AMBIGUITIES IN CHIRAL-SYMMETRY BREAKING USING THE EFFECTIVE POTENTIAL APPROACH

Using a form of the effective potential for composite operators with a variational approach we show that it is possible to get different directions of the chiral phase transition in QCD. Which one occurs depends on the way the Schwinger-Dyson equation for the fermion self-energy is used in the 2-loop term of the effective potential. We must choose the 2-loop term which agrees with phenomenology in each form of the effective potential.

Infrared finite gluon propagator and the structure of chiral symmetry breaking

We study the chiral symmetry breaking in QCD, using an effective potential for composite operators, with infrared finite gluon propagators that have been found by numerical calculation of the Schwinger-Dyson equations as well as in lattice simulations. The existence of a gluon propagator that is finite at k2 = 0 modifies substantially the transition between the phases with and without chiral symmetry.

Compatibility of a model for the QCD-Pomeron and chiral-symmetry breaking phenomenologies

The phenomenology of a QCD-Pomeron model based on the exchange of a pair of non-perturbative gluons, i.e. gluon fields with a finite correlation length in the vacuum, is studied in comparison with the phenomenology of QCD chiral symmetry breaking, based on non-perturbative solutions of Schwinger-Dyson equations for the quark propagator including these non-perturbative gluon effects. We show that these models are incompatible, and point out some possibles origins of this problem.

Critical coupling for dynamical chiral-symmetry breaking with an infrared finite gluon propagator

We compute the critical coupling constant for the dynamical chiral-symmetry breaking in a model of quantum chromodynamics, solving numerically the quark self-energy using infrared finite gluon propagators found as solutions of the Schwinger-Dyson equation for the gluon, and one gluon propagator determined in numerical lattice simulations. The gluon mass scale screens the force responsible for the chiral breaking, and the transition occurs only for a larger critical coupling constant than the one obtained with the perturbative propagator. The critical coupling shows a great sensibility to the gluon mass scale variation, as well as to the functional form of the gluon propagator.

Probing SU(2) symmetry breaking in the nucleon sea

Investigation of invariant cross-sections for production of K*- and K*0, in the fragmentation region of the proton, in p - p and γ - p reactions, gives a direct and unambiguous probe to the symmetry breaking of the nucleon sea. Based on existing data, we clearly found a large asymmetry of the sea. Our result is in excellent agreement with NA51 measurement, signaling lack of any nuclear effect. The measurement can be carried out in a single experimental set up. The ratio K*-/K*0 is equivalent to ū/d̄, with easy access to the x-dependence of the asymmetry. The observed asymmetry from available experimental data is used to improve the valon-recombination model. © 1997 Elsevier Science B.V.

Triple gauge boson production and dynamical symmetry breaking at the Next Linear Collider

We study in a model independent way the role of a techniomega resonance in the process e+e-→ W+W-Z at the Next Linear Collider. © 1998 Elsevier Science B.V.

Critical coupling for chiral symmetry breaking in QCD motivated models

We determine the critical coupling constant above which dynamical chiral symmetry breaking occurs in a class of QCD motivated models where the gluon propagator has an enhanced infrared behavior. Using methods of bifurcation theory we find that the critical value of the coupling constant is always smaller than the one obtained for QCD. ©2000 The American Physical Society.

Variational studies and replica symmetry breaking in the generalization problem of the binary perceptron

We analyze the average performance of a general class of learning algorithms for the nondeterministic polynomial time complete problem of rule extraction by a binary perceptron. The examples are generated by a rule implemented by a teacher network of similar architecture. A variational approach is used in trying to identify the potential energy that leads to the largest generalization in the thermodynamic limit. We restrict our search to algorithms that always satisfy the binary constraints. A replica symmetric ansatz leads to a learning algorithm which presents a phase transition in violation of an information theoretical bound. Stability analysis shows that this is due to a failure of the replica symmetric ansatz and the first step of replica symmetry breaking (RSB) is studied. The variational method does not determine a unique potential but it allows construction of a class with a unique minimum within each first order valley. Members of this class improve on the performance of Gibbs algorithm but fail to reach the Bayesian limit in the low generalization phase. They even fail to reach the performance of the best binary, an optimal clipping of the barycenter of version space. We find a trade-off between a good low performance and early onset of perfect generalization. Although the RSB may be locally stable we discuss the possibility that it fails to be the correct saddle point globally. ©2000 The American Physical Society.

Comment on Time-reversal symmetry-breaking superconductivity

It is pointed out that erroneous Bardeen-Cooper-Schrieffer model equations have been used by Haranath Ghosh in his recent treatment of time-reversal symmetry-breaking superconductivity. Consequently, his numerical results are misleading, and his conclusions are not to the point.

double-struck D signn-forced symmetry breaking of double-struck O sign (2)-equivariant problems

We use singularity theory to classify forced symmetry-breaking bifurcation problems f(z, λ, μ) = f1 (z, λ) + μf2(z, λ, μ) = 0, where f1 is double-struck O sign (2)-equivariant and f2 is double-struck D sign n-equivariant with the orthogonal group actions on z ∈ ℝ2. Forced symmetry breaking occurs when the symmetry of the equation changes when parameters are varied. We explicitly apply our results to the branching of subharmonic solutions in a model periodic perturbation of an autonomous equation and sketch further applications.

Chiral symmetry breaking with a confining propagator and dynamically massive gluons

Chiral symmetry breaking in QCD is studied introducing a confining effective propagator, as proposed recently by Cornwall, and considering the effect of dynamically massive gluons. The effective confining propagator has the form 1/(k2 +m2)2 and we study the bifurcation equation finding limits on the parameter m below which a satisfactory fermion mass solution is generated. Since the coupling constant and gluon propagator are damped in the infrared, due to the presence of a dynamical gluon mass, the major part of the chiral breaking is only due to the confining propagator and related to the low momentum region of the gap equation. We study the asymptotic behavior of the gap equation containing this confinement effect and massive gluon exchange, and find that the symmetry breaking can be approximated by an effective four-fermion interaction generated by the confining propagator. We compute some QCD chiral parameters as a function of m, finding values compatible with the experimental data. We find a simple approximate relation between the fermion condensate and dynamical mass for a given representation as a function of the parameters appearing in the effective confining propagator. © Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

Quasi-homologous spherically symmetric branes and their symmetry breaking

We revisit the dynamical system-based approach of spherically symmetric vacuum braneworlds, pointing out and studying the existence of a transcritical bifurcation as the dark pressure parameter changes its sign, we analyze some consequences of not discard the brane cosmological constant. For instance, it is noteworthy that the existence of an isothermal state equation between the dark fluid parameters cannot be obtained via the requirement of a quasi-homologous symmetry of the vacuum. © 2013 Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica.

Dynamical chiral symmetry breaking: the fermionic gap equation with dynamical gluon mass and confinement

Pós-graduação em Física - IFT

Demixing and symmetry breaking in binary dipolar Bose-Einstein-condensate solitons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)