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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.15946 |
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| _version_ | 1866916855324606464 |
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| author | Martin, Stephen P. |
| author_facet | Martin, Stephen P. |
| contents | I present the leading 3-loop contributions to the Fermi decay constant in the Standard Model, using the tadpole-free pure $\overline{\rm{MS}}$ scheme. The calculation is exact in the limit in which the QCD coupling, the top-quark Yukawa coupling, and the square root of the Higgs self-coupling are all treated as large compared to the electroweak gauge couplings. The effect of the 3-loop contribution is to decrease the estimate of the Higgs VEV, for fixed on-shell inputs, by about 3.5 MeV. The renormalization scale dependence of the computed Fermi constant is greatly reduced compared to the previously known complete 2-loop order result, and as a fraction is now less than $\pm 2 \times 10^{-6}$ for renormalization scales between 90 and 250 GeV. This corresponds to a theoretical uncertainty in the VEV that is well under 1 MeV, and much smaller than the current parametric uncertainties coming mostly from the top-quark mass. I also comment on the impact on the precise prediction of the $W$-boson mass. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three-loop corrections to the Fermi decay constant in the $\overline{\rm{MS}}$ scheme Martin, Stephen P. High Energy Physics - Phenomenology I present the leading 3-loop contributions to the Fermi decay constant in the Standard Model, using the tadpole-free pure $\overline{\rm{MS}}$ scheme. The calculation is exact in the limit in which the QCD coupling, the top-quark Yukawa coupling, and the square root of the Higgs self-coupling are all treated as large compared to the electroweak gauge couplings. The effect of the 3-loop contribution is to decrease the estimate of the Higgs VEV, for fixed on-shell inputs, by about 3.5 MeV. The renormalization scale dependence of the computed Fermi constant is greatly reduced compared to the previously known complete 2-loop order result, and as a fraction is now less than $\pm 2 \times 10^{-6}$ for renormalization scales between 90 and 250 GeV. This corresponds to a theoretical uncertainty in the VEV that is well under 1 MeV, and much smaller than the current parametric uncertainties coming mostly from the top-quark mass. I also comment on the impact on the precise prediction of the $W$-boson mass. |
| title | Three-loop corrections to the Fermi decay constant in the $\overline{\rm{MS}}$ scheme |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2507.15946 |