Sixth order electron and muon (g−2)/2 from second order vacuum polarization insertion

Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen

The sixth-order electron-loop vacuum-polarization contribution to the 2P1/2 − 2S1/2 Lamb shift of the muonic hydrogen (μ−p+ bound state) has been evaluated numerically. Our result is 0.005295 (1) meV. This eliminates the largest uncertainty in the theoretical calculation. Combined with the proposed precision measurement of the Lamb shift it will lead to a very precise determination of the proto...

Induced Pseudoscalar Coupling in Muon Capture and Second-order Corrections

The hyperfine effect in muon capture rate is analyzed with taking into account of the second-order terms in 1/M in the non-relativistic Hamiltonian. It is shown that in the situation of the dominance of the squared first-order terms the interference of zero-order and second-order terms has no significant influence. General expression for neutrino (recoil nucleus) angular distribution in muon ca...

CLNS98/1598 hep-ph/9812442 Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen

The sixth-order electron-loop vacuum-polarization contribution to the 2P1/2 − 2S1/2 Lamb shift of the muonic hydrogen (μ−p+ bound state) has been evaluated numerically. Our result is 0.005295 (1) meV. This eliminates the largest uncertainty in the theoretical calculation. Combined with the proposed precision measurement of the Lamb shift it will lead to a very precise determination of the proto...

THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.    

Second-order polarization-mode dispersion in photonic crystal fibers