Radiative QED corrections to the lepton anomaly from four-loop vacuum polarization insertions with three identical leptons
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866929397821341696 |
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| author | Solovtsova, O. P. Lashkevich, V. I. Kaptari, L. P. |
| author_facet | Solovtsova, O. P. Lashkevich, V. I. Kaptari, L. P. |
| contents | Analytical expressions for the tenth order electromagnetic corrections to the lepton ($L=e, ~μ$ and $τ$) anomaly $a_L$ are derived explicitly for a class of Feynman diagrams with insertions of the vacuum polarization operator consisting of four closed lepton loops. We consider a particular case when one loop is formed by the lepton $L$ of the same kind as the one under consideration, the other three loops being formed by leptons $\ell\neq L$. The method is based on the consecutive application of dispersion relations for the polarization operator and the Mellin--Barnes transform for the propagators of massive particles. The result is expressed in terms of the mass ratio $r=m_\ell/m_L$. We investigate the behaviour of the exact analytical expressions as $r\to 0$ and $r\to \infty$ and compare them with the corresponding asymptotic expansions known in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16645 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Radiative QED corrections to the lepton anomaly from four-loop vacuum polarization insertions with three identical leptons Solovtsova, O. P. Lashkevich, V. I. Kaptari, L. P. High Energy Physics - Phenomenology High Energy Physics - Theory Analytical expressions for the tenth order electromagnetic corrections to the lepton ($L=e, ~μ$ and $τ$) anomaly $a_L$ are derived explicitly for a class of Feynman diagrams with insertions of the vacuum polarization operator consisting of four closed lepton loops. We consider a particular case when one loop is formed by the lepton $L$ of the same kind as the one under consideration, the other three loops being formed by leptons $\ell\neq L$. The method is based on the consecutive application of dispersion relations for the polarization operator and the Mellin--Barnes transform for the propagators of massive particles. The result is expressed in terms of the mass ratio $r=m_\ell/m_L$. We investigate the behaviour of the exact analytical expressions as $r\to 0$ and $r\to \infty$ and compare them with the corresponding asymptotic expansions known in the literature. |
| title | Radiative QED corrections to the lepton anomaly from four-loop vacuum polarization insertions with three identical leptons |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.16645 |