Pinch technique at two loops: The case of massless Yang-Mills theories - art. no. 045006

The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge invariance, unitarit y, and gauge-fixing-parameter independence are instrumental for accomplishi ng this task, and it is explained how the aforementioned requirements singl e out at two loops exactly the same algorithm which has been used to define the pinch technique at one loop, without any additional assumptions. The t wo-loop construction of the pinch technique gluon self-energy, and quark-gl uon vertex are carried out in detail fur the case of massless Yang-Mills th eories, such as perturbative QCD. We present two different but complementar y derivations. First we carry out the construction by directly rearranging two-loop diagrams. The analysis reveals that, quite interestingly, the well -known one-loop correspondence between the pinch technique and the backgrou nd field method in the Feynman gauge persists also at two loops. Since we u se dimensional regularization, the entire construction does not depend on t he value of the space-time dimension d. The renormalization (when d=4) is d iscussed in detail, and is shown to respect the aforementioned corresponden ce. Second, we present an absorptive derivation, exploiting the unitarity o f the S matrix and the underlying Becchi-Rouet-Stora (BRS) symmetry; at thi s stage we deal only with tree-level and one-loop physical amplitudes. The gauge-invariant subamplitudes defined by means of this absorptive construct ion correspond precisely to the imaginary parts of the n-point functions de fined in the full two-loop derivation, thus furnishing a highly nontrivial self-consistency check for the entire method. Various future applications a re briefly discussed.