标题： 重正化，解耦和层次问题 显示英文标题

标题： Renormalization, Decoupling and the Hierarchy Problem

摘要： 层次问题与重整化和隔离有关。 我们可以通过重场的隔离来解释标量质量在环修正中的微小以及其对紫外物理的不敏感性。 正确识别可观测的物理质量作为依赖于外部动量的重整化质量是至关重要的，而不是常数质量。 我们重新考虑了重整化的环修正的性质，这些修正有限，与正则化无关，并且具有明确的微扰展开。 通过显式计算，我们表明任何对标量质量平方的环修正都按$(p^2-m^2)^2/M^2$被抑制，其中$p,m$和$M$分别是外部动量、标量极点质量和环中的重场质量。 这与 Appelquist-Carazzone 隔离定理一致，我们对此进行了显式化并完成了标量质量的情况。 显示英文摘要

摘要： The hierarchy problem is associated with renormalization and decoupling. We can account for the smallness of the scalar mass against loop corrections and its insensitivity to ultraviolet physics through the decoupling of heavy fields. It is essential to correctly identify the observable physical mass as the renormalized one that depends on the external momentum, as opposed to the constant mass. We reconsider the properties of the renormalized loop corrections, which are finite, independent of regularization and admit a well-defined perturbation. By explicit calculation, we show that any loop corrections to the scalar mass-squared are suppressed as $(p^2-m^2)^2/M^2$, where $p,m$ and $M$ are the external momentum, the scalar pole mass and the heavy field mass in the loop, respectively. This is in accordance with the Appelquist-Carazzone decoupling theorem, which we have explicitized and completed for the case of the scalar mass.