eta decay into three pions and the on-mass-shell current algebra. [Su(3)XSU(3) sigma model, quark model, amplitude, rate]

Journal Article · Sat Jan 01 04:00:00 EST 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.121· OSTI ID:7127681

Golestaneh, A A

We use the on-mass-shell current algebra based on the SU(3) x SU(3) sigma model for calculating the G-parity-violating decay eta ..-->.. 3..pi... The model we use consists of the triplet of quarks coupled to the SU(3) scalar and pseudoscalar fields, sigma and phi, and the chiral-symmetry-breaking operators u/sub 8/ and u/sub 3/ (tadpole terms). Owing to the terms phi/sub i/phi/sub j/ with i not-equal j = 0, 3, and 8 in the Lagrangian, the axial-vector current sources and fields associated with the ..pi../sup 0/, eta, and eta' particles are formed by mixtures of terms with opposite G parity; the mixing coefficient epsilon = u/sub 3//(4u/sub 8/). Using these current operators, and having all particles on the mass shell, we evaluate the decay amplitude by the reduction formalism from the <3..pi..vertical-bareta> matrix element, making use of pole dominance. The result is proportional to the coefficient r = 4epsilon, which is determined by the tadpole parts of the masses and decay constants of the mesons through a set of relations which are derived from our Lagrangian. However, since these masses are not known satisfactorily, we first choose r so as to obtain the observed eta ..-->.. ..pi../sup 0/..pi../sup +/..pi../sup -/ decay rate (which is proportional to r/sup 2/), and then we verify that such an r value is consistent with the above set of relations. We find that r = 2.12 x 10/sup -2/, and in turn the tadpole part of the K/sup 0/-K/sup +/ mass difference m/sub K/0 /sup 2/ - m/sub K/+ /sup 2/ = 0.0005 GeV/sup 2/. We also find the branching ratio and the ratio of the rates of the eta and eta' decays in agreement with experiment. Comparing the decay amplitude obtained here with the one derived by the tree-graph method based on the U(3) x U(3) symmetry scheme, we realize the important role of the mixing of the phi/sub 0/, phi/sub 8/, and phi/sub 3/ field components, and the advantage of using the on-mass-shell current algebra for this process. (AIP)

• Research Organization: Fermi National Accelerator Laboratory, Batavia, Illinois 60510
• OSTI ID: 7127681
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 15:1; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645303* -- High Energy Physics-- Particle Invariance Principles &amp; Symmetries-- Applications to Strong Interactions-- (-1987)
645400 -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
BOSONS
CHIRAL SYMMETRY
COMPOSITE MODELS
CURRENT ALGEBRA
DECAY
DECAY AMPLITUDES
ELEMENTARY PARTICLES
ETA MESONS
HADRONS
INVARIANCE PRINCIPLES
KAONS
KAONS NEUTRAL
KAONS PLUS
LIE GROUPS
MASS DIFFERENCE
MATHEMATICAL MODELS
MATRIX ELEMENTS
MESONS
P INVARIANCE
PARTICLE MODELS
PARTICLE PROPERTIES
PIONS
PSEUDOSCALAR MESONS
QUARK MODEL
SCALAR FIELDS
SIGMA MODEL
STRANGE PARTICLES
SU GROUPS
SU-3 GROUPS
SYMMETRY
SYMMETRY BREAKING
SYMMETRY GROUPS
TRANSITION AMPLITUDES