arXiv Analytics

Sign in

arXiv:1209.2757 [nucl-th]AbstractReferencesReviewsResources

Existence and stability of multiple solutions to the gap equation

Kun-lun Wang, Si-xue Qin, Yu-xin Liu, Lei Chang, Craig D. Roberts, Sebastian M. Schmidt

Published 2012-09-13Version 1

We argue by way of examples that, as a nonlinear integral equation, the gap equation can and does possess many physically distinct solutions for the dressed-quark propagator. The examples are drawn from a class that is successful in describing a broad range of hadron physics observables. We apply the homotopy continuation method to each of our four exemplars and thereby find all solutions that exist within the interesting domains of light current-quark masses and interaction strengths; and simultaneously provide an explanation of the nature and number of the solutions, many of which may be associated with dynamical chiral symmetry breaking. Introducing a stability criterion based on the scalar and pseudoscalar susceptibilities we demonstrate, however, that for any nonzero current-quark mass only the regular Nambu solution of the gap equation is stable against perturbations. This guarantees that the existence of multiple solutions to the gap equation cannot complicate the description of phenomena in hadron physics.

Comments: 14 pages, 15 figures
Journal: Phys. Rev. D 86, 114001 (2012)
Categories: nucl-th, hep-lat, hep-ph
Related articles: Most relevant | Search more
arXiv:1305.2955 [nucl-th] (Published 2013-05-13, updated 2013-11-04)
Multiple solutions for the fermion mass function in QED3
arXiv:1108.0603 [nucl-th] (Published 2011-08-02, updated 2011-09-01)
Interaction model for the gap equation
arXiv:nucl-th/0005052 (Published 2000-05-18)
How to Renormalize the Gap Equation in High Density QCD