Since the start of the century the behaviour

of the gluon and ghost propagators have been widely

studied on the lattice at low momenta. In the Landau

gauge the gluon propagator freezes to a non-zero finite

value indicating the presence of a mass scale. Such a

scale could be explained from a field theory point of

view via the Gribov construction. Work by Serreau and

Tissier showed that the effect of Gribov copies could

be modelled by the inclusion of a gluon mass operator in

Yang-Mills theory which effectively corresponds to an

additional gauge parameter. The talk covers two topics

where an effective gluon mass plays a role in studying

infrared dynamics. The first concerns a two loop

computation of the gluon and ghost propagators in

Landau gauge Yang-Mills where the lattice propagators

are fitted over the full momentum range. The effect of

including a quark mass is also discussed. The second

topic deals with the construction of the three loop

effective potential for the gluon mass operator constructed

using the local composite operator method. Estimates of

the effective gluon mass resulting from the absolute

minimum of the potential are given and compared with

values from other techniques.