束缚态组分尺寸的计算
Calculation of size for bound-state constituents
摘要：
本文给出了用量子场论中的有效粒子重整化群方法（RGPEP）计算轻子-质子束缚态薛定谔方程中质子大小的基本方法，该方法只用到耦合常数的二阶幂次展开。在这种粗略的近似下，我们已经发现从束缚态可观测量中提取质子的大小取决于轻子质量，因此轻子质量越小，从相同的可观测束缚态能量分裂中提取的质子大小就越大。在氢和μ子-质子束缚态动力学的比较中，粗略的计算表明，在这两种情况下提取的质子大小之间的差异可以是百分之几。这样的值将与目前讨论的轻子原子中质子大小差异的数量级相匹配。计算使用的RGPEP的高阶比第二需要一个精确的解释的能量分裂的质子大小的薛定谔方程。这种计算应解决两种情况之间的概念差异：基于薛定谔方程的高精度计算所需的重整化群尺度远小于质子质量（在组分的约化质量和平均质量的乘积的根的数量级上）由于物理质子尺寸引起的能量分裂可以忽略薛定谔方程中组分的有效性质引起的修正来解释方程
英文摘要：
Elements are given of a calculation that identifies the size of a proton in the Schroedinger equation for lepton-proton bound states, using the renormalization group procedure for effective particles (RGPEP) in quantum field theory, executed only up to the second order of expansion in powers of the coupling constant. Already in this crude approximation, the extraction of size of a proton from bound-state observables is found to depend on the lepton mass, so that the smaller the lepton mass the larger the proton size extracted from the same observable bound-state energy splitting. In comparison of Hydrogen and muon-proton bound-state dynamics, the crude calculation suggests that the difference between extracted proton sizes in these two cases can be a few percent. Such values would match the order of magnitude of currently discussed proton-size differences in leptonic atoms. Calculations using the RGPEP of higher order than second are required for a precise interpretation of the energy splittings in terms of the proton size in the Schroedinger equation. Such calculations should resolve the conceptual discrepancy between two conditions: that the renormalization group scale required for high accuracy calculations based on the Schroedinger equation is much smaller than the proton mass (on the order of a root of the product of reduced and average masses of constituents) and that the energy splittings due to the physical proton size can be interpreted ignoring corrections due to the effective nature of constituents in the Schrödinger equation.
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