Positronium hyperfine splitting at ordermα7: Light-by-light scattering in the two-photon-exchange channel

Abstract

We have calculated the contribution to the positronium hyperfine splitting at order mα 7 of the light-by-light scattering process in the exchange of two photons between the electron and positron. Our result is ∆E = −0.235355(8)mα 4 α π 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.

Hard three-loop corrections to hyperfine splitting in positronium and muonium

“…This paper was soon followed by the works of Adkins and collaborators [20,21], who calculated contributions of the light-by-light scattering insertion in the scattering and annihilation channels.…”

“…New measurement of the positronium HFS splitting is now planned at J-PARC [17]. All theoretical contributions to HFS in positronium of order mα 6 and logarithmic corrections of order mα 7 are already known, see, e.g., reviews in [18][19][20].…”

A short review about some exotic systems containing electrons, muons, and tauons

“…For the two-body relativistic or QED corrections, such as for the positronium system, some advanced studies have recently been performed [9,10] to calculate the positronium hyperfine splitting and energy levels at order Oða 7 Þ. Similarly, the relativistic or QED corrections for some particular three-and four-body systems have been investigated in various papers (see for examples, [12] and [21]).…”

“…In very recent works, Adkins et al [9,10] calculated the positronium hyperfine splitting and energy levels at order Oða 7 Þ. They obtained a new and more precise result for the light-bylight scattering correction to the real decay of parapositronium into two photons.…”

Testing Quantum Electrodynamics with Positronium State

“…., where we used the two and three-loop result for a e [11,48]. Another example is a recently computed nonannihilation correction due to closed electron loops [49,50], which is also numerically suppressed. In this case the nonannihilation contribution would be given by D sct ≈ 4π 2 7 δ us o ≈ 106, which slightly exceeds the one-photon annihilation contribution (18) in full analogy with the structure of the second-order corrections.…”