Derivation of the gap and Bethe-Salpeter equations at large Nc limit and symmetry preserving truncations

We develop a framework for deriving Dyson-Schwinger equations (DSEs) and the Bethe-Salpeter equation (BSE) in QCD at the large Nc limit. The starting point is a modified form (with auxiliary fields) of the QCD generating functional. This framework provides a natural order-by-order truncation scheme...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. D 2017-11, Vol.96 (9)
Main Authors: Fu, Hui-Feng, Wang, Qing, Jiang, Libo
Format: Article
Language:English
Subjects:
Bethe-Salpeter equation
Mathematical analysis
Quarks
Scattering
Symmetry
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We develop a framework for deriving Dyson-Schwinger equations (DSEs) and the Bethe-Salpeter equation (BSE) in QCD at the large Nc limit. The starting point is a modified form (with auxiliary fields) of the QCD generating functional. This framework provides a natural order-by-order truncation scheme for DSEs and the BSE, and the kernels of the equations up to any order are explicitly given. Chiral symmetry (at the chiral limit) is preserved in any-order truncation, so it exemplifies the symmetry preserving truncation scheme. It provides a method to study DSEs and BSE beyond the rainbow-ladder truncation and is especially useful to study contributions from non-Abelian dynamics (those arising from gluon self-interactions). We also derive the equation for the quark-ghost scattering kernel and discuss the Slavnov-Taylor identity connecting the quark-gluon vertex, the quark propagator, and the quark-ghost scattering kernel.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.96.094023