Abstract
In this talk we present a new method for determining the nonperturbative quark-gluon vertex, which constitutes a crucial ingredient for a variety of theoretical and phenomenological studies. This new method relies heavily on the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. The longitudinal part of this latter quantity is fixed using the standard gauge technique, whereas the transverse is estimated with the help of the so-called transverse Ward identities. This method allows the approximate determination of the nonperturbative behavior of all twelve form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. Numerical results are presented for the form factors in three special kinematical configurations (soft gluon and quark symmetric limit, zero quark momentum), and compared with the corresponding lattice data.
Highlights
One of the major challenges of nonperturbative QCD is to understand the mechanism that drives chiral symmetry breaking and the associated generation of constituent quark masses
We have presented a new methodology for determining the longitudinal and transverse form factors of the nonperturbative quark-gluon vertex within the pinch technique (PT)-background field method (BFM) scheme
This scheme allows us to take the full advantage of the rich amount of information originating from the fundamental underlying symmetries, which are encoded in a set of crucial identities such as WIs, STIs and background-quantum identities (BQIs)
Summary
One of the major challenges of nonperturbative QCD is to understand the mechanism that drives chiral symmetry breaking and the associated generation of constituent quark masses. The main difficulty in dealing with the quark-gluon vertex lies in the fact that one has to determine the behavior of twelve form factors (four “longitudinal” and the eight “transverse”), which are functions of three independent kinematic variables For this reason, the available nonperturbative information on this quantity is rather limited. The behavior of the form factors is governed by a complex system of coupled integral equations, which can be solved only after considerable truncations and drastic simplifying assumptions [21, 22, 11, 23, 24, 25, 26] In this talk we will present a novel nonperturbative approach for calculating the form factors of the quark-gluon vertex in the Landau gauge [27]. While a general qualitative agreement with the available lattice data is found, quantitative discrepancies still remain
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