Dynamical 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.

Influence of a Chern-Simons term in the dynamical fermion masses in reduced or pseudo QED

Mixed-dimensional theories have been used to describe condensed matter systems where fermions are constrained to a plane while the gauge fields they interact with remain four dimensional. Here we investigate dynamical breaking of chiral symmetry in the framework of a mixed-dimensional theory that has been successful in describing graphene and other planar Dirac materials and has been dubbed pseudo or reduced quantum electrodynamics. We explore the interplay between the gauge and fermion sectors when a Chern-Simons term is considered and, by exploring the tensor structure of the fermion self-energy, we show that the radiative corrections may induce both a Dirac and a Haldane mass term. Furthermore, by solving the corresponding Schwinger-Dyson equation in a suitable truncation, we nonperturbatively explore the dynamical generation of fermion masses for different values of the electromagnetic coupling and the Chern-Simons coefficient. We also show that for definite parameter values, the contributions from each chirality cancel out and the chiral symmetry may be restored. Possible implications of this result for physical systems, in particular on what concerns the chiral magnetic effect, are discussed.

Toward a unified equation of state for multi-messenger astronomy

Aims. We aim to present a first step in developing a benchmark equation-of-state (EoS) model for multi-messenger astronomy that unifies the thermodynamics of quark and hadronic degrees of freedom. Methods. A Lagrangian approach to the thermodynamic potential of quark-meson-nucleon matter was used. In this approach, dynamical chiral-symmetry breaking is described by the scalar mean-field dynamics coupled to quarks and nucleons and their chiral partners, whereby its restoration occurs in the hadronic phase by parity doubling, as well as in the quark phase. Quark confinement was achieved by an auxiliary scalar field that parametrizes a dynamical infrared cut-off in the quark sector, serving as an ultraviolet cut-off for the nucleonic phase space. The gap equations were solved for the isospin-symmetric case, as well as for neutron star (NS) conditions. We also calculated the mass-radius (MR) relation of NSs and their tidal deformability (TD) parameter. Results. The obtained EoS is in accordance with nuclear matter properties at saturation density and with the flow constraint from heavy ion collision experiments. For isospin-asymmetric matter, a sequential occurrence of light quark flavors is obtained, allowing for a mixed phase of chirally-symmetric nucleonic matter with deconfined down quarks. The MR relations and TDs for compact stars fulfill the constraints from the latest astrophysical observations for PSR J0740+6620, PSR J0030+0451, and the NS merger GW170817, whereby the tension between the maximum mass and compactness constraints rather uniquely fixes the model parameters. The model predicts the existence of stars with a core of chirally restored but purely hadronic (confined) matter for masses beyond 1.8 M⊙. Stars with pure-quark matter cores are found to be unstable against the gravitational collapse. This instability is shifted to even higher densities if repulsive interactions between quarks are included.

Bulk viscosity for interacting strange quark matter and r-mode instability windows for strange stars * *Supported by National Natural Science Foundation of China (12005005, 11947098, 11705163, 11875052, No. 11575190) and key research projects of universities in Henan province (20A140003)

We investigate the bulk viscosity of strange quark matter in the framework of the equivparticle model, where analytical formulae are obtained for certain temperature ranges, which can be readily applied to those with various quark mass scalings. In the case of adopting a quark mass scaling with both linear confinement and perturbative interactions, the obtained bulk viscosity increases by orders of magnitude compared with those in bag model scenarios. Such an enhancement is mainly due to the large quark equivalent masses adopted in the equivparticle model, which are essentially attributed to the strong interquark interactions and are related to the dynamical chiral symmetry breaking. Due to the high bulk viscosity, the predicted damping time of oscillations for a canonical 1.4 strange star is less than one millisecond, which is shorter than previous findings. Consequently, the obtained -mode instability window for the canonical strange stars well accommodates the observational frequencies and temperatures for pulsars in low-mass X-ray binaries (LMXBs).

Heavy dark matter, neutrino masses, and Higgs naturalness from a strongly interacting hidden sector

We consider the extension of the Standard Model (SM) with a strongly interacting QCD-like hidden sector, at least two generations of right-handed neutrinos and one scalar singlet. Once scalar singlet obtains a nonzero vacuum expectation value, active neutrino masses are generated through type-I seesaw mechanism. Simultaneously, the electroweak scale is generated through the radiative corrections involving these massive fermions. This is the essence of the scenario that is known as the "neutrino option" for which the successful masses of right-handed neutrinos are in the range $10^7-10^8$ GeV. The main goal of this work is to scrutinize the potential to accommodate dark matter in such a realization. The dark matter candidates are Nambu-Goldstone bosons which appear due to the dynamical breaking of the hidden chiral symmetry. The mass spectrum studied in this work is such that masses of Nambu-Goldstone bosons and singlet scalar exceed those of right-handed neutrinos. Having the masses of all relevant particles several orders of magnitude above $\mathcal{O}$(TeV), the freeze-out of dark matter is not achievable and hence we turn to alternative scenarios, namely freeze-in. The Nambu-Goldstone bosons can interact with particles that are not in SM but, however, have non-negligible abundance through their not-too-small couplings with SM. Utilizing this, we demonstrate that the dark matter in the model is successfully produced at temperature scale where the right-handed neutrinos are still stable. We note that the lepton number asymmetry sufficient for the generation of observable baryon asymmetry of the Universe can be produced in right-handed neutrino decays. Hence, we infer that the model has the potential to simultaneously address several of the most relevant puzzles in contemporary high-energy physics.

Chiral symmetry breaking out of the effective locality property of QCD

A few years ago the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of QCD, and called effective locality. This feature of QCD is non-perturbative. It results from a full gauge-fixing independent integration of the gluonic degrees of freedom and avoids the long standing Gribov copy problem. In this paper, at eikonal and quenching approximation at least, it is shown that effective locality involves a dynamical chiral symmetry breaking effect

Differential Dyson\u2013Schwinger equations for quantum chromodynamics

Using a technique devised by Bender, Milton and Savage, we derive the Dyson–Schwinger equations for quantum chromodynamics in differential form. We stop our analysis to the two-point functions. The ’t Hooft limit of color number going to infinity is derived showing how these equations can be cast into a treatable even if approximate form. It is seen how this limit gives a sound description of the low-energy behavior of quantum chromodynamics by discussing the dynamical breaking of chiral symmetry and confinement, providing a condition for the latter. This approach exploits a background field technique in quantum field theory.

Gauge technique approximation to the πγ production and the pion transition form factor

The pion transition form factor $G(q^2)$ is computed on the entire domain of spacelike and timelike momenta using a quantum field theory continuum approach. In analytical continuation of the function $G(Q^2)$ we utilized the Gauge Technique with the quark propagator determined from Minkowski space solution of QCD Dyson-Schwinger equations. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD.

The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space

The hadronic vacuum polarization function $\Pi_h$ for two light flavors is computed on the entire domain of spacelike and timelike momenta using a framework of Dyson-Schwinger equations. The analytical continuation of the function $\Pi_h$ is based on the utilization of the Gauge Technique with the entry of QCD Green's functions determined from generalized quark spectral functions. For the first time, the light quark spectral functions are extracted from the solution of the gap equation for the quark propagator. The scale is set up by the phenomena of dynamical chiral symmetry breaking, which is a striking feature of low energy QCD.

Chiral transition and the chiral charge density of the hot and dense QCD matter.

We study the chirally imbalanced hot and dense strongly interacting matter by means of the Dyson-Schwinger equations (DSEs). The chiral phase diagram is studied in the presence of chiral chemical potential μ5. The chiral quark condensate leftlangle overline{psi}psi rightrangle is obtained with the Cornwall-Jackiw-Tomboulis (CJT) effective action in concert with the Rainbow truncation. Catalysis effect of dynamical chiral symmetry breaking (DCSB) by μ5 is observed. We examine with two popular gluon models and consistency is found within the DSE approach, as well as in comparison with lattice QCD. The critical end point (CEP) location (μE, TE ) shifts toward larger TE but constant μE as μ5 increases. A technique is then introduced to compute the chiral charge density n5 from the fully dressed quark propagator. We find the n5 generally increases with temperature T , quark number chemical potential μ and μ5. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on n5 and find an increase in n5 with smaller system size.

Critical Behavior of (2 + 1)-Dimensional QED: 1/N Expansion

We present recent results on dynamical chiral symmetry breaking in (2 + 1)-dimensional QED with N four-component fermions. The results of the 1 / N expansion in the leading and next-to-leading orders were found exactly in an arbitrary nonlocal gauge.

Impact of dynamical chiral symmetry breaking and dynamical diquark correlations on proton generalized parton distributions

We calculate the leading-twist, helicity-independent generalized parton distributions (GPDs) of the proton, at finite skewness, in the Nambu--Jona-Lasinio (NJL) model of quantum chomodynamics (QCD). The NJL model reproduces low-energy characteristics of QCD, including dynamical chiral symmetry breaking (DCSB). The proton bound-state amplitude is solved for using the Faddeev equation in a quark-diquark approximation, including both dynamical scalar and axial vector diquarks. GPDs are calculated using a dressed non-local correlator, consistent with DCSB, which is obtained by solving a Bethe-Salpeter equation. The model and approximations used observe Lorentz covariance, and as a consequence the GPDs obey polynomiality sum rules. Extractions of electromagnetic and gravitational form factors are performed. We find a D-term of $-1.08$ when the non-local correlator is properly dressed, and $0.85$ when the bare correlator is used instead, suggesting that within this framework proton stability requires the constituent quarks to be dressed consistently with DCSB. We also find that the anomalous gravitomagnetic vanishes, as required by Poincar\'{e} symmetry.

Symmetry, symmetry breaking, and pion parton distributions

Pion valence, glue and sea distributions are calculated using a continuum approach to the two valence-body bound-state problem. Since the framework is symmetry preserving, physical features of the distributions are properly expressed. The analysis reveals that the emergent phenomenon of dynamical chiral symmetry breaking causes a hardening of the valence-quark distribution function, ${q}^\pi(x)$. Nevertheless, this distribution exhibits the $x\simeq 1$ behaviour predicted by quantum chromodynamics (QCD). At the scale $\zeta_2:=2\,$GeV, the following momentum fractions are predicted: $\langle x_{\rm valence} \rangle = 0.48(3)$, $\langle x_{\rm glue} \rangle = 0.41(2)$, $\langle x_{\rm sea} \rangle = 0.11(2)$. Evolving to $\zeta=5.2\,$GeV, the result for ${q}^\pi(x)$ agrees with that computed using lattice QCD. These outcomes should both spur improved analyses of existing experiments and stimulate efforts to obtain new data on the pion distribution functions using available and envisioned facilities.

Drawing insights from pion parton distributions * * Supported by the Chinese Government's Thousand Talents Plan for Young Professionals; Jiangsu Province Hundred Talents Plan for Professionals; and Forschungszentrum Jülich GmbH

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, electromagnetic pion elastic and transition form factors. The analysis reveals the following momentum fractions at the scale , , ; and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function, , exhibits the behaviour predicted by quantum chromodynamics (QCD). After evolution to , the prediction for matches that obtained using lattice-regularised QCD. This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.

Finite volume effects on chiral phase transition and pseudoscalar mesons properties from the Polyakov-Nambu-Jona-Lasinio model

Within the framework of Polyakov-Nambu-Jona-Lasinio model and by means of Multiple Reflection Expansion, we study the finite volume effects on chiral phase transition, especially its influence on the location of the possible critical end point (CEP) and masses of mesons. Our result shows that as the radius of the sphere decreases, the location of CEP shifts toward smaller temperature while remains almost a constant in chemical potential. As for the finite volume effects on the masses of mesons, the masses of π and K increase with decreasing volume, while for σ, η and η′ the situation is the opposite. Especially, the masses of chiral parters π and σ get closer as the volume decreases, indicating that the dynamical chiral symmetry breaking effect reduces with decreasing volume.

Effective locality and chiral symmetry breaking in QCD

A few years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of QCD, and called effective locality. This feature of QCD is non-perturbative as it results from a full integration of the gluonic degrees of freedom. In this paper, at eikonal and quenching approximation at least, the relation of effective locality to dynamical chiral symmetry breaking is examined.

Improving Center Vortex Detection by Usage of Center Regions as Guidance for the Direct Maximal Center Gauge

The center vortex model of quantum chromodynamic states that vortices, a closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using nontrivial center regions—that is, regions whose boundary evaluates to a nontrivial center element—a resolution of this issue seems possible. We use such nontrivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

Chiral vortices and pseudoscalar condensation due to rotation

We investigate the influence of rotation on the dynamical chiral symmetry breaking in strongly interacting matter. We develop a self-consistent Bogoliubov-de Gennes-like theoretical framework to study the inhomogeneous chiral condensate and the possible chiral vortex state in rotating finite-size matter in four-fermion interacting theories. We show that for sufficiently rapid rotation in $2+1$ dimensions, the ground state can be a chiral vortex state, a type of topological defect in analogy to superfluids and superconductors. The vortex state exhibits pion condensation, providing a new mechanism to realize pseudoscalar condensation in strongly interacting matter.

Strange Stars in the Vector Interaction Enhanced Bag Model

The vector interaction enhanced Bag model (vBag) for dense quark matter extends the commonly used thermodynamic Bag model (tdBag) by incorporating effects of dynamical chiral symmetry breaking (D χ SB) and vector repulsion. Motivated by the suggestion that the stability of strange matter is in tension with chiral symmetry breaking (D χ SB) we examine the parameter space for its stability in the vBag model in this work. Assuming the chiral transition occurs at sufficiently low density, we determine the stability region of strange matter as a function of the effective Bag constant and the vector coupling. As an astrophysical application, we construct contours of maximum mass M max and radius at maximum mass R max in this region of parameter space. We also study the stability of strange stars in the vBag model with maximum mass in the 2 M ⊙ range by computing the spectrum of radial oscillations, and comparing to results from the tdBag model, find some notable differences.

Temperature Dependence of the Axion Mass in a Scenario Where the Restoration of Chiral Symmetry Drives the Restoration of the UA(1) Symmetry

The temperature (T) dependence of the axion mass is predicted for T ′ s up to ∼ 2 . 3 × the chiral restoration temperature of QCD. The axion is related to the U A ( 1 ) anomaly. The squared axion mass m a ( T ) 2 is, modulo the presently undetermined scale of spontaneous breaking of Peccei–Quinn symmetry f a (squared), equal to QCD topological susceptibility χ ( T ) for all T. We obtain χ ( T ) by using quark condensates calculated in two effective Dyson–Schwinger models of nonperturbative QCD. They exhibit the correct chiral behavior, including the dynamical breaking of chiral symmetry and its restoration at high T. This is reflected in the U A ( 1 ) symmetry breaking and restoration through χ ( T ) . In our previous studies, such χ ( T ) yields the T-dependence of the U A ( 1 ) -anomaly-influenced masses of η ′ and η mesons consistent with experiment. This in turn supports our prediction for the T-dependence of the axion mass. Another support is a rather good agreement with the pertinent lattice results. This agreement is not spoiled by our varying u and d quark mass parameters out of the isospin limit.