# The Three Loop On-Shell Renormalization of QCD and QED

## Abstract

The authors describe a calculation of the on-shell renormalization factors in QCD and QED at the three loop level. Explicit results for the fermion mass renormalization factor Zm and the on-shell fermion wave function renormalization constant Z{sub 2} are given. They find that at theta(alpha{sub 3}{sup 3}) the wave function renormalization constant Z{sub 2} in QCD becomes gauge dependent also in the on-shell scheme, thereby disproving the gauge-independence conjecture based on an earlier two-loop result. As a byproduct, they derive a theta(alpha{sub s}{sup s}) contribution to the anomalous dimension of the heavy quark field in HQET.

- Authors:

- Publication Date:

- Research Org.:
- Stanford Linear Accelerator Center, Menlo Park, CA (US)

- Sponsoring Org.:
- USDOE Office of Energy Research (ER) (US)

- OSTI Identifier:
- 763774

- Report Number(s):
- SLAC-PUB-8450

TRN: US0004810

- DOE Contract Number:
- AC03-76SF00515

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 16 May 2000

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; QUANTUM CHROMODYNAMICS; QUANTUM ELECTRODYNAMICS; MASS RENORMALIZATION; FERMIONS; WAVE FUNCTIONS

### Citation Formats

```
Melnikov, Kirill.
```*The Three Loop On-Shell Renormalization of QCD and QED*. United States: N. p., 2000.
Web. doi:10.2172/763774.

```
Melnikov, Kirill.
```*The Three Loop On-Shell Renormalization of QCD and QED*. United States. doi:10.2172/763774.

```
Melnikov, Kirill. Tue .
"The Three Loop On-Shell Renormalization of QCD and QED". United States. doi:10.2172/763774. https://www.osti.gov/servlets/purl/763774.
```

```
@article{osti_763774,
```

title = {The Three Loop On-Shell Renormalization of QCD and QED},

author = {Melnikov, Kirill},

abstractNote = {The authors describe a calculation of the on-shell renormalization factors in QCD and QED at the three loop level. Explicit results for the fermion mass renormalization factor Zm and the on-shell fermion wave function renormalization constant Z{sub 2} are given. They find that at theta(alpha{sub 3}{sup 3}) the wave function renormalization constant Z{sub 2} in QCD becomes gauge dependent also in the on-shell scheme, thereby disproving the gauge-independence conjecture based on an earlier two-loop result. As a byproduct, they derive a theta(alpha{sub s}{sup s}) contribution to the anomalous dimension of the heavy quark field in HQET.},

doi = {10.2172/763774},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2000},

month = {5}

}

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