On the gauge invariance of the condensate of dimension two in Yang-Mills theories

We discuss the gauge parameter independence of the condensate of scaling dimension mass squared constructed in Yang-Mills theories. This condensate, which can provide nonperturbative information about the gluon propagator and as well be related to topological excitations of QCD, could be a good order parameter for a dynamical infrared cutoff generation in Yang-Mills theories. The above mentioned gauge invariance is proved by considering Yang-Mills theories as a limiting case of noncommutative gauge field theories where the commutative parameter tends to zero. We assume that these theories admit a gauge invariant regularization and that in the regularized theory the commutative limit is not singular. Outlook and perspectives related to these hypotheses are finally discussed.