Theory of Loosely Bound Composite Systems: Multiloop Corrections to Lamb Shift, Hyperfine Splitting, and g-Factors

近年来，两体束缚系统的高精度实验已经达到了一个新的精度水平，并有望取得进一步的进展。对氢、μ 鎓和其它简单类氢离子的能移测量的实验误差减小了几个数量级。这些最新进展为精确测定许多基本常数（里德伯常数、电子-μ子质量比、原子单位的电子质量、质子电荷半径、氘核结构半径等）开辟了新的前景，对Lamb位移和超精细劈裂的实验结果与理论结果进行了比较，实验进展对理论提出了新的挑战。将氢中1 S Lamb位移值的理论误差降低到低于1 kHz的水平（以及分别将2S Lamb位移降低到低于十分之几kHz）应被视为理论的下一阶段。μ素超精细分裂的理论误差应减小到10 Hz左右。μ子氢2S 2 P兰姆位移的理论误差应减小到0：001 meV以下。在低Z系统理论中的主要问题是：Lamb位移的三圈非反冲修正和氢原子和μ原子的超精细分裂。μ介子超精细分裂的三圈辐射反冲修正。对μ介子氢的Lamb位移的非反冲高阶修正和对包含自旋为j6 = 1= 2的粒子系统的束缚g因子的束缚和反冲修正。所有的计算都将用现代微扰量子电动力学的方法来完成。

High precision experiments with two-body bound systems have achieved a new level of accuracy in recent years and further progress is expected. The experimental errors of measurements of energy shifts in hydrogen, muonium and other simple hydrogenlike ions were reduced by orders of magnitude. These recent developments opened new perspectives for precise determination of many fundamental constants (the Rydberg constant, electron-muon mass ratio, electron mass in atomic units, proton charge radius,deuteron structure radius, etc.), and for comparison of the experimental and theoretical results on the Lamb shifts and hyperfinne splitting.The experimental progress poses new theoretical challenges. Reduction of the theoretical error of the value of the 1S Lamb shift in hydrogen to the level below 1 kHz (and, respectively, of the 2S Lamb shift to below several tenth of kHz) should be considered as a next stage of the theory. The theoretical error of the hyperfine splitting in muonium should be reduced to about 10 Hz. The theoretical error of the 2S 2P Lamb shift in muonic hydrogen should be reduced below 0:001 meV. The problem of the spin dependence of the bound state corrections to g factors should be resolved.The following major problems in the theory of low Z systems will be addressed in the proposed research: Three-loop nonrecoil corrections to the Lamb shift and hyperfine splitting in hydrogen and muoinium. Three-loop radiative-recoil corrections to hyperfine splitting in muonium. Nonrecoil high-order corrections to the Lamb shift in muonic hydrogen and the binding and recoil corrections to the bound g factor in systems including particles with spins j 6= 1=2.Modern methods of perturbative quantum electrodynamics will be used to perform all of the calculations.