5\times 10^{43}/\sqrt{N}$，其中$N$是标量场的数量。 显示英文摘要

摘要： We calculate the one-loop corrections induced by a non-minimally coupled massive scalar to the two gravitational potentials sourced by a static point mass in Minkowski space via solving the effective Einstein field equations. We first obtain a manifestly transverse graviton self-energy and, by performing resummation of the bubble diagrams, derive the associated dressed graviton propagator in the general covariant gauge. For one class of gauges, which include the Landau gauge, the dressed graviton propagator becomes proportional to the tree-level propagator in the on-shell limit. This fact allows us to employ the on-shell renormalization scheme so that the renormalized Newton constant $G$ takes the value measured in the experiments. The resulting corrections to the gravitational potentials share similar structures with the vacuum polarization correction to the Coulomb potential regarding their analytic expressions and long distance behavior. By comparing our results with gravitational slip measurements, we establish a constraint on the non-minimal coupling: $|\xi| \lesssim 5\times 10^{43}/\sqrt{N}$, where $N$ is the number of scalar fields.