| THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS |
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Precise Determination of the Bottom-Quark On-Shell Mass Using Its Four-Loop Relation to the $\overline{\rm MS}$-Scheme Running Mass |
| Shun-Yue Ma1, Xu-Dong Huang2*, Xu-Chang Zheng1, and Xing-Gang Wu1 |
1Department of Physics, Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing University, Chongqing 401331, China
2College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
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| Cite this article: |
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Shun-Yue Ma, Xu-Dong Huang, Xu-Chang Zheng et al 2024 Chin. Phys. Lett. 41 101201 |
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Abstract 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) is 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 $\Delta \alpha_s(M_Z)$, $\Delta {\overline m}_b({\overline m}_b)$, and the estimated magnitude of the higher-order terms.
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Received: 27 June 2024
Editors' Suggestion
Published: 22 October 2024
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| PACS: |
12.38.Bx
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(Perturbative calculations)
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12.15.Ff
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(Quark and lepton masses and mixing)
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12.10.Kt
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(Unification of couplings; mass relations)
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