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arXiv · 0904.2380

Some exact infrared properties of gluon and ghost propagators and long-range force in QCD

Daniel Zwanziger
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Abstract

We derive some exact relations in Landau gauge that follow from a cut-off at the Gribov horizon which is then implemented by a local, renormalizable action involving auxiliary bose and fermi ghosts. The fermi ghost propagator is more singular than $1/k^2$ at $k = 0$, and the relation $α_D + 2 α_G = (D - 4)/2$ holds between the infrared critical exponents of the gluon and ghost propagators $D(k)$ and $G(k)$ in $D$ Euclidean dimensions. Finally, in $D$ Euclidean dimensions, there is a long-range force, transmitted by the propagator of the auxiliary bose ghost that corresponds to a linearly rising potential with tensor coupling to colored quarks that is proportional to the renormalization-group invariant $g^2 D(k) G^2(k)$. A comparison with numerical results is discussed.

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Daniel Zwanziger. 2009-04-15. Some exact infrared properties of gluon and ghost propagators and long-range force in QCD. https://arxiv.org/abs/0904.2380

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