Radiative-recoil corrections to muonium and positronium hyperfine splitting

Journal Article · Tue May 15 00:00:00 EDT 1984 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.29.2290· OSTI ID:6761543

Sapirstein, J R; Terray, E A; Yennie, D R

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.

• Research Organization: Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853
• OSTI ID: 6761543
• Journal Information: Phys. Rev. D; (United States), Vol. 29:10
• Country of Publication: United States
• Language: English

Related Subjects

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