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On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions

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Abstract

We study the low-momentum behaviour of Yang-Mills propagators obtained from Landau-gauge Dyson-Schwinger equations (DSE) in the PT-BFM scheme. We compare the ghost propagator numerical results with the analytical ones obtained by analyzing the low-momentum behaviour of the ghost propagator DSE in Landau gauge, assuming for the truncation a constant ghost-gluon vertex and a simple model for a massive gluon propagator. The asymptotic expression obtained for the regular or decoupling ghost dressing function up to the order \( \mathcal{O}\left( {{q^2}} \right) \) is proven to fit pretty well the numerical PT-BFM results. Furthermore, when the size of the coupling renormalized at some scale approaches some critical value, the numerical PT-BFM propagators tend to behave as the scaling ones. We also show that the scaling solution, implying a diverging ghost dressing function, cannot be a DSE solution in the PT-BFM scheme but an unattainable limiting case.

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  1. Dpto. Física Aplicada, Fac. Ciencias Experimentales, Universidad de Huelva, 21071, Huelva, Spain

    J. Rodríguez-Quintero

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Rodríguez-Quintero, J. On the massive gluon propagator, the PT-BFM scheme and the low-momentum behaviour of decoupling and scaling DSE solutions. J. High Energ. Phys. 2011, 105 (2011). https://doi.org/10.1007/JHEP01(2011)105

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