Gap and Bethe-Salpeter equations in Hamiltonian lattice QCD with Wilson fermions

Journal Article · Thu May 15 04:00:00 EDT 1986 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.33.3098· OSTI ID:5764230

Le Yaouanc, A; Oliver, L; Pene, O; Raynal, J h

The dynamical breaking of symmetries in strong-coupling large-N/sub c/ Hamiltonian lattice QCD with Dirac fermions, thoroughly studied by Smit, is reconsidered and clarified here in another language. We use the Bogoliubov-Valatin variational method to formulate the gap equation and obtain the condensate, the dynamical mass, and the shift in energy density between the invariant and the broken vacua. We also solve the Bethe-Salpeter equation and get the quantum numbers, dispersion laws, and Dirac wave functions of the meson spectra in the whole Brillouin zone. The eightfold fermion multiplicity reflects in the meson spectrum through 8N/sub f/ /sup 2/ Goldstone bosons by the breaking U(4N/sub f/)->U(2N/sub f/) x U(2N/sub f/ ) (N/sub f/ = number of flavors). We repeat the program in the presence of a current mass and a Wilson term; we study the stability of the vacuum and see how the high degeneracy of Goldstone bosons is lifted. Although a massless pseudoscalar can be obtained by adjusting the current mass and the Wilson coupling, we find that the vacuum is not chiral degenerate and therefore this massless pseudoscalar is not a Goldstone boson. Although not chiral degenerate, the vacuum satisfies nevertheless the weaker condition of being a flat minimum: a finite number of derivatives vanish in the chiral direction. We conjecture that higher derivatives will converge to zero as the coupling decreases, chiral degeneracy being recovered only in the continuum weak-coupling limit. For any value of the Wilson term, the mass of a local baryon is just equal to N/sub c/M/sub dyn/ where M/sub dyn/ is the solution of the gap equation.

• Research Organization: Laboratoire de Physique Theorique et Hautes Energies, Btiment 211, Universite de Paris XI, 91405 Orsay, France
• OSTI ID: 5764230
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 33:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645204 -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BETHE-SALPETER EQUATION
BOSONS
COMPOSITE MODELS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELEMENTARY PARTICLES
ENERGY DENSITY
EQUATIONS
FERMIONS
FIELD THEORIES
FUNCTIONS
GOLDSTONE BOSONS
HAMILTONIANS
LATTICE FIELD THEORY
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MULTIPLICITY
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
POSTULATED PARTICLES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUANTUM NUMBERS
QUANTUM OPERATORS
QUARK MODEL
STRONG-COUPLING MODEL
SYMMETRY BREAKING
VARIATIONAL METHODS
WAVE EQUATIONS
WAVE FUNCTIONS