Chiral-symmetry-breaking corrections to the Goldberger-Treiman relation

Journal Article · Thu Apr 01 04:00:00 EST 1982 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.25.1937· OSTI ID:5382731

Dominguez, C A

The problem of accounting for the corrections to the Goldberger-Treiman relation (GTR) in neutron ..beta.. decay, ..delta../sub ..pi../, is examined. It is argued that the failure of the traditional approach, based on dispersion relations of Reggeized one-pion-exchange fits to high-energy hadronic reactions, is probably due to the fact that the radial excitations of the pion have not been explicitly incorporated into these calculations. Although there is now experimental confirmation of the existence of a three-pion resonance, more data is needed in order to update these analysis. A different approach to the calculation of ..delta../sub ..pi../ is proposed here. Starting from the chiral-SU(2) x SU(2)-symmetry limit, where the GTR is exact, one interprets all the GTR parameters as referring strictly to that limit. By calculating the renormalizations induced by symmetry breaking in all four parameters, one can then predict ..delta../sub ..pi../. As a result of this interpretation of new relation between ..delta../sub ..pi../ and the ..pi..N sigma commutator sigma/sub piN/ is obtained. Using the most recent theoretical value of sigma/sub piN/ (35 +- 10 MeV), one predicts ..delta../sub ..pi../ = 0.06 +- 0.02, in good agreement with experiment (..delta../sub ..pi..//sup exp/ = 0.06 +- 0.01). On the other hand, a large sigma term such as sigma/sub piN/approx. =60 MeV, which in itself is very hard to understand in the framework of QCD and SU(3), would lead to ..delta../sub ..pi../approx. =-0.30, in obvious conflict with experiment.

• Research Organization: Department of Physics, Texas A and M University, College Station, Texas 77843
• OSTI ID: 5382731
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 25:7; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645301* -- High Energy Physics-- Particle Invariance Principles & Symmetries-- General-- (-1987)
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYONS
BETA DECAY
BOSON-EXCHANGE MODELS
CHIRAL SYMMETRY
DECAY
ELEMENTARY PARTICLES
FERMIONS
FIELD THEORIES
GOLDBERGER-TREIMAN RELATION
HADRONS
LIE GROUPS
MATHEMATICAL MODELS
NEUTRONS
NUCLEONS
OBE MODEL
OPE MODEL
PARTICLE MODELS
PERIPHERAL MODELS
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
RENORMALIZATION
SU GROUPS
SU-3 GROUPS
SYMMETRY
SYMMETRY BREAKING
SYMMETRY GROUPS