PT-BFM SDE解在Minkowski空间的受限胶子延拓
Confined gluon from Minkowski space continuation of PT-BFM SDE solution
摘要：
最近的晶格研究显示红外有限有效QCD电荷。朗道规范中相应的胶子传播子是有限的且非零的，表明存在一种动力学胶子质量产生机制。本文将胶子传播子Schwinger-Dyson方程的欧氏（类空）箍缩技术-背景场方法（PT-BFM）解解析延拓到$q^2$的类时区域，数值结果表明，对于小的Schwinger耦合，这种延拓与广义Lehman表象有很好的一致性。相关的非正谱函数具有意外行为。虽然红外欧氏空间解天真地认为胶子传播子与单尺度“大质量”传播子一样，但得到的胶子传播子谱并不对应于单尺度下的δ函数$q=m$，而是产生了更多可能的奇异性.该模式取决于假定的Schwinger机制的细节：对于较强的耦合，在$Λ$尺度上几乎没有最大值和最小值，而对于微扰小的Schwinger耦合，光谱函数显示出两个窄峰：粒子和鬼激发，它们具有相反的符号。
英文摘要：
Recent lattice studies exhibit infrared finite effective QCD charges. Corresponding gluon propagator in Landau gauge is finite and nonzero, suggesting a mechanism of dynamical gluon mass generation is in the operation. In this paper, the analytical continuation of the Euclidean (spacelike) Pinch Technique-Background Field Method (PT-BFM) solution of Schwinger-Dyson equation for gluon propagator to the timelike region of $q^2$ is found. We found the continuation numerically showing good agreement with a generalized Lehman representation for small Schwinger coupling. The associate non-positive spectral function has an unexpected behavior. Albeit infrared Euclidean space solution naively suggests like single scale "massive" propagator, the obtained spectrum of gluon propagator does not correspond to the delta function at single scale $q=m$, instead more possible singularities are generated. The pattern depends on the details of assumed Schwinger mechanism: for stronger coupling there are few maxima and minima which appear at the scale $Λ$, while for perturbatively small Schwinger coupling the spectral function shows up two narrow peaks: particle and ghost excitation, which have mutually opposite signs.
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