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 SU$(N_c)$ colour factors. We extract the four-loop HQET anomalous dimension of the heavy quark field and also discuss the application of our result to QED.
Highlights
Heavy quarks play an important role in modern particle physics, in particular in the context of QCD
The wave function renormalization constant is conveniently cast into the form
Besides the on-shell quark mass renormalization constant and the leptonic anomalous magnetic moment, which have been considered in Refs. [1,2,7], respectively, this constitutes a third “classical” application of four-loop on-shell integrals
Summary
Heavy quarks play an important role in modern particle physics, in particular in the context of QCD. Processes which involve heavy quarks require the renormalization constants for the heavy-quark mass and, when they appear as external particles, for the quark wave function. The mass renormalization constant in the on-shell scheme, ZOmS, has been computed to four-loop order in Refs. We compute the wave function renormalization constant in the on-shell scheme, ZO2 S, to the same order in perturbation theory. [3] for the evaluation of ZOmS and ZO2 S reduces all occurring Feynman diagrams to the evaluation of on-shell integrals at the bare mass scale. Inserting Eq (5) into Eq (1) and comparing to Eq (4) leads to the following formulas for the renormalization constants: ZOmS 1⁄4 1 þ Σ1ðM2; MÞ; ðZO2 SÞ−1.
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