Neutrino force at all length scales
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912771602382848 |
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| author | Ghosh, Mitrajyoti Grossman, Yuval Sieng, Chinhsan Yu, Bingrong |
| author_facet | Ghosh, Mitrajyoti Grossman, Yuval Sieng, Chinhsan Yu, Bingrong |
| contents | The Standard Model predicts a long-range force mediated by a pair of neutrinos, known as ``the neutrino force". It scales as $G_F^2/r^5$, where $G_F$ is the Fermi constant. However, as $r \lesssim \sqrt{G_F}$, the four-Fermi theory breaks down and the neutrino force no longer has the $1/r^5$ scaling. For the first time, we derive a complete expression for the neutrino force that is valid at all distances. For $r \gg \sqrt{G_F}$, the result reduces to the known $G_F^2/r^5$; for $r \ll \sqrt{G_F}$, it scales as $1/r$. We explore the implications of this result for atomic parity violation (APV) experiments. A key feature of the neutrino force is that it is a long-range effect compared to the atomic length scale. Thus, in general, it cannot be simply treated as a correction to the tree-level $Z$-exchange diagram without considering the atomic wavefunctions. We calculate the effects in muonium and positronium, finding that the neutrino force contributes about 4\% and 16\%, respectively, compared to the leading $ Z$ exchange. This indicates a significant impact on APV, with important implications for detecting the neutrino force and measuring the weak mixing angle in APV experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19059 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neutrino force at all length scales Ghosh, Mitrajyoti Grossman, Yuval Sieng, Chinhsan Yu, Bingrong High Energy Physics - Phenomenology Atomic Physics The Standard Model predicts a long-range force mediated by a pair of neutrinos, known as ``the neutrino force". It scales as $G_F^2/r^5$, where $G_F$ is the Fermi constant. However, as $r \lesssim \sqrt{G_F}$, the four-Fermi theory breaks down and the neutrino force no longer has the $1/r^5$ scaling. For the first time, we derive a complete expression for the neutrino force that is valid at all distances. For $r \gg \sqrt{G_F}$, the result reduces to the known $G_F^2/r^5$; for $r \ll \sqrt{G_F}$, it scales as $1/r$. We explore the implications of this result for atomic parity violation (APV) experiments. A key feature of the neutrino force is that it is a long-range effect compared to the atomic length scale. Thus, in general, it cannot be simply treated as a correction to the tree-level $Z$-exchange diagram without considering the atomic wavefunctions. We calculate the effects in muonium and positronium, finding that the neutrino force contributes about 4\% and 16\%, respectively, compared to the leading $ Z$ exchange. This indicates a significant impact on APV, with important implications for detecting the neutrino force and measuring the weak mixing angle in APV experiments. |
| title | Neutrino force at all length scales |
| topic | High Energy Physics - Phenomenology Atomic Physics |
| url | https://arxiv.org/abs/2410.19059 |