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| Format: | Preprint |
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2024
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| Online-Zugang: | https://arxiv.org/abs/2406.18025 |
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| _version_ | 1866929580042878976 |
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| author | Ma, Shun-Yue Huang, Xu-Dong Zheng, Xu-Chang Wu, Xing-Gang |
| author_facet | Ma, Shun-Yue Huang, Xu-Dong Zheng, Xu-Chang Wu, Xing-Gang |
| contents | In this paper, we explore the properties of the bottom-quark on-shell mass ($M_b$) by using its relation to the $\overline{\rm MS}$ mass (${\overline m}_b$). At present, this $\overline{\rm MS}$-on-shell relation has been known up to four-loop QCD corrections, which however still has a $\sim 2\%$ scale uncertainty by taking the renormalization scale as ${\overline m}_b({\overline m}_b)$ and varying it within the usual range of $[{\overline m}_b({\overline m}_b)/2, 2 {\overline m}_b({\overline m}_b)]$. The principle of maximum conformality (PMC) has been adopted to achieve a more precise $\overline{\rm MS}$-on-shell relation by eliminating such scale uncertainty. As a step forward, we also estimate the magnitude of the uncalculated higher-order terms by using the Padé approximation approach. Numerically, by using the $\overline{\rm MS}$ mass ${\overline m}_b({\overline m}_b)=4.183\pm0.007$ GeV as an input, our predicted value for the bottom-quark on-shell mass becomes $M_b\simeq 5.372^{+0.091}_{-0.075}$ GeV, where the uncertainty is the squared average of the ones caused by $Δα_s(M_Z)$, $Δ{\overline m}_b({\overline m}_b)$, and the estimated magnitude of the higher-order terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18025 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\rm MS}$-scheme running mass Ma, Shun-Yue Huang, Xu-Dong Zheng, Xu-Chang Wu, Xing-Gang High Energy Physics - Phenomenology In this paper, we explore the properties of the bottom-quark on-shell mass ($M_b$) by using its relation to the $\overline{\rm MS}$ mass (${\overline m}_b$). At present, this $\overline{\rm MS}$-on-shell relation has been known up to four-loop QCD corrections, which however still has a $\sim 2\%$ scale uncertainty by taking the renormalization scale as ${\overline m}_b({\overline m}_b)$ and varying it within the usual range of $[{\overline m}_b({\overline m}_b)/2, 2 {\overline m}_b({\overline m}_b)]$. The principle of maximum conformality (PMC) has been adopted to achieve a more precise $\overline{\rm MS}$-on-shell relation by eliminating such scale uncertainty. As a step forward, we also estimate the magnitude of the uncalculated higher-order terms by using the Padé approximation approach. Numerically, by using the $\overline{\rm MS}$ mass ${\overline m}_b({\overline m}_b)=4.183\pm0.007$ GeV as an input, our predicted value for the bottom-quark on-shell mass becomes $M_b\simeq 5.372^{+0.091}_{-0.075}$ GeV, where the uncertainty is the squared average of the ones caused by $Δα_s(M_Z)$, $Δ{\overline m}_b({\overline m}_b)$, and the estimated magnitude of the higher-order terms. |
| title | Precise determination of the bottom-quark on-shell mass using its four-loop relation to the $\overline{\rm MS}$-scheme running mass |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2406.18025 |