Partial-wave renormalization correction

I. Goidenko, G. Plunien, A. Nefiodov, S. Zschocke, L. Labzowsky, and G. Soff No regularization corrections to the partial-wave renormalization procedure, hep-ph/0006220... 

Regularization Corrections to the Partial-Wave Renormalization Procedure ... 

A description of the partial-wave renormalization (PWR), used for calculating the first-order self energy and certain higher-order effects for the energy levels in highly cllarged ions, is presented. We put special emphasis on correction terms which have to be considered due to the use of the non-covariant subtraction scheme used in PWR. 

In the partial-wave renormalization approach, which we consider in this paper, we have shown that these correction terms vanish for the first-order selfenergy and also for Coulomb screened self-energy. However, in the last case we obtain non-zero correction terms for the different subgroups of diagrams,... 

In this paper we adopt the PWE renormalization scheme. Accordingly, all bound terms in Eqs. (18)-(21) appear as double sums over partial waves. These double sums arise from the product of two matrix elements containing exp(i w r). Each individual partial wave contribution is finite and only the sum over partial waves diverges. In our calculation this divergency is removed by term-by-term subtraction of the corresponding counterterms. The PWE for the sum of all terms in Eq. (17) thus ensures a correct cancellation. 

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