Asymptotic chiral invariance. [Callan-Symanzik equations]

Journal Article · Sun May 15 04:00:00 EDT 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.2979· OSTI ID:7259110

Mtingwa, S K

We discuss the conditions under which chiral symmetries become exact at asymptotic momenta, utilizing the homogeneous Callan-Symanzik equations so that momenta are not restricted to the deep Euclidean domain as others have done previously. In particular, we consider as our prototype the chiral SU(2) x SU(2) sigma model of Gell-Mann and Levy without fermions, where we allow for both spontaneous symmetry breaking and explicit breaking of the symmetry via a term in the Lagrangian linear in the sigma field. To check our general results, we calculate to two-loop order in perturbation theory the coefficients of the homogeneous Callan-Symanzik equations along with the interesting amplitudes of the theory and finally show that under suitable conditions the symmetry-broken theory and the symmetry-conserved theory both approach the same massless, symmetric theory as the momenta become asymptotic.

• Research Organization: Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627
• OSTI ID: 7259110
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 15:10; ISSN PRVDA
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRAIC CURRENTS
ASYMPTOTIC SOLUTIONS
AXIAL-VECTOR CURRENTS
BOSONS
CHIRAL SYMMETRY
CURRENTS
DECAY
ELEMENTARY PARTICLES
EQUATIONS
FUNCTIONS
GELL-MANN THEORY
HADRONS
LAGRANGIAN FUNCTION
LIE GROUPS
MATHEMATICAL MODELS
MATRIX ELEMENTS
MESONS
PARTICLE MODELS
PERTURBATION THEORY
PIONS
PROPAGATOR
PSEUDOSCALAR MESONS
RENORMALIZATION
SIGMA MODEL
SU GROUPS
SU-2 GROUPS
SUM RULES
SYMMETRY
SYMMETRY BREAKING
SYMMETRY GROUPS