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

## TL;DR

This paper predicts an ultrafine splitting in positronium at order α^6, which is the smallest known leading-order QED splitting, and discusses its potential for experimental observation and new physics constraints.

## Contribution

It provides the first QED prediction of an ultrafine positronium splitting at order α^6, highlighting its significance for precision tests and new physics searches.

## Key findings

- Predicted ultrafine splitting of 73.7(1.2) kHz for n=2 states.
- Splitting arises only at order α^6, the smallest known leading-order QED effect.
- Experimental observation could constrain ultralight particles like axions or Z'.

## 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 $Z'$.