The $$\Upsilon (1S)$$ Υ(1S) leptonic decay using the principle of maximum conformality

• Main Authors: Xu-Dong Huang, Xing-Gang Wu, Jun Zeng, Qing Yu, Jian-Ming Shen
• Format: Article
• Language: English
• Published: SpringerOpen 2019-08-01
• Series: European Physical Journal C: Particles and Fields
• Online Access: http://link.springer.com/article/10.1140/epjc/s10052-019-7158-9

Abstract In the paper, we study the $$\Upsilon (1S)$$ Υ(1S) leptonic decay width $$\Gamma (\Upsilon (1S)\rightarrow \ell ^+\ell ^-)$$ Γ(Υ(1S)→ℓ+ℓ-) by using the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct momentum flow of the process, whose value is independent to the choice of the renormalization scale and its prediction thus avoids the conventional renormalization scale ambiguities. Using the known next-to-next-to-next-to-leading order perturbative series together with the PMC single scale-setting approach, we do obtain a renormalization scale independent decay width, $$\Gamma _{\Upsilon (1S) \rightarrow e^+ e^-} = 1.262^{+0.195}_{-0.175}$$ ΓΥ(1S)→e+e-=1.262-0.175+0.195 keV, where the error is squared average of those from $$\alpha _s(M_{Z})=0.1181\pm 0.0011$$ αs(MZ)=0.1181±0.0011 , $$m_b=4.93\pm 0.03$$ mb=4.93±0.03 GeV and the choices of factorization scales within $$\pm 10\%$$ ±10% of their central values. To compare with the result under conventional scale-setting approach, this decay width agrees with the experimental value within errors, indicating the importance of a proper scale-setting approach.