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.

Study of chiral symmetry restoration in linear and nonlinear O(N) models using the auxiliary field method

We consider the O(N) linear {\sigma} model and introduce an auxiliary field to eliminate the scalar self-interaction. Using a suitable limiting process this model can be continuously transformed into the nonlinear version of the O(N) model. We demonstrate that, up to two-loop order in the CJT formalism, the effective potential of the model with auxiliary field is identical to the one of the standard O(N) linear {\sigma} model, if the auxiliary field is eliminated using the stationary values for the corresponding one- and two-point functions. We numerically compute the chiral condensate and the {\sigma}- and {\pi}-meson masses at nonzero temperature in the one-loop approximation of the CJT formalism. The order of the chiral phase transition depends sensitively on the choice of the renormalization scheme. In the linear version of the model and for explicitly broken chiral symmetry, it turns from crossover to first order as the mass of the {\sigma} particle increases. In the nonlinear case, the order of the phase transition turns out to be of first order. In the region where the parameter space of the model allows for physical solutions, Goldstone's theorem is always fulfilled.Comment: 25 pages, 9 figures, 1 table, improved versio

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

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

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)$_A$ 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