Vacuum Properties of Mesons in a Linear Sigma Model with Vector Mesons and Global Chiral Invariance

We present a two-flavour linear sigma model with global chiral symmetry and vector and axial-vector mesons. We calculate pion-pion scattering lengths and the decay widths of scalar, vector, and axial-vector mesons. It is demonstrated that vector and axial-vector meson degrees of freedom play an important role in these low-energy processes and that a reasonable theoretical description requires globally chirally invariant terms other than the vector meson mass term. An important question for meson vacuum phenomenology is the quark content of the physical scalar f0(600) and a0(980) mesons. We investigate this question by assigning the quark-antiquark sigma and a0 states of our model with these physical mesons. We show via a detailed comparison with experimental data that this scenario can describe all vacuum properties studied here except for the decay width of the sigma, which turns out to be too small. We also study the alternative assignment f0(1370) and a0(1450) for the scalar mesons. In this case the decay width agrees with the experimental value, but the pion-pion scattering length $a_{0}^{0}$ is too small. This indicates the necessity to extend our model by additional scalar degrees of freedom.Comment: 22 pages, 6 figure

Alternative Large Nc Schemes and Chiral Dynamics

We compare the dependences on the number of colors of the leading pion pion scattering amplitudes using the single index quark field and two index quark fields. These are seen to have different relationships to the scattering amplitudes suggested by chiral dynamics which can explain the long puzzling pion pion s wave scattering up to about 1 GeV. This may be interesting for getting a better understanding of the large Nc approach as well as for application to recently proposed technicolor models.Comment: RevTex, two-columns, 6 page

Vacuum phenomenology of the chiral partner of the nucleon in a linear sigma model with vector mesons

We investigate a linear sigma model with global chiral $U(2)_{R} \times U(2)_{L}$ symmetry. The mesonic degrees of freedom are the standard scalar and pseudoscalar mesons and the vector and axial-vector mesons. The baryonic degrees of freedom are the nucleon, $N$, and its chiral partner, $N^{*}$, which is usually identified with N(1535). The chiral partner is incorporated in the so-called mirror assignment, where the nucleon mass is not solely generated by the chiral condensate but also by a chirally invariant mass term, $m_{0}$. The presence of (axial-) vector fields modifies the expressions for the axial coupling constants of the nucleon, $g_{A}^{N}$, and its partner, $g_{A}^{N^{*}}$. Using experimental data for the decays $N^{*} \to N \pi$ and $a_{1} \to\pi\gamma$, as well as lattice results for $g_{A}^{N^{*}}$ we infer $m_{0}\sim500$ MeV, i.e., an appreciable amount of the nucleon mass originates from sources other than the chiral condensate. We test our model by evaluating the decay $N^{*} \to N \eta$ and the s-wave nucleon-pion scattering lengths $a_{0}^{(\pm)}$.Comment: 16 pages, 2 figures. To appear in Phys. Rev.

QCD Tests of the Puzzling Scalar Mesons

Motivated by several recent data, we test the QCD spectral sum rules (QSSR) predictions based on different proposals (\bar qq, \bar q\bar q qq, and gluonium) for the nature of scalar mesons. In the I=1 and 1/2 channels, the unusual (wrong) splitting between the a_0(980) and \kappa(900) and the a_0(980) width can be understood from QSSR within a \bar qq assignement. However, none of the \bar qq and \bar q\bar q qq results can explain the large \kappa width, which may suggest that it can result from a strong interference with non-resonant backgrounds. In the I=0 channel, QSSR and some low-energy theorems (LET) require the existence of a low mass gluonium \sigma_B(1 GeV) coupled strongly to Goldstone boson pairs which plays in the U(1)_V channel, a similar role than the \eta' for the value of the U(1)_A topological charge. The observed \sigma(600) and f_0(980) mesons result from a maximal mixing between the gluonium \sigma_B and \bar qq(1 GeV) mesons, a mixing scheme which passes several experimental tests. OZI violating J/\psi--> \phi\pi^+\pi^-, D_s--> 3\pi decays and J/\psi--> \gamma S glueball filter processes may indicate that most of the I=0 mesons above 1 GeV have important gluonium in their wave functions. We expect that the f_0(1500), f_0(1710) and f_0(1790) have significant gluonium component in their wave functions, while the f_0(1370) is mostly \bar qq. Tests of these results can be provided by the measurements of the pure gluonium \eta'\eta and 4\pi specific U(1)_A decay channels.Comment: Version to appear in Phys. Rev. D (one previous figure corrupted

Spontaneous breaking of chiral symmetry, and eventually of parity, in a σ\sigma-model with two Mexican hats

A sigma-model with two linked Mexican hats is discussed. This scenario could be realized in low-energy QCD when the ground state and the first excited (pseudo)scalar mesons are included, and where not only in the subspace of the ground states, but also in that of the first excited states, a Mexican hat potential is present. This possibility can change some basic features of a low-energy hadronic theory of QCD. It is also shown that spontaneous breaking of parity can occur in the vacuum for some parameter choice of the model.Comment: 10 pages, 1 figur