On the decoupling solution for pinch technique gluon propagator

Understand

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.