Relativistic and Recoil Corrections to Vacuum polarization in muonic systems: Three--photon exchange, gauge invariance and numerical values
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| Format: | Preprint |
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2024
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| _version_ | 1866917786841776128 |
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| author | Adkins, Gregory S. Jentschura, Ulrich D. |
| author_facet | Adkins, Gregory S. Jentschura, Ulrich D. |
| contents | For an accurate theoretical description of muonic bound systems, it is crucial to consistently treat relativistic and recoil corrections to vacuum polarization. The one-loop vacuum-polarization effect is by far the dominant quantum electrodynamic (QED) energy correction for bound muons, being of order $α(Zα)^2 m_r$, where $α$ is the fine-structure constant, $Z$ is the nuclear charge number, and $m_r$ is the reduced mass. Gauge invariance of the relativistic and recoil corrections to vacuum polarization of order $α(Zα)^4 m_r$ is investigated with respect to nonretarded and standard, renormalized variants of Coulomb gauge. The invariance is shown after including three-photon exchange diagrams. Our derivation is based on an adapted form of Nonrelativistic Quantum Electrodynamics for bound muon systems (NRQED$_μ$), which is a version of NRQED where the hard scale is set at the muon mass instead of the electron mass. Updated values for the gauge-independent corrections for one-muon ions with nuclear charge numbers $Z = 1,2,6$ are presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17068 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relativistic and Recoil Corrections to Vacuum polarization in muonic systems: Three--photon exchange, gauge invariance and numerical values Adkins, Gregory S. Jentschura, Ulrich D. High Energy Physics - Phenomenology For an accurate theoretical description of muonic bound systems, it is crucial to consistently treat relativistic and recoil corrections to vacuum polarization. The one-loop vacuum-polarization effect is by far the dominant quantum electrodynamic (QED) energy correction for bound muons, being of order $α(Zα)^2 m_r$, where $α$ is the fine-structure constant, $Z$ is the nuclear charge number, and $m_r$ is the reduced mass. Gauge invariance of the relativistic and recoil corrections to vacuum polarization of order $α(Zα)^4 m_r$ is investigated with respect to nonretarded and standard, renormalized variants of Coulomb gauge. The invariance is shown after including three-photon exchange diagrams. Our derivation is based on an adapted form of Nonrelativistic Quantum Electrodynamics for bound muon systems (NRQED$_μ$), which is a version of NRQED where the hard scale is set at the muon mass instead of the electron mass. Updated values for the gauge-independent corrections for one-muon ions with nuclear charge numbers $Z = 1,2,6$ are presented. |
| title | Relativistic and Recoil Corrections to Vacuum polarization in muonic systems: Three--photon exchange, gauge invariance and numerical values |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2409.17068 |