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As of today, color confinement in Quantum Chromodynamics remains a mysteryfrom the theoretical point of view. So far, no analytical proof of colorconfinement has been found and the mechanism that confines colored states fromthe space of physical states is still unknown. Taichiro Kugo and Izumi Ojimaproposed such confinement mechanism, using as basis the BRST-symmetry andderived the requirements for the realization of this mechanism. One suchrequirement, which happens to be the non-trivial one, is that a specialcorrelation function, the Kugo-Ojima correlation function $u(p^2)$, approaches$-1$ at the origin ($p^2=0)$. This correlation function can be obtained on thelattice within the lattice formulation of gauge theories. The present workconsists on lattice results for this correlation function on the Landau gauge.We present results obtained from 4 symmetric large volume lattices $(32^{4},48^{4}, 64^{4}, 80^{4})$ with $\beta = 6.0$ on the Landau gauge. A test on thetransversality of the Kugo-Ojima correlation function is also performed, alongwith some statistical considerations of the results. The results presentfurther evidence that the Kugo-Ojima confinement scenario is not realized onthe lattice and that the Kugo-Ojima correlation function, in the Landau gauge,is transverse. Our findings align qualitatively with existing literature.

Lattice computation of the Kugo-Ojima correlation function