Dynamical Fermion Mass Generation Research Articles

Fermionic fixed-point structure of asymptotically safe QED with a Pauli term

We test the physical viability of a recent proposal for an asymptotically safe modification of quantum electrodynamics (QED), whose ultraviolet physics is dominated by a non-perturbative Pauli spin-field coupling. We focus in particular on its compatibility with the absence of dynamical generation of fermion mass in QED. Studying the renormalization group flow of chiral four-fermion operators and their fixed points, we discover a distinct class of behavior compared to the standard picture of fixed-point annihilation at large gauge couplings and the ensuing formation of chiral condensates. Instead, transcritical bifurcations, where the fixed points merely exchange infrared stability, are observed. Provided that non-chiral operators remain irrelevant, our theory accommodates a universality class of light fermions for Nf>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{\ extrm{f}}> 1$$\\end{document} irreducible Dirac flavors. On the contrary, in the special case of Nf=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{\ extrm{f}}= 1$$\\end{document} flavor, this comes only at the expense of introducing one additional relevant parameter.

Thermodynamic properties of non-Hermitian Nambu–Jona-Lasinio models

We investigate the impact of non-Hermiticity on the thermodynamic properties of interacting fermions by examining bilinear extensions to the $3+1$ dimensional $SU(2)$-symmetric Nambu--Jona-Lasinio (NJL) model of quantum chromodynamics at finite temperature and chemical potential. The system is modified through the anti-$PT$-symmetric pseudoscalar bilinear $\bar{\psi}\gamma_5 \psi$ and the $PT$-symmetric pseudovector bilinear $iB_\nu \,\bar{\psi}\gamma_5\gamma^\nu \psi$, introduced with a coupling $g$. Beyond the possibility of dynamical fermion mass generation at finite temperature and chemical potential, our findings establish model-dependent changes in the position of the chiral phase transition and the critical end-point. These are tunable with respect to $g$ in the former case, and both $g$ and $|B|/B_0$ in the latter case, for both lightlike and spacelike fields. Moreover, the behavior of the quark number, entropy, pressure, and energy densities signal a potential fermion or antifermion excess compared to the standard NJL model, due to the pseudoscalar and pseudovector extension respectively. In both cases regions with negative interaction measure $I = \epsilon-3p$ are found. Future indications of such behaviors in strongly interacting fermion systems, for example in the context of neutron star physics, may point toward the presence of non-Hermitian contributions. These trends provide a first indication of curious potential mechanisms for producing non-Hermitian baryon asymmetry. In addition, the formalism described in this study is expected to apply more generally to other Hamiltonians with four-fermion interactions and thus the effects of the non-Hermitian bilinears are likely to be generic.

Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation

We consider reduced quantum electrodynamics ( {mathrm{RQED}}_{d_{gamma },{d}_e} ) a model describing fermions in a de-dimensional space-time and interacting via the exchange of massless bosons in dγ-dimensions (de ≤ dγ). We compute the two-loop mass anomalous dimension, γm, in general {mathrm{RQED}}_{4,{d}_e} with applications to RQED4,3 and QED4. We then proceed on studying dynamical (parity-even) fermion mass generation in {mathrm{RQED}}_{4,{d}_e} by constructing a fully gauge-invariant gap equation for {mathrm{RQED}}_{4,{d}_e} with γm as the only input. This equation allows for a straightforward analytic computation of the gauge-invariant critical coupling constant, αc, which is such that a dynamical mass is generated for αr> αc, where αr is the renormalized coupling constant, as well as the gauge-invariant critical number of fermion flavours, Nc, which is such that αc → ∞ and a dynamical mass is generated for N < Nc. For RQED4,3, our results are in perfect agreement with the more elaborate analysis based on the resolution of truncated Schwinger-Dyson equations at two-loop order. In the case of QED4, our analytical results (that use state of the art five-loop expression for γm) are in good quantitative agreement with those obtained from numerical approaches.

Fermion and meson mass generation in non-Hermitian Nambu–Jona-Lasinio models

We investigate the effects of non-Hermiticity on interacting fermionic systems. We do this by including non-Hermitian bilinear terms into the 3+1 dimensional Nambu--Jona-Lasinio (NJL) model. Two possible bilinear modifications give rise to $\mathcal{PT}$ symmetric theories; this happens when the standard NJL model is extended either by a pseudovector background field $ig \bar\psi\gamma_5 B_\mu \gamma^\mu \psi$ or by an antisymmetric-tensor background field $g \bar\psi F_{\mu\nu}\gamma^\mu \gamma^\nu \psi$. The three remaining bilinears are {\it anti}-$\mathcal{PT}$-symmetric in nature, $ig \bar\psi B_\mu \gamma^\mu \psi, ig\bar\psi \gamma_5 \psi$ and $ig\bar\psi {1}\psi$, so that the Hamiltonian then has no overall symmetry. The pseudovector $ig \bar\psi\gamma_5 B_\mu \gamma^\mu \psi$ and the vector $ig \bar\psi B_\mu \gamma^\mu \psi$ combinations, are, in addition, chirally symmetric. Thus, within this framework we are able to examine the effects that the various combinations of non-Hermiticity, $\mathcal{PT}$ symmetry, chiral symmetry and the two-body interactions of the NJL model have on the existence and dynamical generation of a real effective fermion mass (a feature which is absent in the corresponding modified massless free Dirac models) as well as on the masses of the composite particles, the pseudoscalar and scalar mesonic modes ($\pi$ and $\sigma$ mesons). Our findings demonstrate that $\mathcal{PT}$ symmetry is not necessary for real fermion mass solutions to exist, rather the two-body interactions of the NJL model supersede the non-Hermitian bilinear effects. The effects of chiral symmetry are evident most clearly in the meson modes, the pseudoscalar of which will always be Goldstone in nature if the system is chirally symmetric. Second solutions of the mesonic equations are also discussed.

Dynamical Majorana neutrino masses and axions II: Inclusion of anomaly terms and axial background

We extend the study of a previous publication [1] on Schwinger-Dyson dynamical mass generation for fermions and pseudoscalar fields (axion-like particles (ALP)), in field theories containing Yukawa type interactions between the fermions and ALPs, by incorporating anomaly terms and/or (constant) axial background fields. The latter are linked to some Lorentz-(and CPT-)violating scenarios for leptogenesis in the early Universe. We discuss both Hermitian and non-Hermitian Yukawa interactions and axial backgrounds, which are motivated in the context of some scenarios for radiative (anomalous) Majorana sterile neutrino masses in some effective field theories, including attractive four-fermion interactions. The reality requirement for the radiative, anomalously generated, mass component for the fermions, restricts our considerations to the cases where Yukawa interactions and the anomaly terms are either both Hermitian or both anti-Hermitian. We show that, for a Hermitian Yukawa interaction, there is no (pseudo)scalar dynamical mass generation, but there is fermion dynamical mass generation, provided one adds a bare (pseudo)scalar mass. For this case, the Hermitian anomaly terms play a similar rôle in inducing dynamical mass generation for fermions as the four-fermion attractive interactions, and as such they can themselves generate a small dynamical mass. For anti-Hermitian Yukawa interactions, an anti-Hermitian anomaly resists mass generation. The axial background terms assist dynamical mass generation induced by anti-Hermitian Yukawa interactions, in the sense that the larger the magnitude of the background, the larger the dynamical mass. For Hermitian Yukawa interactions, however, the situation is the opposite, in the sense that the larger the background the smaller the dynamical mass. We also compare the anomaly-induced dynamical mass with the radiative fermion mass in models of sterile neutrinos, and find that in cases where the dynamical mass occurs, the latter dominates over the anomalously generated radiative sterile-neutrino mass.

Dynamical Majorana neutrino masses and axions I

We discuss dynamical mass generation for fermions and (string-inspired) pseudoscalar fields (axion-like particles (ALP)), in the context of effective theories containing Yukawa type interactions between the fermions and ALPs. We discuss both Hermitian and non-Hermitian Yukawa interactions, which are motivated in the context of some scenarios for radiative (anomalous) Majorana sterile neutrino masses in some effective field theories. The latter contain shift-symmetry breaking Yukawa interactions between sterile neutrinos and ALPs. Our models serve as prototypes for discussing dynamical mass generation in string-inspired theories, where ALP potentials are absent in any order of string perturbation theory, and could only be generated by stringy non perturbative effects, such as instantons. The latter are also thought of as being responsible for generating our Yukawa interactions, which are thus characterised by very small couplings. We show that, for a Hermitian Yukawa interaction, there is no (pseudo)scalar dynamical mass generation, but there is fermion dynamical mass generation, provided one adds a bare (pseudo)scalar mass. The situation is opposite for an anti-Hermitian Yukawa model: there is (pseudo)scalar dynamical mass generation, but no fermion dynamical mass generation. In the presence of additional attractive four-fermion interactions, dynamical fermion mass generation can occur in these models, under appropriate conditions and range of their couplings.

Testing a non-perturbative mechanism for elementary fermion mass generation: numerical results

Based on a recent proposal according to which elementary particle masses could be generated by a non-perturbative dynamical phenomenon, alternative to the Higgs mechanism, we carry out lattice simulations of a model where a non-abelian strongly interacting fermion doublet is also coupled to a doublet of complex scalar fields via a Yukawa and an “irrelevant" Wilson-like term. In this pioneering study we use naive fermions and work in the quenched approximation. We present preliminary numerical results both in the Wigner and in the Nambu-Goldstone phase, focusing on the observables relevant to check the occurrence of the conjectured dynamical fermion mass generation effect in the continuum limit of the critical theory in its spontaneously broken phase.

Chiral phase transition inQED3at finite temperature and impurity potential

In a realistic interacting system described by ($2+1$)-dimensional quantum electrodynamics (${\mathrm{QED}}_{3}$), there is always a certain number of impurities by which fermions are scattered. In general, impurity scattering can generate a finite density of states at the Fermi level, which screens the temporal component of the gauge field. This effect is expected to weaken dynamical fermion mass generation. Within the Born approximation, by introducing a damping term in the energy component of the fermion propagator, the influences of finite temperature and impurity scattering on the chiral phase transition in ${\mathrm{QED}}_{3}$ are investigated. Pursuing this aim, we solve the Dyson-Schwinger equations for the fermion and boson propagators to the leading order in $1/{N}_{f}$ expansion at zero frequency and then calculate the chiral condensate, the chiral susceptibility, and the thermal susceptibility within a range of the impurity scattering rates $\mathrm{\ensuremath{\Gamma}}$ and the numbers of fermion flavors ${N}_{f}$. It is found that impurity scattering leads to an obvious suppression of the dynamical fermion mass generation and critical temperature ${T}_{c}$.

Infrared behavior of dynamical fermion mass generation inQED3

Extensive investigations show that QED$_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We study this problem by means of Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing to the well-established results obtained at zero temperature.

Fermion mass generation and induced current in low-dimensional models with nontrivial topology

We study the process of dynamical fermion mass generation in a three-dimensional model with two types of interacting fermions existing in three dimensions and on a two-dimensional brane with the action of the A3 gauge field taken into account. We investigate the model of a nanotube with the dimension ℝ2 × S1. We establish that in the expression for the fermionic gap, along with the dynamical contribution of the condensate m, the four-fermion interaction results in another kinematic contribution, an Aharonov-Bohm phase calculated from the condition of a minimum of the effective potential of the model. We demonstrate the possibility of induced current generation due to the effect of vacuum polarization with the role played by the nontrivial topology of the problem taken into account.

Intermediate effective interactions and dynamical fermion mass generation of QCD

The functional renormalization group equation is expanded to a two-loop form. This two-loop form equation involves one-loop effective action. An intermediate effective action perspective is adopted toward the one-loop effective action. That is to say, the intermediate effective action could not be of the same form of the bare action and one can make an ansatz to it. Thus by focusing on different high-dimensional operators, effects of the chosen operators can be investigated. QCD through intermediate 4-fermion interactions is investigated. Of the six kinds of 4-fermion interactions generated by one-loop QCD, four kinds generate fermion mass while the other two kinds decrease it. Flow patterns on the ${\stackrel{\texttildelow{}}{m}}_{\mathrm{phys}}^{2}\ensuremath{-}{\stackrel{\texttildelow{}}{g}}^{2}$ plane are drawn.

Vacuum polarization and dynamical chiral symmetry breaking: Phase diagram of QED with four-fermion contact interaction

We study chiral symmetry breaking for fundamental charged fermions coupled electromagnetically to photons with the inclusion of a four-fermion contact self-interaction term, characterized by coupling strengths $\ensuremath{\alpha}$ and $\ensuremath{\lambda}$, respectively. We employ multiplicatively renormalizable models for the photon dressing function and the electron-photon vertex that minimally ensures mass anomalous dimension ${\ensuremath{\gamma}}_{m}=1$. Vacuum polarization screens the interaction strength. Consequently, the pattern of dynamical mass generation for fermions is characterized by a critical number of massless fermion flavors ${N}_{f}={N}_{f}^{c}$ above which chiral symmetry is restored. This effect is in diametrical opposition to the existence of criticality for the minimum interaction strengths, ${\ensuremath{\alpha}}_{c}$ and ${\ensuremath{\lambda}}_{c}$, necessary to break chiral symmetry dynamically. The presence of virtual fermions dictates the nature of phase transition. Miransky scaling laws for the electromagnetic interaction strength $\ensuremath{\alpha}$ and the four-fermion coupling $\ensuremath{\lambda}$, observed for quenched QED, are replaced by a mean field power law behavior corresponding to a second-order phase transition. These results are derived analytically by employing the bifurcation analysis and are later confirmed numerically by solving the original nonlinearized gap equation. A three-dimensional critical surface is drawn in the phase space of $(\ensuremath{\alpha},\ensuremath{\lambda},{N}_{f})$ to clearly depict the interplay of their relative strengths to separate the two phases. We also compute the $\ensuremath{\beta}$ functions (${\ensuremath{\beta}}_{\ensuremath{\alpha}}$ and ${\ensuremath{\beta}}_{\ensuremath{\lambda}}$) and observe that ${\ensuremath{\alpha}}_{c}$ and ${\ensuremath{\lambda}}_{c}$ are their respective ultraviolet fixed points. The power law part of the momentum dependence, describing the mass function, implies ${\ensuremath{\gamma}}_{m}=1+s$, which reproduces the quenched limit trivially. We also comment on the continuum limit and the triviality of QED.

Influence of Fermion Velocity Renormalization on Dynamical Mass Generation in QED3

We study dynamical fermion mass generation in (2 + 1)-dimensional quantum electrodynamics with a gauge field coupling to massless Dirac fermions and non-relativistic scalar bosons. We calculate the fermion velocity renormalization and then examine its influence on dynamical mass generation by using the Dyson—Schwinger equation. It is found that dynamical mass generation takes place even after including the scalar bosons as long as the bosonic compressibility parameter ξ is sufficiently small. In addition, the fermion velocity renormalization enhances the dynamically generated mass.

Dynamical symmetry breaking in hyperbolic 4D spacetime and in extra dimensions

We study the dynamical symmetry breaking in quark matter within two different models. First, we consider the effect of gravitational catalysis of chiral and color symmetries breaking in strong gravitational field of ultrastatic hyperbolic spacetime ℝ ⊗ H 3 in the framework of an extended Nambu-Jona-Lasinio model. Second, we discuss the dynamical fermion mass generation in the flat 4-dimensional brane situated in the 5D spacetime with one extra dimension compactified on a circle. In the model, bulk fermions interact with fermions on the brane in the presence of a constant abelian gauge field A 5 in the bulk. The influence of the A 5-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable.

Dynamical fermion mass generation and exciton spectra in graphene

The Coulomb interaction between massless Dirac fermions may induce dynamical chiral symmetry breaking by forming excitonic pairs in clean graphene, leading to semimetal-insulator transition. If the Dirac fermions have zero bare mass, an exact continuous chiral symmetry is dynamically broken and thus there are massless Goldstone excitons. If the Dirac fermions have a small bare mass, an approximate continuous chiral symmetry is dynamically broken and the resultant Goldstone type excitons become massive, which is analogous to what happens in QCD. In this paper, after solving Dyson-Schwinger gap equation in the presence of a small bare fermion mass, we found a remarkable reduction of the critical Coulomb interaction strength for excitonic pair formation and a strong enhancement of dynamical fermion mass. We then calculate the masses of Goldstone type excitons using the SVZ sum rule method and operator product expansion technique developed in QCD and find that the exciton masses are much larger than bare fermion mass but smaller than dynamical fermion mass gap. We also study the spin susceptibilities and estimate the masses of non-Goldstone type excitons using the same tools.

Quantum-gravity induced Lorentz violation and dynamical mass generation

In Ref. [1] (by J. Alexandre) a minimal extension of (3+1)-dimensional Quantum Electrodynamics has been proposed, which includes Lorentz-Violation (LV) in the form of higher-(spatial)-derivative isotropic terms in the gauge sector, suppressed by a mass scale $M$. The model can lead to dynamical mass generation for charged fermions. In this article I elaborate further on this idea and I attempt to connect it to specific quantum-gravity models, inspired from string/brane theory. Specifically, in the first part of the article, I comment briefly on the gauge dependence of the dynamical mass generation in the approximations of [1], and I propose a possible avenue for obtaining the true gauge-parameter-independent value of the mass by means of Pinch Technique argumentations. In the second part of the work I embed the LV QED model into multibrane world scenarios with a view to provide a geometrical way of enhancing the dynamical mass to phenomenologically realistic values by means of bulk warp metric factors, in an (inverse) Randall-Sundrum hierarchy. Finally in the third part of this note, I demonstrate that such Lorentz Violating QED models may represent parts of a low-energy effective action (of Finsler-Born-Infeld type) of open strings propagating in quantum D0-particle stochastic space-time foam backgrounds, which are viewed as consistent quantum gravity configurations.

DYNAMICAL FERMION MASSES UNDER THE INFLUENCE OF KALUZA–KLEIN FERMIONS AND A BULK ABELIAN GAUGE FIELD

The dynamical fermion mass generation on the 3-brane in the 5D spacetime is discussed in a model with bulk fermions in interaction with fermions on the branes assuming the presence of a constant Abelian gauge field A5 in the bulk. We calculate the effective potential as a function of the fermion masses and the gauge field A5. The masses can be found from the stationarity condition for the effective potential (the gap equation). We formulate the equation for the mass spectrum of the 4D-fermions. The phases with finite and vanishing fermion masses are studied and the dependence of the masses on the radius of the fifth dimension is analyzed. The influence of the A5-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable. The critical values of the A5 field, the coupling constant and the radius are examined.

Fermion flavor mixing in models with dynamical mass generation

We present a model-independent method of dealing with fermion flavor mixing in the case when instead of constant, momentum-independent mass matrices one has rather momentum-dependent self-energies. This situation is typical for strongly coupled models of dynamical fermion mass generation. We demonstrate our approach on the example of quark mixing. We show that quark self-energies with a generic momentum dependence lead to an effective Cabibbo-Kobayashi-Maskawa (CKM) matrix, which turns out to be in general non-unitary, in accordance with previous claims of other authors, and to non-trivial flavor changing electromagnetic and neutral currents. We also discuss some conceptual consequences of the momentum-dependent self-energies and show that in such a case the interaction basis and the mass basis are not related by a unitary transformation. In fact, we argue that the latter is merely an effective concept, in a specified sense. While focusing mainly on the fermionic self-energies, we also study the effects of momentum-dependent radiative corrections to the gauge bosons and to the proper vertices. Our approach is based on an application of the Lehmann-Symanzik-Zimmermann (LSZ) reduction formula and for the special case of constant self-energies it gives the same results as the standard approach based on the diagonalization of mass matrices.

Dynamical chiral symmetry breaking inQED3at finite density and impurity potential

We study the effects of finite chemical potential and impurity scattering on dynamical fermion mass generation in $(2+1)$-dimensional quantum electrodynamics. In any realistic systems, these effects usually cannot be neglected. The longitudinal component of the gauge field develops a finite static length produced by chemical potential and impurity scattering, while the transverse component remains long-ranged because of the gauge invariance. Another important consequence of impurity scattering is that the fermions have a finite damping rate, which reduces their lifetime. By solving the Dyson-Schwinger equation for the fermion mass function, it is found that these effects lead to strong suppression of the critical fermion flavor ${N}_{c}$ and the dynamical fermion mass in the symmetry broken phase.

Matter fields near quantum critical point in [formula omitted]-dimensional [formula omitted] gauge theory

We study chiral phase transition and confinement of matter fields in ( 2 + 1 ) -dimensional U ( 1 ) gauge theory of massless Dirac fermions and scalar bosons. The vanishing scalar boson mass, r = 0 , defines a quantum critical point between the Higgs phase and the Coulomb phase. We consider only the critical point r = 0 and the Coulomb phase with r > 0 . The Dirac fermion acquires a dynamical mass when its flavor is less than certain critical value N f c , which depends quantitatively on the flavor N b and the scalar boson mass r. When N f < N f c , the matter fields carrying internal gauge charge are all confined if r ≠ 0 but are deconfined at the quantum critical point r = 0 . The system has distinct low-energy elementary excitations at the critical point r = 0 and in the Coulomb phase with r ≠ 0 . We calculate the specific heat and susceptibility of the system at r = 0 and r ≠ 0 , which can help to detect the quantum critical point and to judge whether dynamical fermion mass generation takes place.