## Gauge-invariance constraints on the infrared behavior of the quark-gluon vertex    [PDF]

Han-Xin He, Yu-Xin Liu
We derive the gauge-invariance constraints on the infrared-limit behavior of the quark-gluon vertex and the nonperturbative running coupling from the quark-gluon vertex. We find the constraint relations for the infrared-limit behavior of the quark-gluon vertex relating to the ghost dressing function and the quark-gluon running coupling relating to the ghost-gluon running coupling. These model-independent constraints give rigorous upper and lower bounds for allowed infrared-limit values. Hence we show that these constraints exclude the possibility of the quark-gluon vertex possessing the power-law infrared singularity scaling with $(q^2)^{-1/2-\kappa}$ and an infrared divergent running coupling scaling as $1/q^2$ from the quark-gluon vertex.
View original: http://arxiv.org/abs/1307.4485