Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-01-17
JHEP 0806:012,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
17 pages, 3 figures (one new figure and a short paragraph added)
Scientific paper
10.1088/1126-6708/2008/06/012
We solve numerically the Schwinger-Dyson (SD hereafter) ghost equation in the Landau gauge for a given gluon propagator finite at k=0 (alpha_gluon=1) and with the usual assumption of constancy of the ghost-gluon vertex ; we show that there exist two possible types of ghost dressing function solutions, as we have previously inferred from analytical considerations : one singular at zero momentum, satisfying the familiar relation alpha_gluon+2 alpha_ghost=0 between the infrared exponents of the gluon and ghost dressing functions(in short, respectively alpha_G and alpha_F) and having therefore alpha_ghost=-1/2, and another which is finite at the origin (alpha_ghost=0), which violates the relation. It is most important that the type of solution which is realized depends on the value of the coupling constant. There are regular ones for any coupling below some value, while there is only one singular solution, obtained only at a critical value of the coupling. For all momenta k<1.5 GeV where they can be trusted, our lattice data exclude neatly the singular one, and agree very well with the regular solution we obtain at a coupling constant compatible with the bare lattice value.
Boucaud Ph.
Leroy J.-P.
Micheli J.
Pene Olivier
Rodriguez--Quintero J.
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