On the decoupling solution for pinch technique gluon propagator

Within a simple Ansatz for renormalized gluon propagator and using gauge invariant pinch-technique for Schwinger-Dyson equation, the limits on the effective gluon mass is derived. We calculated scheme invariant running coupling, which in order to be well defined, gives the lower limit on the gluon mass. We conclude mass should be larger as $m>0.4\Lambda$ in order to avoid Landau ghost. The upper limit is estimated from assumed quark mass generation which requires gauge coupling must be large enough to trigger chiral symmetry breaking. It allows only small range of $m$, which lead to a reasonably large infrared coupling. Already for $m\simeq \Lambda$ we get no chiral symmetry breaking at all. Further, we observe that sometimes assumed or postulated Khallen-Lehmann representation for running coupling is not achieved for any value of $m$.