TY  - JOUR
AU  - Binosi, D.
AU  - Chang, L.
AU  - Papavassiliou, J.
AU  - Qin, S. X.
AU  - Roberts, C. D.
PY  - 2016
DA  - 2016//
TI  - Symmetry preserving truncations of the gap and Bethe-Salpeter equations
T2  - Phys. Rev. D
JO  - Physical Review D
SP  - 096010
EP  - 7pp
VL  - 93
IS  - 9
PB  - Amer Physical Soc
AB  - 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.
SN  - 2470-0010
UR  - http://arxiv.org/abs/1601.05441
UR  - https://doi.org/10.1103/PhysRevD.93.096010
DO  - 10.1103/PhysRevD.93.096010
LA  - English
N1  - WOS:000376641000007
ID  - Binosi_etal2016
ER  -