Abstract:
We study the self-consistency problem of the generalized Feynman rule (nonperturbatively modified vertex of zeroth perturbative order) for the 4-gluon vertex function in the framework of an extended perturbation scheme accounting for non-analytic coupling dependence through the Λ scale. Tensorial structure is restricted to a minimal dynamically closed basis set. The self-consistency conditions are obtained at one loop, in Landau gauge, and at the lowest approximation level (r=1) of interest for QCD. At this level, they are found to be linear in the nonperturbative 4-gluon coefficients, but strongly overdetermined due to the lack of manifest Bose symmetry in the relevant Dyson-Schwinger equation. The observed near decoupling from the 2-and-3-point conditions permits least-squares quasisolutions for given 2-and-3-point input within an effective one-parameter freedom. We present such solutions for N F=2 massless quarks and for the pure gluon theory, adapted to the 2-and-3-point coefficients determined previously.
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Received: 1 September 1998 / Revised version: 23 December 1998
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Driesen, L., Stingl, M. Extended iterative scheme for QCD: the four-gluon vertex . EPJ A 4, 401–419 (1999). https://doi.org/10.1007/s100500050247
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DOI: https://doi.org/10.1007/s100500050247