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arXiv · 1404.3642

Spurious divergences in Dyson-Schwinger equations

Markus Q. Huber·Lorenz von Smekal
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Abstract

We revisit the treatment of spurious ultraviolet divergences in the equation of motion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance. With present continuum studies of the gluon propagator from its Dyson-Schwinger equation reaching the level of quantitatively accurate descriptions, it becomes increasingly important to understand how to subtract these spurious divergences in an unambiguous way. Here we propose such a method. It is based entirely on the asymptotic perturbative behavior of the QCD Green's functions without affecting non-perturbative aspects such as mass terms or the asymptotic infrared behavior. As a particular example, this allows us to assess the possible influence of the tadpole diagram beyond perturbation theory. Finally, we test this method numerically by solving the system of Dyson-Schwinger equations of the gluon and ghost propagators.

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Markus Q. Huber, Lorenz von Smekal. 2014-04-14. Spurious divergences in Dyson-Schwinger equations. https://doi.org/10.1007/jhep06(2014)015

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