Spontaneous breaking of chiral symmetry for confining potentials

Journal Article · Thu Mar 15 00:00:00 EST 1984 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.29.1233· OSTI ID:6875230

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

Using the Bogoliubov-Valatin variational method, we show that the chiral-invariant vacuum is unstable for a color, fourth-component vector powerlike potential rsup..cap alpha.. (0<..cap alpha..<3) independently of the strength of the coupling constant. The fermion self-energy is negative and dominates over the positive potential energy, destabilizing the vacuum by psi-barpsi pair condensation. This self-energy is finite but infrared singular, reflecting the behavior of the potential at large distances. We give an analytical proof of the fact that the energy of the unbroken vacuum is not minimum. The proof extends to logarithmic potentials as ..cap alpha -->..0, but breaks down for ..cap alpha..> or =3 (number of spatial dimensions) due to severe infrared singularities. If the confining potential possesses a spin-spin piece, there are critical values of its strength, depending on the power ..cap alpha.., beyond which the stability of the chiral-invariant vacuum is restored. In the case of the harmonic oscillator ..cap alpha.. = 2, the gap equation reduces to a nonlinear second-order differential equation. We find (besides the usual chiral degeneracy) an infinite number of solutions breaking chiral symmetry, higher in energy as the number of their nodes increases. We compute the expectation value of psi-barpsi and the mass gap for the new vacuum, the lowest solution in energy. The infrared singularity of the massless fermion self-energy is removed for the stable broken solution.

• Research Organization: Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris-Sud, Btiment 211, 91405 Orsay, France
• OSTI ID: 6875230
• Journal Information: Phys. Rev. D; (United States), Vol. 29:6
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FERMIONS
SELF-ENERGY
QUANTUM CHROMODYNAMICS
CHIRAL SYMMETRY
SYMMETRY BREAKING
COLOR MODEL
COUPLING CONSTANTS
GLUONS
INFRARED DIVERGENCES
POTENTIALS
QUARK-QUARK INTERACTIONS
SPIN
VACUUM STATES
VARIATIONAL METHODS
ANGULAR MOMENTUM
COMPOSITE MODELS
ELEMENTARY PARTICLES
ENERGY
FIELD THEORIES
INTERACTIONS
MATHEMATICAL MODELS
PARTICLE INTERACTIONS
PARTICLE MODELS
PARTICLE PROPERTIES
POSTULATED PARTICLES
QUANTUM FIELD THEORY
QUARK MODEL
SYMMETRY
645400* - High Energy Physics- Field Theory