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Orderα 2 corrections to the positronium hyperfine interval arising from three-photon virtual annihilation

Поправки порядкаα 2 к сверхтонкому расшеплению в поэитронии, воэникаюшему иэ трехфотонной виртуальной аннигиляции

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Il Nuovo Cimento A (1965-1970)

Summary

We present the details of our calculation of three-photon virtual-annihilation contributions to the ground-state triplet-singlet (hyperfine) splitting in positronium. The result is obtained in an analytic form to ordermα 6(α 4 R ∞) and constitutes a contribution of − 0.91 MHz to the hyperfine interval. Potential infra-red (lnα) contributions, which appear at intermediate stages of the calculation, are shown to cancel and the gauge invariance of the result is demonstrated.

Riassunto

Si presentano dettagliatamente i calcoli dei contributi della annichilazione virtuale a tre fotoni alla separazione (iperfine) tripletto-singoletto dello stato fondamentale nel positronio. Si ottiene il risultato in una forma analitica all’ordinemα 6(α 4 R ∞) che costituisce un contributo di −0.91 MHz all’intervallo iperfine. Si mostra che i contributi potenziali nell’infrarosso (lnα), che compaiono a stadi intermedi del calcolo, si eliminano e si dimostra l’invarianza di gauge del risultato.

Реэюме

Предлагается подробное вычисление вкладов трехфотонной виртуальной аннигиляции в триплет-синглетное (сверхтонкое) расшепление основного состояния в поэитронии. Реэультат получен в аналитическом видеmα 6(α 4 R ∞) и представляет вклад −0.91 МГц в сверхтонкое расшепление. Покаэывается, что инфракрасные (lnα) вклады, которые воэникают на промежуточных стадиях вычисления, вэаимно уничтожаются. Отмечается калибровочная инвариантность полученного реэультата.

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Author notes

  1. T. Fulton

    Present address: The Johns Hopkins University, USA

Authors and Affiliations

  1. The Johns Hopkins University, Baltimore, Md.

    V. K. Cung & A. Devoto

  2. CERN, Geneva

    T. Fulton

  3. Michigan State University, East Lansing, Mich.

    W. W. Repko

Authors
  1. V. K. Cung
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  2. A. Devoto
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  3. T. Fulton
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  4. W. W. Repko
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Supported in part by the National Science Foundation.

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Cung, V.K., Devoto, A., Fulton, T. et al. Orderα 2 corrections to the positronium hyperfine interval arising from three-photon virtual annihilation. Nuov Cim A 43, 643–657 (1978). https://doi.org/10.1007/BF02730349

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