arXiv subjects
Publications and source records attributed to P. Labelle.
A detailed presentation is given of the analytic calculation of the single-photon annihilation contributions to the positronium ground state hyperfine splitting to order $m_eα^6$ in the framework of non-relativistic effective theories. The current status of the theoretical description of the positronium ground state hyperfine splitting is reviewed.
Recently, much work has been devoted to the calculation of order $α$ corrections to the decay rate of pionium, the $π^+ π^-$ bound state. In previous calculations, nonrelativistic QED corrections were neglected since they start at order $α^2$ in hydrogen and positronium. In this note, we point out that there is one correction which is actually of order $α$ times a function of the ratio $μ_r α/ m_e$, where $μ_r$ is the reduced mass of the system. When $μ_r α\ll m_e$, this function can be Taylor expanded and leads to higher order corrections. When $μ_r α\approx m_e$, as is the case in pionium, the function is of order one and the correction is of order $α$. We use an effective field theory approach to calculate this correction and find it equal to $0.4298 αΓ_0$. We also calculate the corresponding correction to the dimuonium ($μ^+ μ^-$ bound state) decay rate and obtained a result in agreement with Jentschura et al.
The single photon annihilation contributions for the positronium ground state hyperfine splitting are calculated analytically to order $m_eα^6$ using NRQED. Based on intuitive physical arguments the same result can also be determined by a trivial calculation using results from existing literature. Our result completes the hyperfine splitting calculation to order $m_eα^6$. We compare the theoretical prediction with the most recent experimental measurement.
We compute the next-to-leading, O(m alpha^5), contribution to the hyperfine splitting in positronium within the framework of NRQED. When applied to the ground state, our calculation reproduces known results, providing a further test of NRQED techniques. Besides providing a very simple method of calculation of the standard result, we also obtain new expressions for excited states of positronium with negligible additional effort. Our calculation requires the complete next-to-leading matching of the lowest-dimension NRQED four-fermi couplings, which we publish here for the first time.
We discuss how contributions to the order ${\cal O} (m α^8)$ orthopositronium decay rate can be separated into two categories, one due to relativistic momenta and calculable in terms of QED scattering amplitudes, the other due to low momenta and calculable in the simpler framework of a low-energy effective theory (NRQED). We report new results for all low-momentum contributions, and give a formula relating the remaining contributions to conventional (on-shell) QED scattering amplitudes.