Positronium Hyperfine Splitting in Non-commutative Space at the Order ${\alpha }^6$

Abstract

We obtain positronium Hyperfine Splitting owing to the non-commutativity of space and show that, in the leading order, it is proportional to $\theta {\alpha }^6$ where, $\theta$ is the parameter of non-commutativity. It is also shown that spatial non-commutativity splits the spacing between $n=2$ triplet excited levels $E(2^3{S}_1)\to E(2^3{P}_2)$ which provides an experimental test on the non-commutativity of space.

Comments: 7 pages, 2 figures, to appear in Phys. Rev. D