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arXiv 2201.11714hep-phhep-ex
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QCD求和规则下全重四夸克算符混合的NLO结果

NLO results with operator mixing for fully heavy tetraquarks in QCD sum rules

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

摘要:

在QCD求和规则下研究了$\bar{Q}Q\bar{Q}Q\ (Q=c,b)$系统的质量谱,其中关联函数的微扰QCD部分具有完全的次首阶(NLO)贡献。我们用算符重整化下的对角化流代替介子-介子或双夸克-反双夸克流。我们发现,不同于传统的介子$\bar qq$和重子$qqq$,像$\bar{Q}Q\bar{Q}Q$这样的多夸克系统的一个独特的特征是由非线性光学修正引起的算符混合或色组态混合,这对于理解态的色结构是至关重要的.数值结果表明,非线性光学修正对$\bar{Q}Q\bar{Q}Q$系统有重要的作用,它不仅对系统有显著的贡献,而且能减小系统对格式和尺度的依赖,使Borel平台更加清晰,尤其是对$\overline{\rm{MS}}$格式中的$\bar{b}b\bar{b}b$.我们使用的电流有很好的扰动收敛在我们的唯象分析。利用$\overline{\rm{MS}}$方案,我们得到了三个$J^{PC}=0^{++}$态,质量分别为$6.35^{+0.20}_{-0.17}$ GeV,$6.56^{+0.18}_{-0.20}$ GeV和$6.95^{+0.21}_{-0.31}$ GeV.前两个似乎同意广泛的结构周围$6.2\sim6.8$ GeV测量的LHCb合作的$J/ψJ/ψ$光谱,第三个似乎同意窄共振$X(6900)$。对于$2^{++}$态,我们发现了一个质量为$7.03^{+0.22}_{-0.26}$ GeV的态,它也接近于$X(6900)$的质量,另一个在$7.25^{+0.21}_{-0.35}$ GeV附近的态,它具有良好的尺度依赖性,但略大的方案依赖性。

英文摘要:

We study the mass spectra of $\bar{Q}Q\bar{Q}Q\ (Q=c,b)$ systems in QCD sum rules with the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Instead of meson-meson or diquark-antidiquark currents, we use diagonalized currents under operator renormalization. We find that differing from conventional mesons $\bar qq$ and baryons $qqq$, a unique feature of the multiquark systems like $\bar{Q}Q\bar{Q}Q$ is the operator mixing or color configuration mixing induced by NLO corrections, which is crucial to understand the color structure of the states. Our numerical results show that the NLO corrections are very important for the $\bar{Q}Q\bar{Q}Q$ system, because they not only give significant contributions but also reduce the scheme and scale dependence and make Borel platform more distinct, especially for the $\bar{b}b\bar{b}b$ in the $\overline{\rm{MS}}$ scheme. We use currents that have good perturbation convergence in our phenomenological analysis. With the $\overline{\rm{MS}}$ scheme, we get three $J^{PC}=0^{++}$ states, with masses $6.35^{+0.20}_{-0.17}$ GeV, $6.56^{+0.18}_{-0.20}$ GeV and $6.95^{+0.21}_{-0.31}$ GeV, respectively. The first two seem to agree with the broad structure around $6.2\sim6.8$ GeV measured by the LHCb collaboration in the $J/ψJ/ψ$ spectrum, and the third seems to agree with the narrow resonance $X(6900)$. For the $2^{++}$ states we find one with mass $7.03^{+0.22}_{-0.26}$ GeV, which is also close to that of $X(6900)$, and another one around $7.25^{+0.21}_{-0.35}$ GeV, which has good scale dependence but slightly large scheme dependence.

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