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Title: Confinement, quark mass functions, and spontaneous chiral symmetry breaking in Minkowski space

We formulate the covariant equations for quark-antiquark bound states in Minkowski space in the framework of the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. We show that these equations are charge conjugation invariant, and that in the chiral limit of vanishing bare quark mass, a massless pseudoscalar bound state is produced in a Nambu--Jona-Lasinio (NJL) mechanism, which is associated with the Goldstone boson of spontaneous chiral symmetry breaking. In this introductory paper we test the formalism by using a simplified kernel consisting of a momentum-space $$\delta$$-function with a vector Lorentz structure, to which one adds a mixed scalar and vector confining interaction. The scalar part of the confining interaction is not chirally invariant by itself, but decouples from the equations in the chiral limit and therefore allows the NJL mechanism to work. With this model we calculate the quark mass function, and we compare our Minkowski-space results to LQCD data obtained in Euclidean space. In a companion paper we apply this formalism to a calculation of the pion form factor.
 [1] ;  [2] ;  [1] ;  [3]
  1. CFTP, Institute Superior Tecnico, Lisboa (Portugal)
  2. JLAB, Newport News, VA (United States)
  3. University of Evora, Lisboa (Portugal)
Publication Date:
OSTI Identifier:
Report Number(s):
JLAB-THY-13-1814; DOE/OR-23177-2871
Journal ID: ISSN 0556-2821; arXiv:1310.7545; TRN: US1400138
DOE Contract Number:
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 89; Journal Issue: 01
American Physical Society (APS)
Research Org:
Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)
Sponsoring Org:
USDOE Office of Science (SC)
Country of Publication:
United States