Asymmetry of the dimension-two gluon condensate: The zero temperature case

We provide an algebraic study of the local composite operators A(mu)A(nu) - delta(mu nu)/d A kappa (2) and A(mu)(2), with d = 4 the spacetime dimension. We prove that these are separately renormalizable to all orders in the Landau gauge. This corresponds to a renormalizable decomposition of the operator A(mu)A(nu) into its trace and traceless parts. We present explicit results for the relevant renormalization group functions to three loop order, accompanied by various tests of these results. We then develop a formalism to determine the zero temperature effective potential for the corresponding condensates, and recover the already known result for < A(mu)(2)> not equal 0, together with < A(mu)A(nu) - delta(mu nu)/d A kappa (2)> = 0, a nontrivial check that the approach is consistent with Lorentz symmetry. The formalism is such that it is readily generalizable to the finite temperature case, which shall allow a future analytical study of the electric-magnetic symmetry of the < A(mu)(2)> condensate, which received strong evidence from recent lattice simulations by Chernodub and Ilgenfritz, who related their results to three regions in the Yang-Mills phase diagram.