Mesons as qbar-q Bound States from Euclidean 2-Point Correlators in the Bethe-Salpeter Approach
arXiv:nucl-th/9806011 · doi:10.1103/PhysRevC.59.986
Abstract
We investigate the 2-point correlation function for the vector current. The gluons provide dressings for both the quark self energy as well as the vector vertex function, which are described consistently by the rainbow Dyson-Schwinger equation and the inhomogeneous ladder Bethe-Salpeter equation. The form of the gluon propagator at low momenta is modeled by a 2-parameter ansatz fitting the weak pion decay constant. The quarks are confined in the sense that the quark propagator does not have a pole at timelike momenta. We determine the ground state mass in the vector channel from the Euclidean time Fourier transform of the correlator, which has an exponential falloff at large times. The ground state mass lies around 590 MeV and is almost independent of the model form for the gluon propagator. This method allows us to stay in Euclidean space and to avoid analytic continuation of the quark or gluon propagators into the timelike region.
21 pages (REVTEX), 8 Postscript figures
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- Pion Form Factor and Quark Mass Evolution in a Light-Front Bethe-Salpeter Model
- Nonperturbative Aspect of Axial Vector Vertex in the Global Color Symmetry Model
- Comment to: "A note on failure of the ladder approximation to QCD" [Phys. Lett. B 640 (2006) 196 ]
- The Explicit and Dynamical Chiral Symmetry Breaking in an Effective Quark-quark Interaction Model
- The Chiral Quark Condensate and the Bag Constant with Finite Chemical Potential