Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Positronium energy levels at order $m \alpha^7$: vacuum polarization
  corrections in the two-photon-annihilation channel   We have calculated all contributions to the energy levels of parapositronium
at order $m \alpha^7$ coming from vacuum polarization corrections to processes
involving virtual annihilation to two photons. This work is motivated by
ongoing efforts to improve the experimental determination of the positronium
ground-state hyperfine splitting.

17
The categories of this paper are: q-fin
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The categories of this paper are: econ
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci