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The generalization of the pinch technique beyond one loop is presented. It isshown that the crucial physical principles of gauge-invariance, unitarity, andgauge-fixing-parameter independence single out at two loops exactly the samealgorithm which has been used to define the pinch technique at one loop,without any additional assumptions. The two-loop construction of the pinchtechnique gluon self-energy, and quark-gluon vertex are carried out in detailfor the case of mass-less Yang-Mills theories, such as perturbative QCD. Wepresent two different but complementary derivations. First we carry out theconstruction by directly rearranging two-loop diagrams. The analysis revealsthat, quite interestingly, the well-known one-loop correspondence between thepinch technique and the background field method in the Feynman gauge persistsalso at two-loops. The renormalization is discussed in detail, and is shown torespect the aforementioned correspondence. Second, we present an absorptivederivation, exploiting the unitarity of the $S$-matrix and the underlying BRSsymmetry; at this stage we deal only with tree-level and one-loop physicalamplitudes. The gauge-invariant sub-amplitudes defined by means of thisabsorptive construction correspond precisely to the imaginary parts of the$n$-point functions defined in the full two-loop derivation, thus furnishing ahighly non-trivial self-consistency check for the entire method. Various futureapplications are briefly discussed.Comment: 29 pages, uses Revtex, 22 Figures in a separate ps fil

Pinch technique at two loops: The case of massless Yang-Mills theories