Positronium energy levels at order $m{\alpha }^7$: light-by-light scattering in the two-photon-annihilation channel

Abstract

Recent and ongoing experimental work on the positronium spectrum motivates new efforts to calculate positronium energy levels at the level of three loop corrections. We have obtained results for one set of such corrections involving light-by-light scattering of the photons produced in a two-photon virtual annihilation process. Our result is an energy shift $1.58377(8)m{\alpha }^7/{\pi }^3$ for the n=1 singlet state, correcting the ground state hyperfine splitting by -6.95 kHz. We also obtained a new and more precise result for the light-by-light scattering correction to the real decay of parapositronium into two photons.

arXiv comment9 pages, 1 figure

References in corpus (28)

• Final Report of the Muon E821 Anomalous Magnetic Moment Measurement at BNL
• Complete Tenth-Order QED Contribution to the Muon g-2
• Precision physics of simple atoms: QED tests, nuclear structure and fundamental constants
• Cavity Control of a Single-Electron Quantum Cyclotron:\\Measuring the Electron Magnetic Moment
• Precision Study of Positronium: Testing Bound State QED Theory
• Positronium S state spectrum: analytic results at O(m alpha^6)
• Lamb Shift in Muonic Hydrogen. I. Verification and Update of Theoretical Predictions
• Direct Observation of the Hyperfine Transition of the Ground State Positronium
• New Precision Measurement of Hyperfine Splitting of Positronium
• Order alpha^7 ln(1/alpha) Contribution to Positronium Hyperfine Splitting
• Positronium hyperfine splitting: analytical value at m*alpha^6
• O(alpha^3 ln alpha) corrections to muonium and positronium hyperfine splitting
• New Value of M_mu/M_e from Muonium Hyperfine Splitting
• O(m alpha^7 ln(alpha)^2) corrections to positronium energy levels
• Lamb Shift in Muonic Hydrogen. II. Analysis of the Discrepancy of Theory and Experiment
• Complete Result for Positronium Energy Levels at Order alpha^6 m
• The Single Photon Annihilation Contributions to the Positronium Hyperfine Splitting to Order $m_e{\alpha }^6$
• alpha^2 corrections to parapositronium decay
• Hyperfine splitting in positronium to $\mathcal{O}({\alpha }^7{m}_e)$: one-photon annihilation contribution
• alpha^2 corrections to parapositronium decay: a detailed description
• Positronium hyperfine splitting at order $m{\alpha }^7$: light-by-light scattering in the two-photon-exchange channel
• New Corrections of Order ${\alpha }^6$ to $s$-Levels of Two-Body Systems
• Hard Nonlogarithmic Corrections of Order $m{\alpha }^7$ to Hyperfine Splitting in Positronium
• Positronium as a probe for new physics beyond the standard model
• Decay Rate of a Positronium. Review of Theory and Experiment
• Details on the $\mathcal{O}(m_e{\alpha }^6)$ Positronium Hyperfine Splitting due to Single Photon Annihilation
• Precise measurement of positronium hyperfine splitting using the Zeeman effect
• The "recoil" correction of order $m{\alpha }^6$ to hyperfine splitting of positronium ground state

Cited by in corpus (13)

• Three-photon-annihilation contributions to positronium energies at order $m{\alpha }^7$
• Hard Three-Loop Corrections to Hyperfine Splitting in Positronium and Muonium
• Electroweak Corrections to the True Muonium Hyperfine Splitting
• The QED four -- photon amplitudes off-shell: part 1
• The QED four-photon amplitudes off-shell: part 2
• Positronium energy levels at order $m{\alpha }^7$: Product contributions in the two-photon-annihilation channel
• One More Hard Three-Loop Correction to Parapositronium Energy Levels
• Can Galileons solve the muon problem?
• Three-Loop Corrections to Lamb Shift in Muonium and Positronium
• $P-$state Positronium for Precision Physics: an Ultrafine Splitting at ${\alpha }^6$
• Hyperfine Splitting in True Muonium to $\mathcal{O}(m_{\mu }{\alpha }^6)$: Two Photon Annihilation Contribution from Other Flavors
• Fifth Force and Hyperfine Splitting in Bound Systems
• Measurement of the ${\text{1}}^{\text{3}}{\text{S}}_{\text{1}}\to {\text{2}}^{\text{3}}{\text{S}}_{\text{1}}$ interval in positronium using field-ionization of Rydberg states