Fermion Spectrum Research Articles

General structure of fermion two-point function and its spectral representation in a hot magnetized medium

We have systematically constructed the general structure of the fermion self-energy and the effective quark propagator in the presence of a nontrivial background such as a hot magnetized medium. This is applicable to both QED and QCD. The hard thermal loop approximation has been used for the heat bath. We have also examined transformation properties of the effective fermion propagator under some of the discrete symmetries of the system. Using the effective fermion propagator we have analyzed the fermion dispersion spectra in a hot magnetized medium along with the spinor for each fermion mode obtained by solving the modified Dirac equation. The fermion spectra is found to reflect the discrete symmetries of the two-point functions. We note that for a chirally symmetric theory the degenerate left- and right-handed chiral modes in vacuum or in a heat bath get separated and become asymmetric in the presence of a magnetic field without disturbing the chiral invariance. The obtained general structure of the two-point functions is verified by computing the three-point function, which agrees with the existing results in one-loop order. Finally, we have computed explicitly the spectral representation of the two-point functions which would be very important to study the spectral properties of the hot magnetized medium corresponding to QED and QCD with background magnetic field.

Quasiclassical Theory of Spin Dynamics in Superfluid $$^3$$ 3 He: Kinetic Equations in the Bulk and Spin Response of Surface Majorana States

We develop a theory based on the formalism of quasiclassical Green's functions to study the spin dynamics in superfluid $^3$He. First, we derive kinetic equations for the spin-dependent distribution function in the bulk superfluid reproducing the results obtained earlier without quasiclassical approximation. Then we consider a spin dynamics near the surface of fully gapped $^3$He-B phase taking into account spin relaxation due to the transitions in the spectrum of localized fermionic states. The lifetime of longitudinal and transverse spin waves is calculate taking into account the Fermi-liquid corrections which lead to the crucial modification of fermionic spectrum and spin responses.

Anderson localization in sigma models

In QCD above the chiral restoration temperature there exists an Anderson transition in the fermion spectrum from localized to delocalized modes. We investigate whether the same holds for nonlinear sigma models which share properties like dynamical mass generation and asymptotic freedom with QCD. In particular we study the spectra of fermions coupled to (quenched) CP(N-1) configurations at high temperatures. We compare results in two and three space-time dimensions: in two dimensions the Anderson transition is absent, since all fermion modes are localized, while in three dimensions it is present. Our measurements include a more recent observable characterizing level spacings: the distribution of ratios of consecutive level spacings.

Goldstino in supersymmetric Bose-Fermi mixtures in the presence of a Bose-Einstein condensate

We analyze the spectral properties of the Goldstino excitation in a Bose-Fermi mixture of cold atoms, whose masses and interaction strengths are tuned so that the hamiltonian is supersymmetric. We consider systems at zero temperature and assume that, in the weak coupling regime, the fermions form a Fermi sea, while the bosons form a Bose-Einstein condensate. We study the excitation spectrum within a simple extension of the random phase approximation, taking into account the mixing between the supercharge and the fermion caused by the condensate. This mixing affects the fermion spectrum strongly. We argue that the corresponding modification of the fermion spectrum, and the associated fermion distribution in momentum space, could be accessible experimentally, and potentially allow for a determination of the Goldstino properties.

Pair production processes and flavor in gauge-invariant perturbation theory

Gauge-invariant perturbation theory is an extension of ordinary perturbation theory which describes strictly gauge-invariant states in theories with a Brout–Englert–Higgs effect. Such gauge-invariant states are composite operators which have necessarily only global quantum numbers. As a consequence, flavor is exchanged for custodial quantum numbers in the Standard Model, recreating the fermion spectrum in the process. Here, we study the implications of such a description, possibly also for the generation structure of the Standard Model.In particular, this implies that scattering processes are essentially bound-state–bound-state interactions, and require a suitable description. We analyze the implications for the pair-production process [Formula: see text] at a linear collider to leading order. We show how ordinary perturbation theory is recovered as the leading contribution. Using a PDF-type language, we also assess the impact of sub-leading contributions. To lowest order, we find that the result is mainly influenced by how large the contribution of the Higgs at large [Formula: see text] is. This gives an interesting, possibly experimentally testable, scenario for the formal field theory underlying the electroweak sector of the Standard Model.

Chern insulator with large Chern numbers. Chiral Majorana fermion liquid

In the framework of Hofstadter’s approach we provide a detailed analysis of a realization of exotic topological states such as the Chern insulator (CI) with large Chern numbers. In a transverse homogeneous magnetic field a one-particle spectrum of fermions transforms to an intricate spectrum with a fine topological structure of the subbands. In a weak magnetic field H for a rational magnetic flux, a topological phase with a large Chern number is realized near the half filling. There is an abnormal behavior of the Hall conductance . At half-filling, the number of chiral Majorana fermion edge states increases sharply forming a new state, called the chiral Majorana fermion liquid.

Two-point function of a d=2 quantum critical metal in the limit kF→∞ , Nf→0 with NfkF fixed

We show that the fermionic and bosonic spectrum of $d=2$ fermions at finite density coupled to a critical boson can be determined non-perturbatively in the combined limit $k_F\rightarrow {\infty}$, $N_f \rightarrow 0$ with $N_fk_F$ fixed. In this double scaling limit, the boson two-point function is corrected, but only at one-loop. This double scaling limit therefore incorporates the leading effect of Landau damping. The fermion two-point function is determined analytically in real space and numerically in (Euclidean) momentum space. The resulting spectrum is discontinuously connected to the quenched $N_f\rightarrow 0$ result. For $\omega \rightarrow 0$ with $k$ fixed the spectrum exhibits the distinct non-Fermi-liquid behavior previously surmised from the RPA approximation. However, the exact answer obtained here shows that the RPA result does not fully capture the IR of the theory.

Effect of quintessence on holographic fermionic spectrum

In this letter, we investigate the holographic fermionic spectrum without/with dipole coupling dual to the Reissner–Nordström anti-de Sitter (RN–AdS) black brane surrounded by quintessence. We find that the low energy excitation of this fermionic system without dipole coupling behaves as a non-Fermi liquid. In particular, the introduction of quintessence aggravates the degree of deviation from a Fermi liquid. For the system with dipole coupling, the phase transition from (non-)Fermi liquid to Mott phase can be observed. The ratio between the width of gap and the critical temperature, beyond which the gap closes, is also worked out. We find that this ratio is larger than that of the holographic fermionic system dual to the RN–AdS black brane and even the material of VO_2. It means that our holographic system with quintessence can model new phenomena of the condensed matter system and provide some new insights in their regard.

Low-frequency logarithmic discretization of the reservoir spectrum for improving the efficiency of hierarchical equations of motion approach

An efficient low-frequency logarithmic discretization (LFLD) scheme for the decomposition of fermionic reservoir spectrum is proposed for the investigation of quantum impurity systems. The scheme combines the Padé spectrum decomposition (PSD) and a logarithmic discretization of the residual part in which the parameters are determined based on an extension of the recently developed minimum-dissipaton ansatz [J. J. Ding et al., J. Chem. Phys. 145, 204110 (2016)]. A hierarchical equations of motion (HEOM) approach is then employed to validate the proposed scheme by examining the static and dynamic system properties in both the Kondo and noninteracting regimes. The LFLD scheme requires a much smaller number of exponential functions than the conventional PSD scheme to reproduce the reservoir correlation function and thus facilitates the efficient implementation of the HEOM approach in extremely low temperature regimes.

Eigen spectra and wave functions of the massless Dirac fermions under the nonuniform magnetic fields in graphene

In this research, firstly, by using the new form of Dirac-Weyl equation and the series method with submitting more suitable details, the energy spectrum and wave functions of the massless Dirac fermions are calculated under the inhomogeneous and q-deformed spatially magnetic fields. Although, we discussed about the results of the energy levels, further, we obtained the wave function as the Hessenberg determinant with calculating the elements of it as exact. On the other hand, by using the Mellin-Barnes integral representation and Hurwitz zeta function, we have achieved the thermodynamic physical quantities of the Dirac-Weyl fermions in the absence of a magnetic field for inside of the graphene quantum dot. Finally, our numerical results for the wave functions and probability densities are presented too.

Lepton-flavor universality violation in RK and {R}_{D^{{}_{left(ast right)}}} from warped space

Some anomalies in the processes b → sℓℓ (ℓ = μ, e) and bto cell {overline{nu}}_{ell } (ℓ = τ, μ, e), in particular in the observables RK and {R}_{D^{{}_{left(ast right)}}} , have been found by the BaBar, LHCb and Belle collaborations, leading to a possible lepton flavor universality violation. If these anomalies were confirmed they would inevitably lead to physics beyond the Standard Model. In this paper we try to accommodate the present anomalies in an extra dimensional theory, solving the naturalness problem of the Standard Model by means of a warped metric with a strong conformality violation near the infra-red brane. The RK anomaly can be accommodated provided that the left-handed bottom quark and muon lepton have some degree of compositeness in the dual theory. The theory is consistent with all electroweak and flavor observables, and with all direct searches of Kaluza-Klein electroweak gauge bosons and gluons. The fermion spectrum, and fermion mixing angles, can be reproduced by mostly elementary right-handed bottom quarks, and tau and muon leptons. Moreover the {R}_{D^{{}_{left(ast right)}}} anomaly requires a strong degree of compositeness for the left-handed tau leptons, which turns out to be in tension with experimental data on the {g}_{tau_L}^Z coupling, possibly unless some degree of fine-tuning is introduced in the fixing of the CKM matrix.

Structures of the neutrino mass spectrum and of lepton mixing as results of mirror-symmetry breaking

The specific violated mirror symmetry model is capable of generating the observed lepton weak mixing matrix with a structure similar to the observed one that almost lacks any visible regularities (the "flavor riddle"). The peculiarities of the Standard Model (SM): quark and lepton mass hierarchy and the neutrino spectrum different from this hierarchy appear to be necessary conditions for reproduction of such a structure. The inverse order of the neutrino spectrum and a small value of the mass $m_{3}$ are here two other necessary conditions. The smallness of the angle $\Theta_{1,3}$ is determined then just by small mass ratios in the hierarchical lepton spectrum. The explanation is proposed for differences between the neutrino spectrum and other fermion spectra of SM. The inverse order of the neutrino spectrum and the observed $\Theta_{1,3}$ angle permit evaluation of the absolute values of neutrino masses: $m_{1}\sim m_{2}\sim 0.05$eV, $m_{3}\leq 0.01$eV.

Coleman–Weinberg symmetry breaking in SU(8) induced by a third rank antisymmetric tensor scalar field II: the fermion spectrum

We continue our study of Coleman–Weinberg symmetry breaking induced by a third rank antisymmetric tensor scalar, in the context of the SU(8) model (Adler 2014 Int. J. Mod. Phys. A 29 1450130) we proposed earlier. We focus in this paper on qualitative features that will determine whether the model can make contact with the observed particle spectrum. We discuss the mechanism for giving the spin field a mass by the BEH mechanism, and analyze the remaining massless spin fermions, the global chiral symmetries, and the running couplings after symmetry breaking. We note that the smallest gluon mass matrix eigenvalue has an eigenvector suggestive of U(1)B−L, and conjecture that the theory runs to an infrared fixed point at which there is a massless gluon with 3 to −1 ratios in generator components. Assuming this, we discuss a mechanism for making contact with the standard model, based on a conjectured asymmetric breaking of Sp(4) to SU(2) subgroups, one of which is the electroweak SU(2), and the other of which is a ‘technicolor’ group that binds the original SU(8) model fermions, which play the role of ‘preons’, into composites. Quarks can emerge as 5 preon composites and leptons as 3 preon composites, with consequent stability of the proton against decay to a single lepton plus a meson. A composite Higgs boson can emerge as a two preon composite. Since anomaly matching for the relevant conserved global symmetry current is not obeyed by three fermion families, emergence of three composite families requires formation of a Goldstone boson with quantum numbers matching this current, which can be a light dark matter candidate.

Neutrino and CP -even Higgs boson masses in a nonuniversal U(1)′ extension

We propose a new anomaly-free and family nonuniversal $\mathrm{U}(1)'$ extension of the standard model with the addition of two scalar singlets and a new scalar doublet. The quark sector is extended by adding three exotic quark singlets, while the lepton sector includes two exotic charged lepton singlets, three right-handed neutrinos and three sterile Majorana leptons to obtain the fermionic mass spectrum of the standard model. The lepton sector also reproduces the elements of the PMNS matrix and the squared-mass differences data from neutrino oscillation experiments. Also, analytical relations of the PMNS matrix are derived via the inverse see-saw mechanism, and numerical predictions of the parameters in both normal and inverse order scheme for the mass of the phenomenological neutrinos are obtained. We employed a simple seesaw-like method to obtain analytical mass eigenstates of the CP-even $3\times 3$ mass matrix of the scalar sector.

Anarchy with hierarchy: A probabilistic appraisal

The masses of the charged fermion and the mixing angles among quarks are observed to be strongly hierarchical, while analogous parameters in the neutrino sector appear to be structure-less or anarchical. We develop a class of unified models based on SU(5) symmetry that explains these differing features probabilistically. With the aid of three input parameters that are hierarchical, and with the assumption that all the Yukawa couplings are uncorrelated random variables described by Gaussian distributions, we show by Monte Carlo simulations that the observed features of the entire fermion spectrum can be nicely reproduced. We extend our analysis to an SU(5)-based flavor U(1) model making use of the Froggatt-Nielsen mechanism where the order one Yukawa couplings are modeled as random variables, which also shows good agreement with observations.

Dirac equation for spherically symmetric AdS5 spacetime and application to a boson star in EGB gravity

We discuss the Dirac equation in a curved 5-dimensional spherically symmetric spacetime. The angular part of the solutions is thoroughly studied, in a formulation suited for extending to rotating spacetimes with equal angular momenta. It has a symmetry [Formula: see text] and is implemented by the Wigner functions. The radial part forms a Dirac–Schrödinger type equation, and existence of the analytical solutions of the massless and the massive modes is confirmed. The solutions are described by the Jacobi polynomials. Also, the spinor of the both large and small components is obtained numerically. As a direct application of our formulation, we evaluate the spectrum of the Dirac fermion in Einstein–Gauss–Bonnet spacetime and the spacetime of a boson star.

Excitonic pairing and insulating transition in two-dimensional semi-Dirac semimetals

A sufficiently strong long-range Coulomb interaction can induce excitonic pairing in gapless Dirac semimetals, which generates a finite gap and drives semimetal-insulator quantum phase transition. This phenomenon is in close analogy to dynamical chiral symmetry breaking in high energy physics. In most realistic Dirac semimetals, including suspended graphene, Coulomb interaction is too weak to open an excitonic gap. The Coulomb interaction plays a more important role at low energies in a two-dimensional semi-Dirac semimetal, in which the fermion spectrum is linear in one component of momenta and quadratic in the other, than a Dirac semimetal, and indeed leads to breakdown of Fermi liquid theory. We study dynamical excitonic gap generation in a two-dimensional semi-Dirac semimetal by solving the Dyson-Schwinger equation, and show that a moderately strong Coulomb interaction suffices to induce excitonic pairing. Additional short-range four-fermion coupling tends to promote excitonic pairing. Among the available semi-Dirac semimetals, we find that TiO$_{2}$/VO$_{2}$ nanostructure provides a promising candidate for the realization of excitonic insulator. We also apply the renormalziation group method to analyze the strong coupling between the massless semi-Dirac fermions and the quantum critical fluctuation of excitonic order parameter at the semimetal-insulator quantum critical point, and reveal non-Fermi liquid behaviors of semi-Dirac fermions.

Influence of the pseudoscalar condensate gradient on the cooling regime of compact stars

We consider the processes in compact stars that arise during the potential formation of a pseudoscalar condensate in finite volumes. We do not propose specific hypotheses about the nature of this condensate. Considering that in the regions with a changing pseudoscalar density, photon propagation can be described in the framework of Maxwell–Chern–Simons electrodynamics, we find the reflection/transmission coefficients for regions with different densities. We study the fermion spectrum in the presence of an axial field considering the pseudoscalar condensate gradient. We also study the influence of the modified photon and fermion spectra on the cooling process of compact stars.

Yukawa sector of minimal SO(10) unification

We show that in SO(10) models, a Yukawa sector consisting of a real 10H, a real 120H and a complex 126H of Higgs fields can provide a realistic fit to all fermion masses and mixings, including the neutrino sector. Although the group theory of SO(10) demands that the 10H and 120H be real, most constructions complexify these fields and impose symmetries exterior to SO(10) to achieve predictivity. The proposed new framework with real 10H and real 120H relies only on SO(10) gauge symmetry, and yet has a limited number of Yukawa parameters. Our analysis shows that while there are restrictions on the observables, a good fit to the entire fermion spectrum can be realized. Unification of gauge couplings is achieved with an intermediate scale Pati-Salam gauge symmetry. Proton decay branching ratios are calculable, with the leading decay modes being pto overline{nu}{pi}^{+} and p → e+π0.

Capacitance spectroscopy of a system of gapless Dirac fermions in a HgTe quantum well

Information on the density of states of two-dimensional Dirac fermions in a 6.6-nm-thick HgTe quantum well that corresponds to a transition from the direct to inverted spectrum is obtained for the first time by means of capacitance measurements. It is found that the density of states of Dirac electrons is a linear function of the Fermi energy at EF > 30 meV with the corresponding velocity vDF = 8.2 × 105 m/s. At lower energies, this dependence deviates from the linear law, indicating a strong effect of disorder, which is associated with fluctuations of a built-in charge, on the density of states of the studied system near the Dirac point. At negative energies, a sharp increase in the density of states is observed, which is associated with the tail of the density of states of valleys of heavy holes. The described behavior is in agreement with the proposed model, which includes both the features of the real spectrum of Dirac fermions and the effect of the fluctuation potential.