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LargeN expansion of QED: asymptotic photon propagator and contributions to the muon anomaly,for any number of loops
Authors:D J Broadhurst
Institution:1. Physics Department, Open University, MK7 6AA, Milton Keynes, UK
Abstract:We calculate analytical contributions to then-loop asymptotic photon propagator from diagrams withn–1 electron loops, i.e. theO(1/N) terms in the largeN limit. The corresponding contributions to the on-shell beta-function, beta(agr)=tau6 log agr/part logm reduced to rational combinations of zeta s =sum p p s . For the beta-function of the MOM scheme (i.e. the Gell-Man-Low function) we obtain theO(1/N) terms of

$$\Psi (\alpha _{MOM} ) = \beta (\alpha )\partial \log \alpha _{MOM} /\partial \log \alpha  = \sum\nolimits_n {\Psi _n (\alpha _{MOM} /\pi )^n } $$
Keywords:
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