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arXiv 2107.05352hep-phhep-lathep-th
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关于Landau规范Yang-Mills理论中的质量产生

On mass generation in Landau-gauge Yang-Mills theory

Gernot Eichmann, Jan M. Pawlowski, João M. Silva

备注：
33 pages, 24 figures. Identical to the version published in Phys. Rev. D
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摘要：

QCD中一个长期存在的问题是QCD的杨米尔斯部门的质量间隙的起源，即，没有夸克的QCD在朗道规范量子色动力学中，这个质量隙，以及由此产生的禁闭，被编码在胶子传播子的质量隙中，这在晶格模拟和泛函方法中都可以找到。虽然泛函方法非常适合于解开背后的质量间隙的产生机制，一个完全令人满意的答案尚未found. In这项工作中，我们解决了耦合Dyson-Schwinger方程的鬼传播子，胶子传播子和三胶子顶点。我们证实了早期工作的结果，即质量间隙的产生是绑在胶子自能，作为一个有效的质量项在方程中的纵向投影。由于显式质量项与规范不变性相冲突，这留下了两种可能的情况：如果它被视为人工产物，则只有标度解存在;如果它是动力学的，则规范不变性只能在任何一个顶点上存在纵向无质量极点时才能保持。我们发现在鬼胶子顶点确实存在一个无质量的极点，但是在我们的近似中，假设鬼胶子完全以红外线为主导，这个极点只存在于标度解中。我们还提出了一个可能的机制，可以调和的标度解，与红外优势的鬼，与去耦解决方案的基础上纵向极点在三胶子顶点中看到的PT-BFM计划。

英文摘要：

A longstanding question in QCD is the origin of the mass gap in the Yang-Mills sector of QCD, i.e., QCD without quarks. In Landau gauge QCD this mass gap, and hence confinement, is encoded in a mass gap of the gluon propagator, which is found both in lattice simulations and with functional approaches. While functional methods are well suited to unravel the mechanism behind the generation of the mass gap, a fully satisfactory answer has not yet been found. In this work we solve the coupled Dyson-Schwinger equations for the ghost propagator, gluon propagator and three-gluon vertex. We corroborate the findings of earlier works, namely that the mass gap generation is tied to the longitudinal projection of the gluon self-energy, which acts as an effective mass term in the equations. Because an explicit mass term is in conflict with gauge invariance, this leaves two possible scenarios: If it is viewed as an artifact, only the scaling solution survives; if it is dynamical, gauge invariance can only be preserved if there are longitudinal massless poles in either of the vertices. We find that there is indeed a massless pole in the ghost-gluon vertex, however in our approximation with the assumption of complete infrared dominance of the ghost this pole is only present for the scaling solution. We also put forward a possible mechanism that may reconcile the scaling solution, with an infrared dominance of the ghost, with the decoupling solutions based on longitudinal poles in the three-gluon vertex as seen in the PT-BFM scheme.

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