Understanding the puzzle of angular momentum conservation in beta decay and related processes
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arXiv
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| Format: | Preprint |
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2024
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| author | Baym, Gordon Peng, Jen-Chieh Pethick, C. J. |
| author_facet | Baym, Gordon Peng, Jen-Chieh Pethick, C. J. |
| contents | We ask the question of how angular momentum is conserved in electroweak interaction processes. To introduce the problem with a minimum of mathematics, we first raise the same issue in elastic scattering of a circularly polarized photon by an atom, where the scattered photon has a different spin direction than the original photon, and note its presence in scattering of a fully relativistic spin-1/2 particle by a central potential. We then consider inverse beta decay in which an electron is emitted following the capture of a neutrino on a nucleus. While both the incident neutrino and final electron spins are antiparallel to their momenta, the final spin is in a different direction than that of the neutrino -- an apparent change of angular momentum. However, prior to measurement of the final particle, in all these cases angular momentum is indeed conserved, The apparent non-conservation of angular momentum arises in the quantum measurement process in which the measuring apparatus does not have an initially well-defined angular momentum, but is localized in the outside world. We generalize the discussion to massive neutrinos and electrons, and examine nuclear beta decay and electron-positron annihilation processes through the same lens, enabling physically transparent derivations of angular and helicity distributions in these reactions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15011 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Understanding the puzzle of angular momentum conservation in beta decay and related processes Baym, Gordon Peng, Jen-Chieh Pethick, C. J. High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory Quantum Physics We ask the question of how angular momentum is conserved in electroweak interaction processes. To introduce the problem with a minimum of mathematics, we first raise the same issue in elastic scattering of a circularly polarized photon by an atom, where the scattered photon has a different spin direction than the original photon, and note its presence in scattering of a fully relativistic spin-1/2 particle by a central potential. We then consider inverse beta decay in which an electron is emitted following the capture of a neutrino on a nucleus. While both the incident neutrino and final electron spins are antiparallel to their momenta, the final spin is in a different direction than that of the neutrino -- an apparent change of angular momentum. However, prior to measurement of the final particle, in all these cases angular momentum is indeed conserved, The apparent non-conservation of angular momentum arises in the quantum measurement process in which the measuring apparatus does not have an initially well-defined angular momentum, but is localized in the outside world. We generalize the discussion to massive neutrinos and electrons, and examine nuclear beta decay and electron-positron annihilation processes through the same lens, enabling physically transparent derivations of angular and helicity distributions in these reactions. |
| title | Understanding the puzzle of angular momentum conservation in beta decay and related processes |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Nuclear Theory Quantum Physics |
| url | https://arxiv.org/abs/2405.15011 |