Chiral nonet mixing inππscattering

Abstract

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.

Chiral nonet mixing inπKscattering

“…In the case of ππ scattering [59] the first pole clearly captured the properties of light and broad sigma and the second pole resembled the f 0 (980). For interpretation of the physical resonances it is conventional to look at the pole positions in the complex plane of the analytically continued expression for T 1 2 0 .…”

“…These are (a) the values of the SU(3) symmetry breaking parameter A 3 /A 1 , and (b) choices of the only roughly known "heavy pion" mass m[Π(1300)]. Similar to the case of ππ scattering amplitude studied in [59], we see that, without using any new parameters, the mixing mechanism of [64] predicts the scattering amplitude in reasonable qualitative agreement with the low-energy experimental data up to around 900 MeV. This provides further support for the validity of this mixing mechanism.…”

“…The free parameters of the leading order of the model are completely determined by fitting to various low-energy data. After these parameters are determined several predictions of the model are studied in follow up works, including the prediction of ππ scattering amplitude in [59] which, after unitarizing the amplitude using the K-matrix method, gives a reasonable agreement with data up to around 1 GeV. In the work of [59], the poles of the K-matrix unitarized amplitude are determined and used to calculate the physical masses and decay widths of the isosinglet scalar mesons.…”

Chiral symmetry breaking patterns in theUL(n)×UR(n)meson model

“…This means that although due to explicit symmetry breaking terms several nonzero condensate components might appear [3,5,14,15], spontaneous symmetry breaking and its recovery has been observed in the piece proportional to the unit matrix [5]. Besides [24], there were no attempts to search for spontaneous symmetry breaking in other order parameters.…”

“…Due to difficulties of solving QCD at low energies, effective models built upon the approximate chiral symmetry can give reasonable results regarding the properties of the chiral transition and therefore the phase diagram of the strongly interacting matter. The n-flavored matrix model displaying a U L (n) × U R (n) symmetry [2] gives decent results on the mesonic spectra and phase diagram [3][4][5] of QCD, and can be extended with quark degrees of freedom (quark-meson model) [6,7] and/or the Polyakov loop [8][9][10][11][12][13], tetraquark excitations [14,15], and vector mesons [16]. Although none of these models can be solved exactly either, they provide a simpler theoretical framework than QCD to describe the behavior of the strongly interacting matter at finite temperature and density.…”