Quark and lepton mixing in the asymptotically safe Standard Model
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913958924910592 |
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| author | Eichhorn, Astrid Gyftopoulos, Zois Held, Aaron |
| author_facet | Eichhorn, Astrid Gyftopoulos, Zois Held, Aaron |
| contents | The quark mixing (CKM) matrix is near-diagonal, whereas the lepton mixing (PMNS) matrix is not. We learn that both observations can generically be explained within an ultraviolet completion of the Standard Model with gravity. We find that certain relations between CKM matrix elements should hold approximately because of asymptotically safe regimes, including $|V_{ud}|^2+|V_{us}|^2 \approx 1$ and $|V_{cd}|^2+|V_{cs}|^2\approx 1$. Theoretically, the accuracies of these relations determine the length of the asymptotically safe regimes. Experimental data confirms these relations with an accuracy of $10^{-5}$ and $10^{-3}$, respectively. This difference in accuracies is also expected, because the ultraviolet completion consists in a fixed-point cascade during which one relation is established already much deeper in the ultraviolet. This results in $|V_{ub}|^2 < |V_{cb}|^2$ and translates into measurable properties of $B$-mesons.
Similar results would hold for the PMNS matrix, if neutrino Yukawa couplings were large. The ultraviolet complete theory therefore must -- and in fact can -- avoid such an outcome. It contains a mechanism that dynamically limits the size of neutrino Yukawa couplings. Below an upper bound on the sum of Dirac neutrino masses, this allows the PMNS matrix to avoid a near-diagonal structure like the CKM matrix. Thus, large neutrino mixing is intimately tied to small Dirac neutrino masses, $\sum m_ν \lesssim {\mathcal{O}} (1)\, \rm eV$ and a mass gap in the Standard Model fermion masses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18304 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quark and lepton mixing in the asymptotically safe Standard Model Eichhorn, Astrid Gyftopoulos, Zois Held, Aaron High Energy Physics - Phenomenology General Relativity and Quantum Cosmology High Energy Physics - Theory The quark mixing (CKM) matrix is near-diagonal, whereas the lepton mixing (PMNS) matrix is not. We learn that both observations can generically be explained within an ultraviolet completion of the Standard Model with gravity. We find that certain relations between CKM matrix elements should hold approximately because of asymptotically safe regimes, including $|V_{ud}|^2+|V_{us}|^2 \approx 1$ and $|V_{cd}|^2+|V_{cs}|^2\approx 1$. Theoretically, the accuracies of these relations determine the length of the asymptotically safe regimes. Experimental data confirms these relations with an accuracy of $10^{-5}$ and $10^{-3}$, respectively. This difference in accuracies is also expected, because the ultraviolet completion consists in a fixed-point cascade during which one relation is established already much deeper in the ultraviolet. This results in $|V_{ub}|^2 < |V_{cb}|^2$ and translates into measurable properties of $B$-mesons. Similar results would hold for the PMNS matrix, if neutrino Yukawa couplings were large. The ultraviolet complete theory therefore must -- and in fact can -- avoid such an outcome. It contains a mechanism that dynamically limits the size of neutrino Yukawa couplings. Below an upper bound on the sum of Dirac neutrino masses, this allows the PMNS matrix to avoid a near-diagonal structure like the CKM matrix. Thus, large neutrino mixing is intimately tied to small Dirac neutrino masses, $\sum m_ν \lesssim {\mathcal{O}} (1)\, \rm eV$ and a mass gap in the Standard Model fermion masses. |
| title | Quark and lepton mixing in the asymptotically safe Standard Model |
| topic | High Energy Physics - Phenomenology General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.18304 |