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Nonperturbative study of the four gluon vertex

ECT* Seminar

Daniele Binosi

07 Jan 2015 - 11:15
Villa Tambosi 2nd Floor, Seminar Room

We review our recent results on the nonperturbative structure of the SU(3) four-gluon vertex in  the Landau gauge obtained by employing an approximation scheme where ``one-loop''  diagrams are computed using fully  dressed gluon and ghost propagators, and tree-level vertices.
When a suitable  kinematical configuration depending  on a single  momentum  scale $p$  is  chosen, only  two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is  proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular  divergence does not  affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of  momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates  from the connected Green's   function all one-particle  reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by  this possibility,  we discuss  in detail  how a  hypothetical  lattice measurement  of  this quantity  would compare to the results presented here, and the potential interference  from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.