K. Naito

Effective potential of the O(N) linear sigma-model at finite temperature

Abstract:We study the O(N) symmetric linear sigma-model at finite temperature as the low-energy effective models of quantum chromodynamics (QCD) using the Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators. It has so far been claimed that the Nambu-Goldstone theorem is not satisfied at finite temperature in this framework unless the large-N limit in the O(N) symmetry is taken. We show that this is not the case. The pion is always massless below the critical temperature, if one determines the propagator within the form such that the symmetry of the system is conserved, and defines the pion mass as the curvature of the effective potential. We use a regularization for the CJT effective potential in the Hartree approximation, which is analogous to the renormalization of auxiliary fields. A numerical study of the Schwinger-Dyson equation and the gap equation is carried out including the thermal and quantum loops. We point out a problem in the derivation of the sigma meson mass without quantum correction at finite temperature. A problem about the order of the phase transition in this approach is also discussed.

Dynamical chiral symmetry breaking in effective models of QCD in the Bethe-Salpeter approach

Dynamical breaking of chiral symmetry in effective models of QCD is studied. Introducing a cut-off function or a non-local interaction, the Noether current must be modified and thus the Ward-Takahashi identity and the PCAC relation are modified accordingly. We point out that the pion decay constant must be defined consistently with the Noether current so that the low-energy relations are satisfied. We define the proxy of the Noether current for general effective models, which is consistent with loop expansion of the Cornwall-Jackiw-Tomboulis effective action. A general formula for the pion decay constant in terms of the Bethe-Salpeter amplitude is derived. The effective Pagels-Stokar formula is proposed which is useful to estimate the decay constant without solving the Bethe-Salpeter equation.

Approximation of the Schwinger-Dyson and the Bethe-Salpeter equations and chiral symmetry of QCD

The Bethe--Salpeter equation for the pion in chiral symmetric models is studied with a special care to consistency with low-energy relations. We propose a reduction of the rainbow Schwinger--Dyson and the ladder Bethe--Salpeter equations with a dressed gluon propagator. We prove that the reduction preserves the Ward--Takahashi identity for the axial-vector current and the PCAC relation.

η and η′ mesons in the improved ladder Bethe–Salpeter approach

We study the properties of the η and η′ mesons using the improved ladder Schwinger-Dyson and Bethe-Salpeter equations in which the one gluon exchange kernel with the one-loop running coupling constant is used. The effect of the U A (1) anomaly is introduced by the U A (1) breaking 6-quark flavor-mixing interaction. The masses of η and η′ mesons are reproduced by a relatively weak flavor-mixing interaction, for which the chiral symmetry breaking is dominantly induced by the soft-gluon exchange interaction. The decay constants are calculated and the anomalous PCAC relation is numerically checked.

η and η′ mesons in the improved ladder Bethe-Salpeter approach

We study the properties of the η and η′ mesons using the improved ladder Schwinger-Dyson and Bethe-Salpeter equations in which the one gluon exchange kernel with the one-loop running coupling constant is used. The effect of the UA(1) anomaly is introduced by the UA(1) breaking 6-quark flavor-mixing interaction. The masses of η and η′ mesons are reproduced by a relatively weak flavor-mixing interaction, for which the chiral symmetry breaking is dominantly induced by the soft-gluon exchange interaction. The decay constants are calculated and the anomalous PCAC relation is numerically checked.

Finite quark mass effects in the improved ladder Bethe-Salpeter amplitudes

We study the finite quark mass effects of the low-energy QCD using the improved ladder Schwinger-Dyson and Bethe-Salpeter equations which are derived in the manner consistent with the vector and axial-vector Ward-Takahashi identities. The non-perturbative mass-independent renormalization allows us to calculate the quark condensate for a non-zero quark mass. We explicitly show that the PCAC relation holds. The key ingredients are the Cornwall-Jackiw-Tomboulis effective action, the generalized Noether current and the introduction of the regularization function to the Lagrangian. The reasonable values of the pion mass, the pion decay constant and the quark condensate are obtained with a rather large

Finite quark mass effect in the improved ladder approximation of QCD

\Lambda_{QCD}

Electromagnetic Energy Shift of Nucleus between Conducting Plates

. The pion mass square and the pion decay constant are almost proportional to the current quark mass up to the strange quark mass region. It suggests that the chiral perturbation is applicable up to the strange quark mass region. We study the validity of the approximation often used in solving the Bethe-Salpeter equations too.

Light scalar mesons in the improved ladder QCD

Abstract We study the finite quark mass effects of the low-energy QCD using the improved ladder Schwinger-Dyson and Bethe-Salpeter equations. We find that the first order chiral perturbation is good in rather wide range of the current quark mass for the low-lying pseudoscalar meson mass.

Non-perturbative Renormalization Group approach to The NJL model at Finite Density

Electromagnetic energy shifts of a single particle quantum state sandwiched between parallel conducting plates are studied. We find an energy shift of order 1/b 2 , with b the interval of the boundary plates. Applying the calculation to a polarized nucleus in a uniform magnetic field, we find significant energy shifts which depend on the magnetic quantum number. The relation of this effect and the enhancement factor in E1 photo nuclear reactions is discussed.