3 research outputs found
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
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
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