Viscosities in chiral symmetry breaking phase

In the chiral symmetry breaking phase described by the NJL model at quark level,along with the chiral symmetry restoration the ratio of shear viscosity to entropy density η/s drops down monotonously and reaches the minimum at the critical point,while the ratio of bulk viscosity to entropy density ζ/s behaves oppositely.     

On chiral symmetry breaking. II

We study the restrictions imposed on chiral symmetry breaking terms by a set of postulates, whose main content is furnished by certain ideas of Michel and Radicati. We then test certain particular cases by utilizing an effective Lagrangian and calculating meson-meson scattering lengths. A convenient technique for calculating traces of matrices which appear in our model is presented in an appendix.     

Magnetic rotation and chiral symmetry breaking

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.     

Massless QCD and chiral symmetry breaking

It is well known that chiral symmetry is spontaneously broken in QCD. To relate this fact to non-perturbative features of the theory, like instantons, we start with a massless lagrangian and perform a non-linear chiral colored singlet transformation on the quark fields which yields (by means of Fujikawa's method) essentially two terms in the lagrangian. First a quark mass term induced by instantons and secondly a coupling between pseudoscalar mesons and the axial anomaly. Ward-Takahashi identities can be derived. To clarify the presence of this induced mass term we calculate its first perturbative part up to the two-loop level.     

Viscosities in chiral symmetry breaking phase

In the chiral symmetry breaking phase described by the NJL model at quark level,along with the chiral symmetry restoration the ratio of shear viscosity to entropy density η/s drops down monotonously and reaches the minimum at the critical point,while the ratio of bulk viscosity to entropy density ζ/s behaves oppositely.     

Baryon sum rules and chiral symmetry breaking

In an SVZ-type approach sum rules for baryonic currents have been investigated, without radiative QCD corrections but with the inclusion of non-perturbative terms due to the non-vanishing vacuum expectation value of the quark-antiquark condensate. We give upper bounds for baryon masses, which allow a choice of optimal interpolating operators for low-lying baryon states. The results show that the mentioned vacuum expectation value not only sets the scale for parity splitting but also for the masses of the baryons directly. The alternative way of explicit symmetry breaking by quark masses has also been investigated in the same technical framework.     

Spontaneous breaking of chiral symmetry in QCD

The consistency of iso-spin (SU(3)) symmetry of the vacuum with the spontaneous breakdown of chiral symmetry without the appearance of a U(1) Goldstone boson, is investigated.     

Facets of confinement and dynamical chiral symmetry breaking

The gap equation is a cornerstone in understanding dynamical chiral symmetry breaking and may also provide clues to confinement. A symmetry-preserving truncation of its kernel enables proofs of important results and the development of an efficacious phenomenology. We describe a model of the kernel that yields: a momentum-dependent dressed-quark propagator in fair agreement with quenched lattice-QCD results; and chiral limit values, MeV and . It is compared with models inferred from studies of the gauge sector.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.Aw General properties of QCD (dynamics, confinement, etc.) - 11.30.Rd Chiral symmetries     

Supersymmetric quantum electrodynamics and dynamical chiral symmetry breaking

Spontaneous chiral symmetry breaking in supersymmetric quantum electrodynamics is studied by examining the self-consistent Schwinger-Dyson equations. The equations admit only the trivial solution indicating an absence of mass generation. This is consistent with a non-perturbative, non-renormalization theorem. We also address the case of an explicitly softly broken supersymmetry and find non-trivial solutions to the gap equation for sufficiently strong coupling.     

Pion phase transition in chiral symmetry breaking model

We show that in the non-linear σ-model, we have a phase transition when the isospin chemical potential is equal to the meson mass. This result is shown to be generally true in the SU(2)×SU(2) symmetry breaking model.     

Effective potentials in QCD and chiral symmetry breaking

We consider chiral symmetry breaking through nontrivial vacuum structure with an explicit construct for the vacuum with quark antiquark condensates in QCD with Coulomb gauge for different phenomenological potentials. The dimensional parameter for the condensate function gets related to \(\left\langle {\bar \psi \psi } \right\rangle \) of Shifman, Vainshtein and Zakharov. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode of vacuum. We then calculate different pionic properties using the wave function as obtained from the vacuum structure.     

A model for chiral symmetry breaking in QCD

A recently proposed model for dynamical breaking of chiral symmetry in QCD is extended and developed for the calculation of pion and chiral symmetry breaking parameters. The pion is explicitly realized as a massless Goldstone boson and as a bound state of the constituent quarks. We compute, in the limit of exact chiral symmetry, M_Q, the constituent quark mass $\text{?}{}_{\mathrm{\pi }}$ the pion decay coupling, $\text{〈}\text{u}\text{u〉}$, the constituent quark loop density, μ_π²/m_q, the ratio of the Goldstone boson mass squared to the bare quark mass, and 〈r²〉_π, the pion electromagnetic charge radius squared.