横向Slavnov-Taylor恒等式对动力学手征对称性破缺的影响
The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
摘要：
我们扩展了早期的横向Ward-Fradkin-Green-Takahashi恒等式在QED中的研究，它们对约束横向费米子玻色子顶点的有用性以及它们对乘法重整化的重要性，到QCD中的等效规范恒等式。为此，我们考虑横向Slavnov-Taylor恒等式，约束横向夸克胶子顶点，并导出其八个相关的标量形状因子。完整的顶点可以用夸克的质量和波重整化函数、鬼敷料函数、夸克鬼散射振幅和一组八个形状因子来表示。后者参数化迄今为止未知的非局部张量结构中的横向斯拉夫诺夫-泰勒恒等式所产生的傅立叶变换的四点函数涉及威尔逊线在坐标空间中。在Bashir-Schmiddez顶点的约束下，我们确定了这八个形状因子的函数形式，并利用格点量子色动力学输入胶子和鬼传播子，研究了这个新的顶点对Dyson-Schwinger方程中夸克的影响.我们观察到显着的动力学手征对称性打破和质量差距，导致一个组成质量的顺序为500兆电子伏的轻夸克。研究了质量和波重整化函数的味依赖性以及它们在复动量平面上的解析行为，并作为应用计算了手征极限下的夸克凝聚和π介子弱衰变常数。两者都与其参考值非常一致。
英文摘要：
We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quark's mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pion's weak decay constant in the chiral limit. Both are in very good agreement with their reference values.
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