Toy model for two chiral nonets
- Department of Mathematics/Science, State University of New York Institute of Technology, Utica, New York 13504-3050 (United States)
- Department of Physics, Syracuse University, Syracuse, New York 13244-1130 (United States)
Motivated by the possibility that nonets of scalar mesons might be described as mixtures of 'two quark' and 'four quark' components, we further study a toy model in which corresponding chiral nonets (containing also the pseudoscalar partners) interact with each other. Although the 'two quark' and 'four quark' chiral fields transform identically under SU(3){sub L}xSU(3){sub R} transformations, they transform differently under the U(1){sub A} transformation which essentially counts total (quark+antiquark) content of the mesons. To implement this, we formulate an effective Lagrangian which mocks up the U(1){sub A} behavior of the underlying QCD. We derive generating equations which yield Ward identity type relations based only on the assumed symmetry structure. This is applied to the mass spectrum of the low lying pseudoscalars and scalars, as well as their 'excitations'. Assuming isotopic spin invariance, it is possible to disentangle the amount of 'two quark' vs 'four quark' content in the pseudoscalar {pi},K,{eta}-type states and in the scalar {kappa}-type states. It is found that a small 'four quark' content in the lightest pseudoscalars is consistent with a large 'four quark' content in the lightest of the scalar {kappa} mesons. The present toy model also allows one to easily estimate the strength of a 'four quark' vacuum condensate. There seems to be a rich and interesting structure.
- OSTI ID:
- 20711209
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 72, Issue 3; Other Information: DOI: 10.1103/PhysRevD.72.034001; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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