Dynamical Fermion Mass Research Articles

Particle Density in Zero Temperature Symmetry Restoring Phase Transitions in Four-Fermion Interaction Models**The project supported by National Natural Science Foundation of China

By means of critical behaviors of the dynamical fermion mass in four-fermion interaction models, we show by explicit calculations that when T = 0 the particle density will have a discontinuous jumping across the critical chemical potential μc in 2D and 3D Gross-Neveu (GN) model and these physically explain the first-order feature of the corresponding symmetry restoring phase transitions. For the second-order phase transitions in the 3D GN model when T → 0 and in 4D Nambu–Jona–Lasinio (NJL) model when T = 0, it is proven that the particle density itself will be continuous across μc but its derivative over the chemical potential μ will have a discontinuous jumping. The results give a physical explanation of implications of the tricritical point in the 3D GN model. The discussions also show effectiveness of the critical analysis approach of phase transitions.

Symmetry Restoring Phase Transitions at High Density in a 4D Nambu-Jona-Lasinio Model with a Single Order Parameter**The project supported by National Natural Science Foundation of China

High density phase transitions in a 4-dimensional Nambu-Jona-Lasinio model containing a single symmetry breaking order parameter coming from the fermion-antifermion condensates are researched and expounded by means of both the gap equation and the effective potential approach. The phase transitions are proven to be second-order at a high temperature T; however at T=0 they are first- or second-order, depending on whether , the ratio of the momentum cutoff Λ in the fermion-loop integrals to the dynamical fermion mass at zero temperature, is less than 3.387 or not. The former condition cannot be satisfied in some models. The discussions further show complete effectiveness of the critical analysis based on the gap equation for second order phase transitions including determination of the condition of their occurrence.

Critical Analyses of Order Parameter and Phase Transitions at High Density in Gross-Neveu Model**The project partially supported by National Natural Science Foundation of China

By critical analyses of the order parameter of symmetry breaking, we have researched the phase transitions at high density in and Gross-Neveu (GN) model and shown that the gap equation obeyed by the dynamical fermion mass has the same effectivenesss as the effective potentials for such analyses of all the second order and some special first order phase transitions. In the meantime we also further ironed out a theoretical divergence and proven that in model a first order phase transition does occur in the case of zero temperature and finite chemical potential.

Gap Equations and Effective Potentials at Finite Temperature and Chemical Potential in D-Dimensional Four-Fermion Models**The project supported by National Natural Science Foundation of China

We have proven the general relations between the gap equations obeyed by dynamical fermion mass and the corresponding effective potentials at finite temperature and chemical potential in D-dimensional four-fermion interaction models. This gives an easy approach to get effective potentials directly from the gap equations. We find out explicit expressions for the effective potentials at zero temperature in the cases of D = 2, 3, and 4 for practical use.

LargeNdynamics in QED in a magnetic field

The expression for the dynamical mass of fermions in QED in a magnetic field is obtained for a large number of the fermion flavor N in the framework of 1/N expansion. The existence of a threshold value N_{thr}, dividing the theories with essentially different dynamics, is established. For the number of flavors N << N_{thr}, the dynamical mass is very sensitive to the value of the coupling constant \alpha_b, related to the magnetic scale \mu = |eB|. For N of order N_{thr} or larger, a dynamics similar to that in the Nambu-Jona-Lasinio model with cutoff of order |eB| and the dimensional coupling constant G \sim 1/(N|eB|) takes place. In this case, the value of the dynamical mass is essentially \alpha_b independent (the dynamics with an infrared stable fixed point). The value of N_{thr} separates a weak coupling dynamics (with \tilde{\alpha}_b \equiv N\alpha_b << 1) from a strong coupling one (with \tilde{\alpha}_b \gtrsim 1) and is of order 1/\alpha_b.

Schwinger-Dyson analysis of dynamical symmetry breaking on a brane with bulk Yang-Mills theory

The dynamically generated fermion mass is investigated in the flat brane world with (4+delta)-dimensional bulk space-time, and in the Randall-Sundrum (RS) brane world. We consider the bulk Yang-Mills theory interacting with the fermion confined on a four-dimensional brane. Based on the effective theory below the reduced cutoff scale on the brane, we formulate the Schwinger-Dyson equation of the brane fermion propagator. By using the improved ladder approximation we numerically solve the Schwinger-Dyson equation and find that the dynamical fermion mass is near the reduced cutoff scale on the brane for the flat brane world with delta >= 3 and for the RS brane world. In RS brane world KK excited modes of the bulk gauge field localized around the y = pi R brane and it enhances the dynamical symmetry breaking on the brane. The decay constant of the fermion and the anti-fermion composite operator can be taken to be the order of the electroweak scale much smaller than the Planck scale. Therefore electroweak mass scale can be realized from only the Planck scale in the RS brane world due to the fermion and the anti-fermion pair condensation. That is a dynamical realization of Randall-Sundrum model which solves the weak-Planck hierarchy problem.

Electron mass operator in a strong magnetic field and dynamical chiral symmetry breaking.

The electron mass operator in a strong magnetic field is calculated. The contribution of higher Landau levels of virtual electrons, along with the ground Landau level, is shown to be essential in the leading log approximation. The effect of the electron dynamical mass generation by a magnetic field is investigated. In a model with N charged fermions, it is shown that some critical number N(cr) exists for any value of the electromagnetic coupling constant alpha, such that the fermion dynamical mass is generated with a doublet splitting for N<N(cr), and the dynamical mass does not arise at all for N>N(cr), thus leaving the chiral symmetry unbroken.

Remark on the momentum dependence of the magnetic catalysis in QED

We propose a new derivation of the fermion dynamical mass generated in four-dimensional QED in the presence of an external constant magnetic field, taking into account the momentum dependence of the fermion self-energy. The result confirms previous analytical studies, and we extend the computation to the finite temperature case where we find that the critical temperature is of the order of the dynamical mass at zero temperature.

Spinons and holons on the lattice

We point out that the dynamical fermion mass generation in the 3D compact U(1) lattice gauge theory with charged fermion and scalar fields (χ Uφ 3 model) may be of relevance for the spinon-holon theory with local gauge symmetry in the condensed matter physics. However, many properties of the χ Uφ 3 model are uncertain, so we make some conjectures to motivate their future investigation. Most probably, for strong gauge coupling the model is by universality equivalent to the familiar 3D four-fermion coupling models with N f = 2. Available numerical results indicate that at the intermediate and weak gauge coupling two universality classes with new interesting physics may arise. One of them is associated with a tricritical point which probably exists in the phase diagram of the χ Uφ 3 model. The other one is determined by the dynamical fermion mass generation in the compact QED 3, which is insufficiently understood but of much interest by itself.

Nonstandard magnetic oscillations in the Nambu-Jona-Lasinio model

The Nambu-Jona-Lasinio model at nonzero values of an external magnetic field H and of the chemical potential is considered in the strong-coupling region G>Gc. The phase portrait of the model exhibits an infinitely large number of massless chiral-invariant phases and massive phases resulting from a spontaneous breakdown of chiral invariance. This phase structure is responsible for aperiodic oscillations of some thermodynamic parameters of the system, including the dynamical fermion mass, as functions of H−1.

Flavor gauge bosons at the Fermilab Tevatron

We investigate collider signals for gauged flavor symmetries that have been proposed in models of dynamical electroweak symmetry breaking and fermion mass generation. We consider the limits on the masses of the gauge bosons in these models which can be extracted from Tevatron Run I data in dijet production. Estimates of the Run II search potential are provided. We show that the models also give rise to significant signals in single top production which may be visible at Run II. In particular we study chiral quark family symmetry and SU(9) chiral flavor symmetry. The Run I limits on the gauge bosons in these models lie between (1.5-2) TeV and should increase to about 3 TeV in Run II. Finally, we show that an SU(12) enlargement of the SU(9) model, including leptonic interactions, is constrained by low energy atomic parity violation experiments to lie outside the reach of the Tevatron.

Magnetic catalysis in the presence of scalar fields

The influence of scalar field interactions in the magnetic catalysis phenomenon is studied in a gauge theory with scalar and fermion fields. It is shown that the external magnetic field catalyzes the appearance of a fermion-antifermion condensate along with a non-zero scalar vev, hence generating a fermion dynamical mass and breaking the discrete chiral symmetry of the theory. The model does not require the introduction of a scalar mass term with a wrong sign in the original Lagrangian to generate the scalar vev, nor does it exhibit dimensional transmutation ”a la Coleman–Weinberg.” The scalar vev noticeably enhances the dynamically generated fermion mass. Possible cosmological applications of these results are suggested.

Real-Time Thermal Field Theory Analyses of 2D Gross-Neveu Model**The project partially supported by National Natural Science Foundation of China and by Grant No. LWTZ-1298 of the Chinese Academy of Sciences

The discrete symmetry breaking and possible restoration at finite temperature are analyzed in 2D Gross-Neveu model by the real-time thermal field theory in the fermion bubble approximation. The dynamical fermion mass m is proven to, be scale-independent and this fact indicates the equivalence between the fermion bubble diagram approximation and the meanfield approximation used in the auxiliary scalar field approach. Reproducing of the nonzero critical temperature is the dynamical fermion mass at , shows the equivalence between the real-time and the imaginary-time thermal. field theories in this problem. However, in the real-time formalism, more results including absence of scalar bound state, the equation of criticality curve of chemical potential-temperature and the behavior of at can be easily obtained. The last one indicates the second-order phase transition feature of the symmetry restoration.

DYNAMICAL FERMION MASSES UNDER THE INFLUENCE OF KALUZA–KLEIN FERMIONS IN EXTRA DIMENSIONS

The dynamical fermion mass generation in the four-dimensional brane is discussed in a model with five-dimensional Kaluza–Klein fermions in interaction with four-dimensional fermions. It is found that the dynamical fermion masses are generated beyond the critical radius of the compactified extra dimensional space and may be made small compared with the masses of the Kaluza–Klein modes.

Bounds on flavor gauge bosons from precision electroweak data

Gauged flavor symmetries at low energies have been proposed in models of dynamical electroweak symmetry breaking and fermion mass generation. The massive flavor gauge bosons give rise to corrections to precisely measured electroweak quantities. We perform a fit to the collider electroweak data and place indirect limits on such new physics. In particular we study several models from the literature: universal coloron, chiral top color, chiral quark family symmetry, SU(9) and SU(12) chiral flavor symmetry. The $95%$ exclusion limits on the mass of the heavy gauge bosons for these models, at their critical coupling for chiral symmetry breaking, typically lie between 1 and 3 TeV. We discuss the robustness of these bounds with respect to changes in Higgs boson mass, b-quark asymmetry data, the SLD left right asymmetry data, or additional new physics.

Dynamical fermion masses under the influence of Kaluza-Klein fermions in extra dimensions

The dynamical fermion mass generation in the 4-dimensional brane is discussed in a model with 5-dimensional Kaluza-Klein fermions in interaction with 4-dimensional fermions. It is found that the dynamical fermion masses are generated beyond the critical radius of the compactified extra dimensional space and may be made small compared with masses of the Kaluza-Klein modes.

Theory of the magnetic catalysis of chiral symmetry breaking in QED

The theory of the magnetic catalysis of chiral symmetry breaking in QED is developed. An approximation for the Schwinger–Dyson equations describing reliably this phenomenon is established, i.e. it is shown that there exists a consistent truncation of those equations in this problem. The equations are solved both analytically and numerically, and the dynamical mass of fermions is determined.

Dynamical mass generation of a two-component fermion in three-dimensional Maxwell-Chern-Simons QED: The lowest ladder approximation

Dynamical mass generation of a two-component fermion in $QED_3$ with a Chern-Simons term is investigated by solving the Schwinger-Dyson equation formulated in the lowest ladder approximation. Dependence of the dynamical fermion mass on a gauge-fixing parameter, a gauge coupling constant, and a topological mass is examined by approximated analytical and also numerical methods. The inclusion of the Chern-Simons term makes impossible to choose a peculiar gauge in which a wave function renormalization is absent. The numerical evaluation shows that the wave function renormalization is fairly close to 1 in the Landau gauge. It means that this gauge is still a specific gauge where the Ward-Takahashi identity is satisfied approximately. We also find that the dynamical mass is almost constant if the topological mass is larger than the coupling constant, while it decreases when the topological mass is comparable to or smaller than the coupling constant and tends to the value in $QED_3$ without the Chern-Simons term.

Effective potential of composite fields in weakly coupled QED in a uniform external magnetic field

The effective potential for the composite fields responsible for chiral symmetry breaking in weakly coupled QED in a magnetic field is derived. The global minimum of the effective potential is found to acquire a non-vanishing expectation value of the composite fields that leads to generating the dynamical fermion mass by an external magnetic field. The results are compared with those for the Nambu--Jona-Lasinio model.

Physical spectrum of conformalSU(N)gauge theories

We investigate the physical spectrum of vector-like $\mathrm{SU}(N)$ gauge theories with infrared coupling close to but above the critical value for a conformal phase transition. We use dispersion relations, the momentum dependence of the dynamical fermion mass and resonance saturation. We argue that the second spectral function sum rule is substantially affected by the continuum contribution, allowing for a reduction of the axial-vector--vector mass splitting with respect to QCD-like theories. Possible consequences for technicolor theories are described.