arXiv 2303.030612023-03-06hep-phhep-thnucl-th

瞬子真空中的胶子、轻夸克和重夸克及其相互作用

Gluons, light and heavy quarks and their interactions in the instanton vacuum

Mirzayusuf Musakhanov

备注：: arXiv admin note: text overlap with arXiv:2103.16628

摘要：

瞬子尺寸$ρ$和瞬子间距离$R$是QCD真空瞬子液体模型（ILM）的主要参数。各种估计表明，$ρ\approx1/3$ fm和$R\approx1$ fm，以及相应的填充参数$κ=ρ^{4}/R^{4}\approx0.01$。由于动力学轻夸克质量$M_{q}$和动力学胶子质量$M_{g}$由$M_{q}\approx M_{g}\approx 360$ MeV $\simκ^{1/2}ρ^{-1}$给出，因此轻夸克-瞬子相互作用的强度是相当大的，并且接近胶子-瞬子相互作用的强度.另一方面，重夸克-瞬子相互作用的强度很弱--瞬子对重夸克质量的直接贡献为$ΔM_{Q}^{\rm dir}\approx70$ MeV $\simκρ^{-1}.$瞬子负责穿过同一瞬子场的有色粒子之间的相互作用，就像$N_{f}$轻夸克的类特霍夫相互作用（$N_{f}$是轻夸克的味数）。在瞬子场中，轻夸克传播子具有零模，这是主要的贡献。在ILM中，我们能够导出轻夸克行列式和轻夸克配分函数。这些工具完美地描述了轻夸克物理及其最重要和最基本的现象-手征对称性自发破缺（SBChS）的细节。这使得我们可以发现轻重夸克相互作用的性质，并得到轻重夸克和轻重夸克系统中的SBChS迹。因此，我们需要找到重$Q\bar{Q}$夸克偶素谱和它们的波函数。这里我们有两个尺度的相互作用：短（$\sim(M_{Q}v)^{-1}\leq0.15$ fm）微扰QCD和大（$\sim(M_{Q}v^{2})^{-1}\sim0.5$ fm）非微扰QCD尺度，其中$v$是$Q\bar{Q}$中的速度。我们在ILM中计算了带微扰修正的重夸克双折射子。

英文摘要：

The instanton size $ρ$ and inter-instanton distance $R$ are the main parameters of Instanton Liquid Model (ILM) of the QCD vacuum. Various estimates show that $ρ\approx1/3$ fm and $R\approx1$ fm, and the corresponding packing parameter $κ=ρ^{4}/R^{4}\approx0.01$. The strength of the light quark-instanton interaction is sizable and close to that of the gluon-instanton one since the dynamical light quark mass $M_{q}$ and dynamical gluon mass $M_{g}$ are given by $M_{q}\approx M_{g}\approx 360$ MeV$\simκ^{1/2}ρ^{-1}$. On the other hand, the strength of the heavy quark-instanton interaction is weak - the direct instanton contribution to the heavy quark mass $ΔM_{Q}^{\rm dir}\approx70$ MeV$\simκρ^{-1}.$ The instantons are responsible for mutual interactions among colored particles which are crossing the field of the same instanton, like t'Hooft-like interactions of $N_{f}$ light quarks ($N_{f}$ is the light quark flavors number). The light quark propagators in the instanton field have zero modes, which give dominant contributions. Within ILM we are able to derive the light quarks determinants and the light quarks partition function. These tools perfectly describe the light quark physics and its most important and basic phenomena - the spontaneous breaking of the chiral symmetry (SBChS) in details. These one allows us to find the properties of light and heavy quarks interactions and get SBChS traces in light-heavy and heavy-heavy quarks systems. So, we need to find heavy $Q\bar{Q}$ quarkonia spectra and their wave functions. Here we have interplay of two scales: short ($\sim(M_{Q}v)^{-1}\leq0.15$ fm) perturbative QCD and large ($\sim(M_{Q}v^{2})^{-1}\sim0.5$ fm) nonperturbative QCD scales, where $v$ is the velocity in $Q\bar{Q}$. We calculate the heavy quarks correlators with perturbative corrections within ILM.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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