Mechanism Of Chiral Symmetry Breaking Research Articles

Historical Introduction to Chiral Quark Models

Chiral symmetry, and its dynamical breaking, has become a cornerstone in the description of the hadron’s phenomenology at low energy. The present manuscript gives a historical survey on how the quark model of hadrons has been implemented along the last decades trying to incorporate, among other important non-perturbative features of quantum chromodynamics (QCD), the dynamical chiral symmetry breaking mechanism. This effort has delivered different models such as the chiral bag model, the cloudy bag model, the chiral quark model or the chiral constituent quark model. Our main aim herein is to provide a brief introduction of the Special Issue “Advances in Chiral Quark Models” in Symmetry and contribute to the clarification of the differences among the above-mentioned models that include the adjective chiral in their nomenclature.

Deconfined, massive quark phase at high density and compact stars: A holographic study

In Hoyos et al. (arXiv:1603.02943) a holographic D3/D7 system was used to describe a deconfined yet massive quark phase of QCD at finite density, concluding that the equation of state of such a phase was not stiff enough to support exotic dense stars. That analysis used a hard quark mass to represent the dynamical mass and assumed a conformal gauge background. Here we phenomenologically adjust the D3/D7 system to include a running anomalous dimension for the quark condensate. This introduces a dynamical mechanism for chiral symmetry breaking yet the model still has a deconfined massive phase at intermediate densities. We show that these systems, dependent on the running profile in the deep IR, generate much stiffer equations of state and non-monotonic behaviour in the speed of sound. The results suggest that these equations of state may be closer to supporting hybrid stars with quark cores.

Finite temperature Landau gauge lattice quark propagator

The quark propagator at finite temperature is investigated using quenched gauge configurations. The propagator form factors are investigated for temperatures above and below the gluon deconfinement temperature T_c and for the various Matsubara frequencies. Significant differences between the functional behaviour below and above T_c are observed both for the quark wave function and the running quark mass. The results for the running quark mass indicate a link between gluon dynamics, the mechanism for chiral symmetry breaking and the deconfinement mechanism. For temperatures above T_c and for low momenta, our results support also a description of quarks as free quasiparticles.

Spin-Wave Chirality and Its Manifestations in Antiferromagnets.

As first demonstrated by Tang and Cohen in chiral optics, the asymmetry in the rate of electromagnetic energy absorption between left and right enantiomers is determined by an optical chirality density. Here, we demonstrate that this effect can exist in magnetic spin systems. By constructing a formal analogy with electrodynamics, we show that in antiferromagnets with broken chiral symmetry, the asymmetry in local spin-wave energy absorption is proportional to a spin-wave chirality density, which is a direct counterpart of optical zilch. We propose that injection of a pure spin current into an antiferromagnet may serve as a chiral symmetry breaking mechanism, since its effect in the spin-wave approximation can be expressed in terms of additional Lifshitz invariants. We use linear response theory to show that the spin current induces a nonequilibrium spin-wave chirality density.

The extreme walking behavior in a 331-TC model

It is quite possible that the Technicolor problems are related to the poorly known self-energy expression, or the way chiral symmetry breaking (CSB) is realized in non-abelian gauge theories. Actually, the only known laboratory to test the CSB mechanism is QCD. The TC dynamics may be quite different from the QCD , this fact has led to the walking TC proposal making the new strong interaction almost conformal and changing appreciably its dynamical behavior. There are different ways to obtain of extreme walking (or quasi-conformal) technicolor theories, in this paper we propose an scheme to obtain this behavior based on an extension of the electroweak sector of the standard model, in the context of so called 331-TC model.

QCD: Restoration of chiral symmetry and deconfinement for largeNf

Exploiting the recent lattice results for the infrared gluon propagator with light dynamical quarks, we solve the gap equation for the quark propagator. We thus model the chiral symmetry breaking mechanism with increasing number of flavours and study confinement (intimately tied with the analytic properties of QCD Schwinger functions) order parameters. We obtain, with this approach, clear signals of chiral symmetry restoration and deconfinement when the number of light quark flavors exceeds a critical value of $N_f^c \approx 8 \pm 1$, in agreement with the state-of-the-art direct lattice analysis of chiral symmetry restoration in QCD.

Dispersion theory of nucleon Compton scattering and polarizabilities

AbstractA status report on the topic nucleon Compton scattering and polarizabilities is presented with emphasis on the scalar t‐channel as entering into dispersion theory. Precise values for the polarizabilities are obtained leading to αp = 12.0 ± 0.6 (12.0), βp= 1.9∓ 0.6 (1.9), αn= 12.5 ± 1.7 (13.4), βn= 2.7 ∓ 1.8 (1.8) in units of 10−4 fm3 and γ(p)π= −36.4 ± 1.5 (−36.6), γ(n)π= 58.6 ± 4.0 (58.3), (γ(p)0 = −0.58 ± 0.20), (γ(n)0 = +0.38 ± 0.22) in units of 10−4 fm4, for the proton (p) and neutron (n), respectively. The data given with an error are recommended experimental values with updates compared to [1] where necessary, the data in parentheses are predicted values. These predicted values are not contained in [1], but are the result of a newly developed analysis which is the main topic of the present paper. The most important recent discovery is that the largest part of the electric polarizability and the total diamagnetic polarizability of the nucleon are properties of the σ meson as part of the constituent‐quark structure, as expected from the mechanism of chiral symmetry breaking. This view is supported by an experiment on Compton scattering by the proton carried out in the second resonance region, where a large contribution from the σ meson enters into the scattering amplitudes. This experiment led to a determination of the mass of the σ meson of mσ= 600± 70 MeV. From the experimental αp and predicted differences (αn‐αp) neutron polarizabilities in the range αn = 12.0 – 13.4 are predicted, where the uncertainties are related to the f0(980) and a0(980) scalar mesons.

Formation of chiral nanotubes by the novel anthraquinone containing-achiral molecule

Self-assembled lipid nanotubes arouse lots of interest due to their exceptional properties such as very simple production procedures, large variety of applications and high biocompatibility. In this study, the new eccentric but simple molecule, AQua (AQ-NH-(CH2)10COOH; where AQ is anthraquinone), which integrates redox-active and pH sensitive character with nanotube forming capability has been designed. AQua forms self-assembled nanotubes by the chiral symmetry-breaking mechanism, in a high yield in the presence of ethanolamine. The nanotubes obtained in AQua-ethanolamine mixture are stable with time and resistant against drying and dilution at constant pH. However, pH change with dilution (without pH control) causes the unfolding of the nanotubes indicating the pH sensitive character. Existence of redox active anthraquinone group along with the carboxylic acid moiety gives the probability of reversibly controllable character to our nanotubes. The effect of the base type which is used to adjust the pH of the dispersion has also been investigated, and helix–tube–ribbon mixture is obtained when NaOH is used instead of ethanolamine. Although there are limited number of studies particularly in the field of reversibly controllable and/or redox active lipid nanotubes, controlled self-assembly and disassembly of these appreciable aggregates are very important for their usage in special applications. Thus, this study is hoped to be one of the remarkable studies for the development of reversibly controllable, redox active self assembled nanotubes.

Crystal Chirality Selected by Mutual Antagonism

To explore the mechanism of chiral symmetry breaking in a process of crystal growth under grinding, we propose a simple irreversible growth model of a lattice-gas with four possible states on a site: occupied by an achiral molecule A, or by a chiral enantiomer R or S, or empty. After two A molecules on neighboring sites form a chiral dimer R 2 or S 2 , clusters grow by incorporating A's at cluster periphery, irreversibly. Only the grinding recycles products R or S back to A. It is then demonstrated in kinetic Monte Carlo (KMC) simulations that chirality selection takes place in the presence of the grinding. The cause for this realization is attributed to mutual antagonistic inhibition: that is, clusters of opposite enantiomeric types are brought into contact through stirring, and they block crystallization sites on cluster peripheries each other. The density evolution obtained by time integration of the rate equations with this antagonistic inhibition fits well with results of KMC simulations.

The origin of mass and experiments on future high-energy accelerators

The observable world is the one consisting of nucleons and electrons. The mass of the nucleon arises from chiral symmetry breaking in quantum chromodynamics (QCD), so that high-energy accelerator experiments cannot give any clues to the nature of the mass of matter in the observable world. The origin of the mass of matter will be clarified when the mechanism of chiral symmetry breaking in QCD will be established.

A quantum gravitational relaxation of the cosmological constant

Similar to QCD, general relativity has a Θ sector due to large diffeomorphisms. We make explicit, for the first time, that the gravitational CP violating Θ parameter is nonperturbatively related to the cosmological constant. A gravitational pseudoscalar coupling to massive fermions gives rise to general relativity from a topological B∧F theory through a chiral symmetry breaking mechanism. We show that a gravitational Peccei–Quinn like mechanism can dynamically relax the cosmological constant.

Zero Modes of the Dirac Operator in Vortex-Type Gauge Fields

We consider the D4 Euclidean Dirac equation in a SU(2) gauge field with the form of intersecting central vortices and obtain its solutions corresponding to normalizable zero modes. In the context of the problem of constructing the mechanism of chiral symmetry breaking based on the model with randomly distributed central vortices, we study a possibility for splitting fermionic zero modes in the case of a superposition of many vortices with Pontryagin indices of different signs.

Effective potential, the structure of fermion vacuum, and the mechanism of chiral symmetry breaking in QED3

Effective potential, the structure of fermion vacuum, and the mechanism of chiral symmetry breaking in QED3

Structure of Chiral Phase Transitions at Finite Temperature in Abelian Gauge Theories

The mechanism of chiral symmetry breaking is investigated in strong-coupling Abelian gauge theories at finite temperature. The Schwinger-Dyson equation in the Landau gauge is employed in the real time formalism and is solved numerically within the framework of the instantaneous exchange approximation, including the effect of the thermal mass for the photon propagator. It is found that the chiral symmetry is broken below the critical temperature T for sufficiently large coupling α. The chiral phase transition is found to be of second order, and the phase diagram in the T-α plane is obtained. It is investigated how the structure of the chiral phase transition is affected by the thermal mass in the photon propagator.

QCD-based analysis of the weak kaon decays

Starting directly from the QCD Lagrangian, effective actions describing weak K-meson decays in different channels have been constructed. To construct effective Lagrangians a bilocal bosonization method, which incorporates the chiral symmetry-breaking mechanism, has been used. The decay rates of K mesons calculated with the derived weak Lagrangians essentially depend on the ``dressing'' mechanism of quarks. This mechanism is generated by the gluonic forces mediated by the two-point gluonic propagators. A reasonable agreement with experiment of calculated decay rates of charged K mesons in leptonic, semileptonic, and the two-pion decay channels has been achieved. The employed parametrization of quark propagators simultaneously gives a correct description of the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ dynamics.

Pattern formation and chiral phase separation by compression: Racemic monolayer viewed as Bragg-Williams binary cholesterics

In nature, it is so abundant that the two molecular enantiomers of left- and right-handed chirality usually combine to form a racemic dimer. The means of separation of the dimers into distinct phases of optical activity, the chiral phase separation ~CPS!, are of critical importance in physics, chemistry, biology, and geology @1#, and have been realized through experiments going back to Pasteur in 1848 in isolation of enantiomers of sodium tartrate by crystallization @2#, and to Jungfleish in 1882 in the localization of crystallization of individual enantiomers on suitably disposed seeds @3#. However, the major challenge in the study is, on the theoretical side, to understand the mechanism of chiral symmetry breaking ~CSB! in CPS. The study of CPS in the threedimensional ~3D! state is especially difficult because both left- and right-handed chiral molecules have been classically regarded as exact mirror images and, therefore, are energetically equivalent in bulk due to the molecular rotation. It is natural to think that this difficulty may be reduced in a monolayer of racemic amphiphiles at the air/water interface, because the molecular rotation of the amphiphiles is limited due to the hydrophobic interaction between the amphiphiles and the water. In fact, a remarkable progress of the study in a 2D system was performed by Lundquist in the 1960s @4#. Recognizing the importance of steric factors in the living system, such as in the architecture of the lipoprotein membranes of cells, Lundquist found that at a temperature below 20 °C the racemic monolayer of the methyl ester of 2-methylhexacosanoic acid shows a pressure plateau in each pressure-area isotherm. This was interpreted as a 2D phase transition region, from the expanded phase to the condensed 2D crystalline phase. At that time, however, there were no methods available for the direct crystallographic study for the crystalline phase. In 1993, a significant advance was made by Eckhardt et al. @5#. By transferring such a monolayer of surface pressure from a water surface onto mica, and using atomic-force microscopy, they detected that the phase transition at the region of small molecular areas is a CPS transition, specifically a transition from rectangular lattices of a molecular packing structure ~racemic phase! into a chiral phase in which the enantiomers form two antipodal oblique lattices distinguished by some stripes ~see Figs. 1‐4 in @5#!. In physics, the CSB and stripe formation have been extensively studied in hexatic liquid-crystal ~LC! films @6#,

QCD with large number of quarks: effects of the instanton – anti-instanton pairs

We calculate the contribution of instanton – anti-instanton ( I I ̄ ) pairs to the vacuum energy of QCD-like theories with N f light fermions, using the saddle point method. A qualitative change of behavior is found around N f =6. We discuss the relation of this phenomenon to the mechanism of chiral symmetry breaking and the asymptotic of the perturbative series associated with I I ̄ contributions.

Hadron masses in qQCD with Wilson fermions near the chiral limit

In quenched lattice QCD with standard Wilson fermions the quark propagator is computed very close to the chiral limit in the zero-temperature case. Starting from our experience with lattice QED we employ a modified statistical method in order to estimate reliably hadron masses. We discuss the implications for the mechanism of chiral symmetry breaking.

Soliton formation inσmodels

In the past, considerable attention has been devoted to various s models @1# in order to get a better understanding of the mechanism of chiral symmetry breaking in QCD. More recently, the Nambu‐Jona-Lasinio ~NJL! model @2# has gained prominence in this respect. The linear s model is generally applied to valence quarks in order to describe the properties of low-lying states of the baryonic sector @3,4# .O n the other hand, the NJL model is usually used to describe mesons that are seen as quark-antiquark ( qq ¯ ) excitations of the chirally deformed vacuum @5,6#. Although widely studied in the literature, a deeper understanding of the s model is lacking and this is the first motivation of our paper. The linear s model with quarks is often regarded as an approximation to the NJL model. The connection between both models has been discussed in the literature using the technique of path integration over collective fields @7# .W e discuss the connection between both models on the basis of Hartree-Fock techniques. This framework, which is familiar to the nuclear physics community, provides in a very intuitive way the connection between the ‘‘Mexican hat’’ and the polarization of the Dirac sea of quarks. We try to establish the missing link between the linear s model with ‘‘Mexican

Foundations of the constitutent quark model

‘Constituent quarks’ means massive quarks, in contrast to the nearly massless u, d, s quarks of the QCD lagrangian. The dynamical or constituent masses appear owing to the spontaneous chiral symmetry breaking in QCD. A realistic mechanism of the chiral symmetry breaking is provided by instantons. Therefore, I review the present status of the QCD instanton vacuum, emphasizing the mechanism of chiral symmetry breaking and of the generation of the constituent quark mass. I end up with the Nambu-Jona-Lasinio-type effective theory to which QCD is reduced at low momenta.