论文标题
NLO结果与QCD总规则中完全沉重的四夸克的操作员混合
NLO results with operator mixing for fully heavy tetraquarks in QCD sum rules
论文作者
论文摘要
我们研究$ \ bar {q} q \ bar {q} q \（q = c，b）QCD总规则中的$ systems的质谱，并具有对相关功能的扰动QCD部分的完整近代订单（NLO）贡献。我们使用对角线的电流，而不是在操作员重归于的对角电流。 我们发现，与传统的介子$ \ bar qq $和baryons $ qqq $不同，这是多quark系统的独特功能，例如$ \ bar {q} q \ bar {q} q $是操作员混合或颜色配置混合，由NLO校正引起的混合，这对于了解该州的颜色结构至关重要。我们的数值结果表明，NLO更正对于$ \ bar {q} q \ bar {q} q $系统非常重要，因为它们不仅提供了重大贡献，而且还会减少方案和规模依赖性，并使Borel平台更加独特，尤其是$ \ bar {b} b} b \ bar {b} b {b} b $在$ \ overline $ \ overline $ \ clime {mss中{\ rmm {\ rmmmms {\ rmmmmmm {\ rmm {\ rm {我们在现象学分析中使用具有良好扰动收敛的电流。 使用$ \ Overline {\ rm {MS}} $ scheme，我们得到了三个$ j^{pc} = 0^{++} $状态，弥撒$ 6.35^{+0.20} _ { - 0.17} $ gev，$ 6.56 $ 6.95^{+0.21} _ { - 0.31} $ GEV。前两个似乎与LHCB协作在$ J/ψJ/ψ$ Spectrum中衡量的$ 6.2 \ sim6.8 $ GEV的广泛结构一致，而第三个似乎与狭窄的共振$ x（6900）$一致。对于$ 2^{++} $状态，我们发现一个质量为$ 7.03^{+0.22} _ { - 0.26} $ gev，它也接近$ x（6900）$的$ GEV，另一个约为$ 7.25^{+0.21} _ {+0.21} _ {+0.21} _ { - 0.35} $ GEV，略有尺度依赖依赖性，但具有较大的依赖性，但具有较大的依赖性。
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.
