We aim to show the effects of the magnetic monopoles and instantons in quantum chromodynamics (QCD) on observables; therefore, we introduce a monopole and anti-monopole pair in the QCD vacuum of a quenched SU(3) by applying the monopole creation operator to the vacuum. We calculate the eigenvalues and eigenvectors of the overlap Dirac operator that preserves the exact chiral symmetry in lattice gauge theory using these QCD vacua. We then investigate the effects of magnetic monopoles and instantons. First, we confirm the monopole effects as follows: (i) The monopole creation operator makes the monopoles and anti-monopoles in the QCD vacuum. (ii) A monopole and anti-monopole pair creates an instanton or anti-instanton without changing the structure of the QCD vacuum. (iii) The monopole and anti-monopole pairs change only the scale of the spectrum distribution without affecting the spectra of the Dirac operator by comparing the spectra with random matrix theory. Next, we find the instanton effects by increasing the number density of the instantons and anti-instantons as follows: (iv) The decay constants of the pseudoscalar increase. (v) The values of the chiral condensate, which are defined as negative numbers, decrease. (vi) The light quarks and the pseudoscalar mesons become heavy. The catalytic effect on the charged pion is estimated using the numerical results of the pion decay constant and the pion mass. (vii) The decay width of the charged pion becomes wider than the experimental result, and the lifetime of the charged pion becomes shorter than the experimental result. These are the effects of the monopoles and instantons in QCD.

中文翻译：

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QCD 中的单极子和瞬子效应

我们旨在展示量子色动力学 (QCD) 中的磁单极子和瞬子对可观察量的影响；因此，我们通过将单极子创建算子应用于真空，在淬火 SU(3) 的 QCD 真空中引入单极子和反单极子对。我们使用这些 QCD 真空计算重叠狄拉克算子的特征值和特征向量，该算子在晶格规范理论中保持精确的手征对称性。然后我们研究磁单极子和瞬子的影响。首先，我们确认单极子效应如下：（i）单极子产生算子在 QCD 真空中制造单极子和反单极子。(ii) 单极子和反单极子对在不改变 QCD 真空结构的情况下产生瞬时子或反瞬时子。(iii) 单极子和反单极子对通过将光谱与随机矩阵理论进行比较，仅改变光谱分布的尺度而不影响狄拉克算子的光谱。接下来，我们通过增加瞬时子和反瞬时子的数量密度来找到瞬时子效应，如下所示： (iv) 伪标量的衰减常数增加。(v) 被定义为负数的手性缩合物的值减少。(vi) 轻夸克和伪标量介子变重。使用 pion 衰减常数和 pion 质量的数值结果估计对带电 pion 的催化作用。(vii) 带电介子的衰减宽度比实验结果宽，带电介子的寿命比实验结果短。