Positronium hyperfine splitting at order $m{\alpha }^7$: light-by-light scattering in the two-photon-exchange channel

Abstract

We have calculated the contribution to the positronium hyperfine splitting at order $m{\alpha }^7$ of the light-by-light scattering process in the exchange of two photons between the electron and positron. Our result is $\Delta E=-0.235355(8)m{\alpha }^4{\left(\frac{\alpha }{\pi }\right)}^3=-1.034kHz$. As a check of our approach we confirm earlier evaluations of the analogous correction for a bound system (such as muonium) with unequal masses.

Comments: 10 pages, 2 figures