The pinch technique at two-loops: The case of mass-less Yang-Mills theories

Details The pinch technique at two-loops: The case of mass-less Yang-Mills theories The pinch technique at two-loops: The case of mass-less Yang-Mills theories

1999-12-14

arxiv.org/abs/hep-ph/9912338v1

Phys.Rev. D62 (2000) 045006

Physics

High Energy Physics

High Energy Physics - Phenomenology

29 pages, uses Revtex, 22 Figures in a separate ps file

Scientific paper

10.1103/PhysRevD.62.045006

The generalization of the pinch technique beyond one loop is presented. It is shown that the crucial physical principles of gauge-invariance, unitarity, and gauge-fixing-parameter independence single 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 two-loop construction of the pinch technique gluon self-energy, and quark-gluon vertex are carried out in detail for the case of mass-less Yang-Mills theories, such as perturbative QCD. We present two different but complementary 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 background field method in the Feynman gauge persists also at two-loops. The renormalization is discussed in detail, and is shown to respect the aforementioned correspondence. Second, we present an absorptive derivation, exploiting the unitarity of the $S$-matrix and the underlying BRS symmetry; at this stage we deal only with tree-level and one-loop physical amplitudes. The gauge-invariant sub-amplitudes defined by means of this absorptive construction correspond precisely to the imaginary parts of the $n$-point functions defined in the full two-loop derivation, thus furnishing a highly non-trivial self-consistency check for the entire method. Various future applications are briefly discussed.

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