426 research outputs found
Toy model for two chiral nonets
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) SU(3)
transformations they transform differently under the U(1) 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)
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 type states and in the scalar 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
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.Comment: Numerical results updated, typos corrected, references update
Two chiral nonet model with massless quarks
We present a detailed study of a linear sigma model containing one chiral
nonet transforming under U(1) as a quark-antiquark composite and another
chiral nonet transforming as a diquark-anti diquark composite (or, equivalently
from a symmetry point of view, as a two meson molecule). The model provides an
intuitive explanation of a current puzzle in low energy QCD: Recent work has
suggested the existence of a lighter than 1 GeV nonet of scalar mesons which
behave like four quark composites. On the other hand, the validity of a
spontaneously broken chiral symmetric description would suggest that these
states be chiral partners of the light pseudoscalar mesons, which are two quark
composites. The model solves the problem by starting with the two chiral nonets
mentioned and allowing them to mix with each other. The input of physical
masses in the SU(3) invariant limit for two scalar octets and an "excited" pion
octet results in a mixing pattern wherein the light scalars have a large four
quark content while the light pseudoscalars have a large two quark content. One
light isosinglet scalar is exceptionally light. In addition, the pion pion
scattering is also studied and the current algebra theorem is verified for
massless pions which contain some four quark admixture.Comment: 22 pages, 8 figure
Mass Uncertainties of f0(600) and f0(1370) and their Effects on Determination of the Quark and Glueball Admixtures of the I=0 Scalar Mesons
Within a nonlinear chiral Lagrangian framework the correlations between the
quark and glueball admixtures of the isosinglet scalar mesons below 2 GeV and
the current large uncertainties on the mass of the f0(600) and the f0(1370) are
studied. The framework is formulated in terms of two scalar meson nonets (a
two-quark nonet and a four-quark nonet) together with a scalar glueball. It is
shown that while some properties of these states are sensitive to the mass of
f0(600) and f0(1370), several relatively robust conclusions can be made: The
f0(600), the f0(980), and the f0(1370) are admixtures of two and four quark
components, with f0(600) being dominantly a non-strange four-quark state, and
f0(980) and f0(1370) having a dominant two-quark component. Similarly, the
f0(1500) and the f0(1710) have considerable two and four quark admixtures, but
in addition have a large glueball component. For each state, a detailed
analysis providing the numerical estimates of all components is given. It is
also shown that this framework clearly favors the experimental values:
m[f0(600)] < 700 MeV and m[f0(1370)] = 1300-1450 MeV. Moreover, an overall fit
to the available data shows a reciprocal substructure for the f0(600) and the
f0(1370), and a linear correlation between their masses of the form m
[f0(1370)] = 0.29 m[f0(600)] + 1.22 GeV. The scalar glueball mass of 1.5-1.7
GeV is found in this analysis.Comment: placement of figures inside text improved. Content unchange
Chiral Nonet Mixing in pi pi Scattering
Pion pion scattering is studied in a generalized linear sigma model which
contains two scalar nonets (one of quark-antiquark type and the other of
diquark-antidiquark type) and two corresponding pseudoscalar nonets. An
interesting feature concerns the mixing of the four isosinglet scalar mesons
which yield poles in the scattering amplitude. Some realism is introduced by
enforcing exact unitarity via the K-matrix method.
It is shown that a reasonable agreement with experimental data is obtained up
to about 1 GeV. The poles in the unitarized scattering amplitude are studied in
some detail. The lowest pole clearly represents the sigma meson (or f0(600))
with a mass and decay width around 500 MeV. The second pole invites comparison
with the f0(980) which has a mass around 1 GeV and decay width around 100 MeV.
The third and fourth poles, resemble some of the isosinglet state in the
complicated 1-2 GeV region. Some comparison is made to the situation in the
usual SU(3) linear sigma model with a single scalar nonet
Are three flavors special?
It has become clearer recently that the regular pattern of three flavor
nonets describing the low spin meson multiplets seems to require some
modification for the case of the spin 0 scalar mesons. One picture which has
had some success, treats the scalars in a chiral Lagrangian framework and
considers them to populate two nonets. These are, in turn, taken to result from
the mixing of two "bare" nonets, one of which is of quark- antiquark type and
the other of two quark- two antiquark type. Here we show that such a mixing is,
before chiral symmetry breaking terms are included, only possible for three
flavors. In other cases, the two types of structure can not have the same
chiral symmetry transformation property. Specifically, our criterion would lead
one to believe that scalar and pseudoscalar states containing charm would not
have "four quark" admixtures.
This work is of potential interest for constructing chiral Lagrangians based
on exact chiral symmetry which is then broken by well known specific terms. It
may also be of interest in studying some kinds of technicolor theories
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