Renormalization group improved QCD prediction for $\Upsilon(1S)$ leptonic decay
Renormalization group improved QCD prediction for $\Upsilon(1S)$ leptonic decay
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发表时间：
2015-01
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通讯作者：
Jian-Ming Shen;Xing-Gang Wu;Hong-Hao Ma;H. Bi;Sheng-Quan Wang
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作者：
Jian-Ming Shen;Xing-Gang Wu;Hong-Hao Ma;H. Bi;Sheng-Quan Wang
Beneke等人完成了对轻子衰变率\Gamma（\Uppersons（1 S）\to \ell^+\ell^-）的次首阶短程和束缚态QCD修正[5]的文件。在此基础上，利用最大共形性原理（PMC）给出了$\Gamma（\Uppersons（1 S）\to \ell^+\ell^-）$的重整化群（RG）改进的pQCD预言. PMC是基于RG-不变性，旨在解决重整化方案和规模模糊性。应用PMC的$\Upperdom（1 S）$轻子衰变，所有已知类型的$\beta$-项在所有的订单，这是由RG-方程控制的，被编程，以确定最佳的重整化标度在每个微扰级的强运行耦合.然后，我们得到了一个更收敛的pQCD序列，一个与方案无关的更精确的pQCD预测，即$\Gamma_{\Upplane（1 S）\to e^+ e^-}|_{\rm PMC} = 1.361^{+0.154}_{-0.214}$ keV，其中不确定度是所提到的pQCD误差源的平方平均。这个RG改进的pQCD预测与误差范围内的实验测量吻合得很好。
The complete next-to-next-to-next-to-leading order short-distance and bound-state QCD corrections to $\Upsilon(1S)$ leptonic decay rate $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ has been finished by Beneke {\it etal.} [5]. Based on those improvements, we present a renormalization group (RG) improved pQCD prediction for $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ by applying the principle of maximum conformality (PMC). The PMC is based on RG-invariance and is designed to solve the renormalization scheme and scale ambiguities. After applying the PMC for $\Upsilon(1S)$ leptonic decay, all known-type of $\beta$-terms at all orders, which are controlled by the RG-equation, are resummed to determine optimal renormalization scales for its strong running coupling at each perturbative order. We then achieve a more convergent pQCD series, a scheme-independent and more accurate pQCD prediction, i.e. $\Gamma_{\Upsilon(1S) \to e^+ e^-}|_{\rm PMC} = 1.361^{+0.154}_{-0.214}$ keV, where the uncertainty is squared average of the mentioned pQCD error sources. This RG-improved pQCD prediction agrees well with the experimental measurement within errors.