# Radiative-recoil corrections to muonium and positronium hyperfine splitting

## Abstract

We present a detailed description of the calculation of radiative-recoil corrections to the ground-state hyperfine splitting in muonium and positronium to order ..cap alpha../sup 2/E/sub F/, the results of which were previously reported. All these corrections involve two-photon exchanges with one-loop radiative corrections to either a photon or a lepton. The QED vacuum polarization corrections are evaluated completely analytically to the order of interest. The hadronic contributions are estimated and found to be very small. As a preliminary to the lepton line calculation, a compact expression is derived for the radiative correction to such lines. This factor is then applied in a number of different contexts: the recalculation of the old nonrecoil result, which is known analytically; the analytic evaluation of terms of order ..cap alpha../sup 2/(m/sub e//m/sub ..mu../)ln(m/sub ..mu..//m/sub e/ )E/sub F/, which arise from the electron leg; and the nonlogarithmic terms from both lines, which require numerical calculations. The muonium results are ..nu..+e/sup -/ = (..cap alpha../..pi..)/sup 2/(m/sub e//m /sub ..mu../) (-2ln/sup 2/(m/sub ..mu..//m/sub e/)+(13/1 2)ln(m/sub ..mu..//m/sub e/)+18.18 +- 0. 58)E/sub F/ and those for positronium are ..nu../sub e//sup +/e/sup -/ = ..cap alpha../sup 2/(-1.788 +- 0 .004)E/sub F/, where E/sub F/ for positronium does not include themore »

- Authors:

- Publication Date:

- Research Org.:
- Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853

- OSTI Identifier:
- 6761543

- Resource Type:
- Journal Article

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

- Additional Journal Information:
- Journal Volume: 29:10

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; MUONIUM; HYPERFINE STRUCTURE; POSITRONIUM; ANNIHILATION; BOUND STATE; PHOTONS; QUANTUM ELECTRODYNAMICS; RADIATIVE CORRECTIONS; RECOILS; VACUUM POLARIZATION; BASIC INTERACTIONS; CORRECTIONS; ELECTRODYNAMICS; ELECTROMAGNETIC INTERACTIONS; ELEMENTARY PARTICLES; FIELD THEORIES; INTERACTIONS; MASSLESS PARTICLES; QUANTUM FIELD THEORY; 640303* - Atomic, Molecular & Chemical Physics- Positronium, Muonium, & Muonic & Mesic Atoms & Molecules; 645400 - High Energy Physics- Field Theory

### Citation Formats

```
Sapirstein, J R, Terray, E A, and Yennie, D R.
```*Radiative-recoil corrections to muonium and positronium hyperfine splitting*. United States: N. p., 1984.
Web. doi:10.1103/PhysRevD.29.2290.

```
Sapirstein, J R, Terray, E A, & Yennie, D R.
```*Radiative-recoil corrections to muonium and positronium hyperfine splitting*. United States. doi:10.1103/PhysRevD.29.2290.

```
Sapirstein, J R, Terray, E A, and Yennie, D R. Tue .
"Radiative-recoil corrections to muonium and positronium hyperfine splitting". United States. doi:10.1103/PhysRevD.29.2290.
```

```
@article{osti_6761543,
```

title = {Radiative-recoil corrections to muonium and positronium hyperfine splitting},

author = {Sapirstein, J R and Terray, E A and Yennie, D R},

abstractNote = {We present a detailed description of the calculation of radiative-recoil corrections to the ground-state hyperfine splitting in muonium and positronium to order ..cap alpha../sup 2/E/sub F/, the results of which were previously reported. All these corrections involve two-photon exchanges with one-loop radiative corrections to either a photon or a lepton. The QED vacuum polarization corrections are evaluated completely analytically to the order of interest. The hadronic contributions are estimated and found to be very small. As a preliminary to the lepton line calculation, a compact expression is derived for the radiative correction to such lines. This factor is then applied in a number of different contexts: the recalculation of the old nonrecoil result, which is known analytically; the analytic evaluation of terms of order ..cap alpha../sup 2/(m/sub e//m/sub ..mu../)ln(m/sub ..mu..//m/sub e/ )E/sub F/, which arise from the electron leg; and the nonlogarithmic terms from both lines, which require numerical calculations. The muonium results are ..nu..+e/sup -/ = (..cap alpha../..pi..)/sup 2/(m/sub e//m /sub ..mu../) (-2ln/sup 2/(m/sub ..mu..//m/sub e/)+(13/1 2)ln(m/sub ..mu..//m/sub e/)+18.18 +- 0. 58)E/sub F/ and those for positronium are ..nu../sub e//sup +/e/sup -/ = ..cap alpha../sup 2/(-1.788 +- 0 .004)E/sub F/, where E/sub F/ for positronium does not include the annihilation contribution.},

doi = {10.1103/PhysRevD.29.2290},

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

number = ,

volume = 29:10,

place = {United States},

year = {1984},

month = {5}

}