$P-$state Positronium for Precision Physics: an Ultrafine Splitting at ${\alpha }^6$

Abstract

An "ultrafine" splitting in positronium between the $L=1$ spin-singlet state and the spin-average of the spin-triplet states is shown to arise only at order ${\alpha }^6$. The QED prediction for $n=2$ states is ${\Delta }_{2,P}=(683/172800)m{\alpha }^6=73.7(1.2)$ kHz. This represents the smallest leading-order QED splitting known. Current experimental efforts could observe this splitting, and its observation can constrain new ultralight interactions, such as axions or $Z^{\prime }$.

Comments: 4 pages, no figures