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We solve numerically the Schwinger-Dyson (SD hereafter) ghost equation in theLandau gauge for a given gluon propagator finite at k=0 (alpha_gluon=1) andwith the usual assumption of constancy of the ghost-gluon vertex ; we show thatthere exist two possible types of ghost dressing function solutions, as we havepreviously inferred from analytical considerations : one singular at zeromomentum, satisfying the familiar relation alpha_gluon+2 alpha_ghost=0 betweenthe infrared exponents of the gluon and ghost dressing functions(in short,respectively alpha_G and alpha_F) and having therefore alpha_ghost=-1/2, andanother which is finite at the origin (alpha_ghost=0), which violates therelation. It is most important that the type of solution which is realizeddepends on the value of the coupling constant. There are regular ones for anycoupling below some value, while there is only one singular solution, obtainedonly at a critical value of the coupling. For all momenta k<1.5 GeV where theycan be trusted, our lattice data exclude neatly the singular one, and agreevery well with the regular solution we obtain at a coupling constant compatiblewith the bare lattice value.

IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation