%0 Journal Article
%T Symmetry preserving truncations of the gap and Bethe-Salpeter equations
%A Binosi, D.
%A Chang, L.
%A Papavassiliou, J.
%A Qin, S. X.
%A Roberts, C. D.
%J Physical Review D
%D 2016
%V 93
%N 9
%I Amer Physical Soc
%@ 2470-0010
%G English
%F Binosi_etal2016
%O WOS:000376641000007
%O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=2689), last updated on Fri, 17 Jun 2016 14:31:55 +0000
%X Ward-Green-Takahashi (WGT) identities play a crucial role in hadron physics, e.g. imposing stringent relationships between the kernels of the one-and two-body problems, which must be preserved in any veracious treatment of mesons as bound states. In this connection, one may view the dressed gluon-quark vertex, Gamma(alpha)(mu), as fundamental. We use a novel representation of Gamma(alpha)(mu), in terms of the gluon-quark scattering matrix, to develop a method capable of elucidating the unique quark-antiquark Bethe-Salpeter kernel, K, that is symmetry consistent with a given quark gap equation. A strength of the scheme is its ability to expose and capitalize on graphic symmetries within the kernels. This is displayed in an analysis that reveals the origin of H-diagrams in K, which are two-particle-irreducible contributions, generated as two-loop diagrams involving the three-gluon vertex, that cannot be absorbed as a dressing of Gamma(alpha)(mu) in a Bethe-Salpeter kernel nor expressed as a member of the class of crossed-box diagrams. Thus, there are no general circumstances under which the WGT identities essential for a valid description of mesons can be preserved by a Bethe-Salpeter kernel obtained simply by dressing both gluon-quark vertices in a ladderlike truncation; and, moreover, adding any number of similarly dressed crossed-box diagrams cannot improve the situation.
%R 10.1103/PhysRevD.93.096010
%U http://arxiv.org/abs/1601.05441
%U https://doi.org/10.1103/PhysRevD.93.096010
%P 096010-7pp