# Gribov&#x27;s horizon and the ghost dressing function - High Energy Physics - Phenomenology

Abstract: We study a relation recently derived by K. Kondo at zero momentum between theZwanziger-s horizon function, the ghost dressing function and Kugo-s functions$u$ and $w$. We agree with this result as far as bare quantities areconsidered. However, assuming the validity of the horizon gap equation, weargue that the solution $w0=0$ is not acceptable since it would lead to avanishing renormalised ghost dressing function. On the contrary, when thecut-off goes to infinity, $u0 \to \infty$, $w0 \to -\infty$ such that$u0+w0 \to -1$. Furthermore $w$ and $u$ are not multiplicativelyrenormalisable. Relaxing the gap equation allows $w0=0$ with $u0 \to -1$.In both cases the bare ghost dressing function, $F0,\Lambda$, goeslogarithmically to infinity at infinite cut-off. We show that, although thelattice results provide bare results not so different from the $F0,\Lambda=3$solution, this is an accident due to the fact that the lattice cut-offs lie inthe range 1-3 GeV$^{-1}$. We show that the renormalised ghost dressing functionshould be finite and non-zero at zero momentum and can be reliably estimated onthe lattice up to powers of the lattice spacing ; from published data on a$80^4$ lattice at $\beta=5.7$ we obtain $F R0,\mu=1.5$ GeV$\simeq 2.2$.

Author: Ph. Boucaud, J.P. Leroy, A. Le Yaouanc, J. Micheli, O. Pène, J. Rodríguez-Quintero

Source: https://arxiv.org/