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.     

Phenomenology of dynamical symmetry breaking in QCD

A consistent treatment of the QCD quark propagator and quark-antiquark bound state equations is presented which follows the Nambu and Jona-Lasinio approach to the discussion of chiral symmetry breaking. An expression is obtained for the dynamical, momentum dependent, mass. In the approximation used here the dynamical mass is determined byM ₀, its value at zero momentum, and by the strong coupling constant α _s and bare quark massm ₀. In the limiting case of no explicit chiral symmetry breaking. i.e.,m ₀=0, this expression coincides in form with the one obtained by Chang and Chang in their renormalization-group analysis. In this limit chiral symmetry remains broken and we show the explicit appearance of a Nambu-Goldstone pion. A consistent calculation of the pseudoscalar, scalar and vector meson masses gives values ofm ₀, α _s andM ₀ well in step with other estimates. This makes possible a calculation off _π, the pion decay constant, in reasonable agreement with experiment.     

Chiral symmetry breaking parameters from QCD sum rules

We obtain new QCD sum rules by considering vacuum expectation values of two-point functions, taking all the five quark bilinears into account. These sum rules are employed to extract values of different chiral symmetry breaking parameters in QCD theory. We find masses of light quarks, $\text{m}\text{?}\text{=}\text{1}\text{2}\text{(m}{}_{\mathrm{<mtext>u</mtext>}}\text{+m}{}_{\mathrm{<mtext>d</mtext>}}\text{) = 8.4 ± 1.2}\text{MeV}\text{, m}{}_{\mathrm{<mtext>s</mtext>}}\text{= 205 ± 65}\text{MeV}$. Further, we obtain corrections to certain soft pion (kaon) PCAC relations and the violation of SU(3) flavour symmetry by the non-strange and strange quark-antiquark vacuum condensate.     

Chiral symmetry breaking condensates from baryonic sum rules

We analyse baryonic sum rules in order to determine chiral symmetry breaking condensates. We especially investigate the influence of the choice of the interpolating field and of the factorization hypothesis for the four quark condensate. Our results are consistent with those obtained from pseudoscalar sum rules and PCAC.     

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.     

Quantum and statistical fluctuations in dynamical symmetry breaking

Dynamical symmetry breaking in an expanding nuclear system is investigated in a semi-classical and quantum framework by employing a collective transport model which is constructed to mimic the collective behavior of expanding systems. It is shown that the fluctuations in collective coordinates during the expansion are developed mainly by the enhancement of the initial fluctuations by the driving force, and that statistical and quantum fluctuations have similar consequences. It is pointed out that the quantal fluctuations may play an important role in the development of instabilities by reducing the time needed to break the symmetry, and the possible role of quantal fluctuations in spinodal decomposition of nuclei is discussed.     

Solitons in models with dynamical spontaneous symmetry breaking

An approximate quasi-classical method for the investigation of solitons appearing at quantum level is described. The existence of the soliton in the model with Yukawa coupling in two-dimensional space-time is established with the help of this method. The existence of solitons in the Georgi-Glashow type model with dynamical spontaneous symmetry breaking is shown.     

Chiral bands, dynamical spontaneous symmetry breaking, and the selection rule for electromagnetic transitions in the chiral geometry

A model for a special configuration in triaxial odd-odd nuclei is constructed which exhibits degenerate chiral bands with a sizable rotation, a manifestation of dynamical spontaneous symmetry breaking. A quantum number obtained from the invariance of the model Hamiltonian, which characterizes observable states, is given and selection rules for electromagnetic transition probabilities in chiral bands is derived in terms of this quantum number. The degeneracy of the lowest two bands is indeed obtained in the numerical diagonalization of the Hamiltonian at an intermediate spin range, over which electromagnetic transitions follow exactly the selection rule expected for the chiral geometry.     

Horizontal symmetries,dynamical symmetry breaking and neutrino masses

We study experimental and theoretical constraints which can prevent the introduction of horizontal gauge ssymmetries. To allow for the possibility of dynamical symmetry breaking, we restrict the symmetry breaking interactions to have the quantum numbers of spin-zero bound states of the fermions in the theory. Under these circumstances we find that horizontal interactions, which do not violete any of the present bounds on flavor changing processes, are only allowed if the symmetry breakdown introduces a large Majorana mass for the neutrinos. Some phenomenological consequences of this result are discussed.     

Spontaneous dynamical breaking of gauge symmetry in dual models

The consequences of gauge invariance are re-examined in dual models with unit intercept when the dimension of space-time has the maximum value compatible with the absence of ghosts. In that case, reggeon-reggeon bound states of zero mass are formed already at second order of perturbation theory. Gauge invariance no longer guarantees that the initially massless SU(3) singlet vector meson remains massless, and the mixing between the reggeon and pomeron sectors of the model yields a massive unitary singlet vector meson already at order g². A Lagrangian model which exhibits similar features to the dual situation is discussed.     

Finite temperature vacuum excitations for a field theory with dynamical symmetry breaking

The renormalized finite-temperature σ-propagator for the Gross-Neveu model is constructed in the large -N limit. The singularity structure of this Green function is used to analyze the finite-temperature vacuum excitations. It is shown that, at a finite temperature below the critical one, a fermion-antifermion bound state is formed with a non-vanishing binding energy in contrast to the zero-temperature case, where the binding energy is known to vanish.     

Inflation and cosmic strings in models with dynamical symmetry breaking

We derive the effective action for the composite field which in dynamical symmetry breaking plays the role of the Higgs field. We show that this effective action does not give rise to inflation. It is, however, possible to obtain topological defects such as cosmic strings. There will be fermionic zero modes trapped on the strings, and the strings will therefore be superconducting in a generalized sense.