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arXiv 2104.07384hep-ph
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QCD求和规则中$Ω_{QQQ}$重子的NLO效应

NLO effects for $Ω_{QQQ}$ Baryons in QCD Sum Rules

Ren-Hua Wu, Yu-Sheng Zuo, Ce Meng, Yan-Qing Ma, Kuang-Ta Chao

摘要:

我们在QCD求和规则下研究了三重重子$Ω_{QQQ}$ $(Q=c, b)$,首次计算了次首阶(NLO)对微扰QCD关联函数的贡献。通过与首阶(LO)结果的比较,发现非线性光学对$Ω_{QQQ}$的贡献是非常重要的。这是因为NLO不仅导致大的校正,而且还降低了参数依赖性,使得Borel平台更加明显,特别是对于$\overline{\rm{MS}}$方案中的$Ω_{bbb}$,其中平台仅出现在NLO而不出现在LO。特别地,由于包含NLO贡献,重整化方案($\bar {MS}$和On-Shell)的依赖性和尺度依赖性显着降低。因此,在QCD求和规则中包括了NLO对微扰部分的贡献后,质量估计为$Ω_{ccc}$的$4.53^{+0.26}_{-0.11}$ GeV和$Ω_{bbb}$的$14.27^{+0.33}_{-0.32}$ GeV,其中结果是在$μ=M_B$得到的,误差包括重整化标度$μ$在$(0.8-1.2) M_B$范围内变化的误差。进一步研究了$μ$在宽范围内的依赖性,结果表明,LO结果对$μ$的选择非常敏感,而NLO结果要好得多。除了$μ=M_B$的结果,一个更稳定的值,(4.75 - 4.80)GeV,$Ω_{ccc}$的质量被发现在$μ=(1.2-2.0) M_B$的范围内,这应该被视为一个更相关的预测,在我们的NLO方法,因为$μ$的依赖。

英文摘要:

We study the triply heavy baryons $Ω_{QQQ}$ $(Q=c, b)$ in the QCD sum rules by performing the first calculation of the next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Compared with the leading order (LO) result, the NLO contribution is found to be very important to the $Ω_{QQQ}$. This is because the NLO not only results in a large correction, but also reduces the parameter dependence, making the Borel platform more distinct, especially for the $Ω_{bbb}$ in the $\overline{\rm{MS}}$ scheme, where the platform appears only at NLO but not at LO. Particularly, owing to the inclusion of the NLO contribution, the renormalization schemes ($\bar {MS}$ and On-Shell) dependence and the scale dependence are significantly reduced. Consequently, after including the NLO contribution to the perturbative part in the QCD sum rules, the masses are estimated to be $4.53^{+0.26}_{-0.11}$ GeV for $Ω_{ccc}$ and $14.27^{+0.33}_{-0.32}$ GeV for $Ω_{bbb}$, where the results are obtained at $μ=M_B$ with errors including those from the variation of the renormalization scale $μ$ in the range $(0.8-1.2) M_B$. A careful study of the $μ$ dependence in a wide range is further performed, which shows that the LO results are very sensitive to the choice of $μ$ whereas the NLO results are considerably better. In addition to the $μ=M_B$ result, a more stable value, (4.75-4.80) GeV, for the $Ω_{ccc}$ mass is found in the range of $μ=(1.2-2.0) M_B$, which should be viewed as a more relevant prediction in our NLO approach because of $μ$ dependence.

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