Symmetry preserving truncations of the gap and Bethe-Salpeter equations - INSPIRE

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Symmetry preserving truncations of the gap and Bethe-Salpeter equations

Daniele Binosi
(
- ECT, Trento and
- Fond. Bruno Kessler, Povo
)
,
Lei Chang
(
- Nankai U.
)
,
Joannis Papavassiliou
(
- Valencia U. and
- Valencia U., IFIC
)
,
Si-Xue Qin
(
- Argonne, PHY
)
,
Craig D. Roberts
(
- Argonne, PHY
)

Jan 20, 2016

7 pages

Published in:

Phys.Rev.D 93 (2016) 9, 096010

Published: May 24, 2016

e-Print:

1601.05441 [nucl-th]

DOI:

10.1103/PhysRevD.93.096010

View in:

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Abstract: (APS)

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, Γμa, as fundamental. We use a novel representation of Γμa, 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 Γμa 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.

Note:

6 pages, 8 figures

quark gluon: scattering
S-matrix
Bethe-Salpeter equation
Ward-Takahashi identity
quark antiquark
gap equation
bound state
meson
hadron
quark

References(62)

Figures(8)

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