21 research outputs found
Exploring \pp scattering in the \1N picture
In the large approximation to , the leading \pp scattering
amplitude is expressed as the sum of an infinite number of tree diagrams. We
investigate the possibility that an adequate approximation at energies up to
somewhat more than one can be made by keeping diagrams which involve the
exchange of resonances in this energy range in addition to the simplest chiral
contact terms. In this approach crossing symmetry is automatic but individual
terms tend to drastically violate partial wave unitarity. We first note that
the introduction of the meson in a chirally invariant manner
substantially delays the onset of drastic unitarity violation which would be
present for the {\it current algebra} term alone. This suggests a possibility
of local (in energy) cancellation which we then explore in a phenomenological
way. We include exchanges of leading resonances up to the region.
However, unitarity requires more structure which we model by a four derivative
contact term or by a low lying scalar resonance which is presumably subleading
in the \1N expansion, but may nevertheless be important. The latter two
flavor model gives a reasonable description of the phase shift up
until around , before the effects associated which the
threshold come into play.Comment: 27 LaTex pages + 13 figures (also available in hard-copy
Effective Chiral Lagrangian from Dual Resonance Models
Parameters of the effective chiral lagrangian (EChL) of orders and
are extracted from low--energy behaviour of dual resonance models for
and scattering amplitudes. Dual resonance models are
considered to be good candidates for the resonance spectrum and for hadronic
scattering amplitudes in the large limit of QCD. We discuss dual
resonance models in the presence of spontaneous and explicit chiral symmetry
breaking. Obtained parameters of the EChL are used to estimate chiral
corrections up to the sixth order to various low--energy characteristics of
and scattering amplitudes.Comment: 32 pages, the references list is updated, comparison with chiral
quark model is done in more detail
Effective chiral lagrangian in the chiral limit from the instanton vacuum
We study the effective chiral Lagrangian in the chiral limit from the
instanton vacuum. Starting from the nonlocal effective chiral action, we derive
the effective chiral Lagrangian, using the derivative expansion to order
in the chiral limit. The low energy constants, , , and
are determined and compared with various models and the corresponding empirical
data. The results are in a good agreement with the data. We also discuss about
the upper limit of the sigma meson, based on the present results.Comment: 14 pages, 5 figures, submitted to Phys.Rev.
Large Nc and Chiral Dynamics
We study the dependence on the number of colors of the leading pi pi
scattering amplitude in chiral dynamics. We demonstrate the existence of a
critical number of colors for and above which the low energy pi pi scattering
amplitude computed from the simple sum of the current algebra and vector meson
terms is crossing symmetric and unitary at leading order in a truncated and
regularized 1/Nc expansion. The critical number of colors turns out to be Nc=6
and is insensitive to the explicit breaking of chiral symmetry.
Below this critical value, an additional state is needed to enforce the
unitarity bound; it is a broad one, most likely of "four quark" nature.Comment: RevTeX4, 6 fig., 5 page
Simple Description of Pion-Pion Scattering to 1 GeV
Motivated by the 1/Nc expansion, we present a simple model of pion-pion
scattering as a sum of a `current-algebra' contact term and resonant pole
exchanges. The model preserves crossing symmetry as well as unitarity up to 1.2
GeV. Key features include chiral dynamics, vector meson dominance, a broad low
energy scalar (sigma) meson and a `Ramsauer-Townsend' mechanism for the
understanding of the 980 MeV region. We discuss in detail the `regularization'
(corresponding to rescattering effects) necessary to make all these nice
features work.Comment: 35 pages (LaTeX), 13 PostScript figures are included as
uuencoded-compressed-ta
Putative Light Scalar Nonet
We investigate the "family" relationship of a possible scalar nonet composed
of the a_0(980), the f_0(980) and the \sigma and \kappa type states found in
recent treatments of \pi\pi and \pi K scattering. We work in the effective
Lagrangian framework, starting from terms which yield "ideal mixing" according
to Okubo's original formulation. It is noted that there is another solution
corresponding to dual ideal mixing which agrees with Jaffe's picture of scalars
as qq\bar q \bar q states rather than as q\bar q states. At the Lagrangian
level there is no difference in the formulation of the two cases (other than
the numerical values of the coefficients). In order to agree with experiment,
additional mass and coupling terms which break ideal mixing are included. The
resulting model turns out to be closer to dual ideal mixing than to
conventional ideal mixing; the scalar mixing angle is roughly -17 degrees in a
convention where dual ideal mixing is 0 degrees.Comment: 24 pages, 3 figure
eta' to eta pi pi Decay as a Probe of a Possible Lowest-Lying Scalar Nonet
We study the eta' to eta pi pi decay within an effective chiral Lagrangian
approach in which the lowest lying scalar meson candidates sigma(560) and
kappa(900) together with the f0(980) and a0(980) are combined into a possible
nonet. We show that there exists a unique choice of the free parameters of this
model which, in addition to fitting the pi pi and pi K scattering amplitudes,
well describes the experimental measurements for the partial decay width of
eta' to eta pi pi and the energy dependence of this decay. As a by-product, we
estimate the a0(980) width to be 70 MeV, in agreement with a new experimental
analysis.Comment: 25 pages, 11 figure
Phenomenological amplitude and the modelling of the OlssonâTurner and ChewâLow approaches
The phenomenological amplitude for the reaction fixed by fittings to the experimental data in the energy region
MeV/c is used for modelling the ChewâLowâ
extrapolation and OlssonâTurnerOlssonâTurnerâthreshold approach. It is shown that the uncritical
application of the former results in enermous theoretical errors, the
extracted values being in fact random numbers. The results of the OlssonâTurnerOlssonâTurnerâ
method are characterized by significant systematic
errors coming from unknown details of the isobar physics