# Four-loop wave function renormalization in QCD and QED

Marquard, Peter (Deutsches Elektronen-Synchrotron, DESY, 15738 Zeuthen, Germany) ; Smirnov, Alexander V. (Research Computing Center, Moscow State University, 119991 Moscow, Russia) ; Smirnov, Vladimir A. (Skobeltsyn Institute of Nuclear Physics of Moscow State University, 119991 Moscow, Russia) ; Steinhauser, Matthias (Institut für Theoretische Teilchenphysik, Karlsruhe Institute of Technology (KIT), 76128 Karlsruhe, Germany)

29 March 2018

Abstract: We compute the on-shell wave function renormalization constant to four-loop order in QCD and present numerical results for all coefficients of the $\mathrm{SU}\left({N}_{c}\right)$ color factors. We extract the four-loop Heavy Quark Effective Theory anomalous dimension of the heavy-quark field and also discuss the application of our result to QED.

Published in: Phys. Rev. D 97 (2018)