# Effective field theories and higher-dimension operators

## Abstract

The contribution of heavy fermions (muons) to the electron anomalous moment in quantum electrodynamics is considered within the context of effective field theories, correct to order ..cap alpha../sup 2/m/sup 2//M/sup 2/. Although no violation of decoupling is found, it is shown that the leading contribution of the muon to the electron magnetic moment is incorrectly given by the local effective Lagrangian obtained from functional integration over heavy fields. It is also shown that this same local effective Lagrangian, with all terms retained of arbitrary order in (1/M/sup 2/), has the wrong analyticity in this variable in that the electron anomalous moment has a term of O(..cap alpha../sup 2/(m/sup 4//M/sup 4/)ln(M/sup 2//m/sup 2/)) which cannot be obtained from this local effective Lagrangian. The correct calculation of these effects requires calculation of mixed light-heavy contributions, an issue previously discussed for contributions to operators of dimension < or =4.

- Authors:

- Publication Date:

- Research Org.:
- Department of Physics, Brandeis University, Waltham, Massachusetts 02254

- OSTI Identifier:
- 6135631

- DOE Contract Number:
- EY-76-S-02-3230-A002

- Resource Type:
- Journal Article

- Journal Name:
- Phys. Rev. D; (United States)

- Additional Journal Information:
- Journal Volume: 24:6

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ELECTRONS; MAGNETIC MOMENTS; QUANTUM ELECTRODYNAMICS; COUPLING CONSTANTS; DECOUPLING; FERMIONS; GAUGE INVARIANCE; LAGRANGIAN FUNCTION; PROPAGATOR; RENORMALIZATION; VACUUM POLARIZATION; ELECTRODYNAMICS; ELEMENTARY PARTICLES; FIELD THEORIES; FUNCTIONS; INVARIANCE PRINCIPLES; LEPTONS; QUANTUM FIELD THEORY; 645400* - High Energy Physics- Field Theory

### Citation Formats

```
Ovrut, B A, and Schnitzer, H J.
```*Effective field theories and higher-dimension operators*. United States: N. p., 1981.
Web. doi:10.1103/PhysRevD.24.1695.

```
Ovrut, B A, & Schnitzer, H J.
```*Effective field theories and higher-dimension operators*. United States. doi:10.1103/PhysRevD.24.1695.

```
Ovrut, B A, and Schnitzer, H J. Tue .
"Effective field theories and higher-dimension operators". United States. doi:10.1103/PhysRevD.24.1695.
```

```
@article{osti_6135631,
```

title = {Effective field theories and higher-dimension operators},

author = {Ovrut, B A and Schnitzer, H J},

abstractNote = {The contribution of heavy fermions (muons) to the electron anomalous moment in quantum electrodynamics is considered within the context of effective field theories, correct to order ..cap alpha../sup 2/m/sup 2//M/sup 2/. Although no violation of decoupling is found, it is shown that the leading contribution of the muon to the electron magnetic moment is incorrectly given by the local effective Lagrangian obtained from functional integration over heavy fields. It is also shown that this same local effective Lagrangian, with all terms retained of arbitrary order in (1/M/sup 2/), has the wrong analyticity in this variable in that the electron anomalous moment has a term of O(..cap alpha../sup 2/(m/sup 4//M/sup 4/)ln(M/sup 2//m/sup 2/)) which cannot be obtained from this local effective Lagrangian. The correct calculation of these effects requires calculation of mixed light-heavy contributions, an issue previously discussed for contributions to operators of dimension < or =4.},

doi = {10.1103/PhysRevD.24.1695},

journal = {Phys. Rev. D; (United States)},

number = ,

volume = 24:6,

place = {United States},

year = {1981},

month = {9}

}