High-energy Fermions Research Articles

Conditions for l=1 Pomeranchuk instability in a Fermi liquid

We perform a microscropic analysis of how the constraints imposed by conservation laws affect $q=0$ Pomeranchuk instabilities in a Fermi liquid. The conventional view is that these instabilities are determined by the static interaction between low-energy quasiparticles near the Fermi surface, in the limit of vanishing momentum transfer $q$. The condition for a Pomeranchuk instability is set by $F^{c(s)}_l =-1$, where $F^{c(s)}_l$ (a Landau parameter) is a properly normalized partial component of the anti-symmetrized static interaction $F(k,k+q; p,p-q)$ in a charge (c) or spin (s) sub-channel with angular momentum $l$. However, it is known that conservation laws for total spin and charge prevent Pomeranchuk instabilities for $l=1$ spin- and charge- current order parameters. Our study aims to understand whether this holds only for these special forms of $l=1$ order parameters, or is a more generic result. To this end we perform a diagrammatic analysis of spin and charge susceptibilities for charge and spin density order parameters, as well as perturbative calculations to second order in the Hubbard $U$. We argue that for $l=1$ spin-current and charge-current order parameters, certain vertex functions, which are determined by high-energy fermions, vanish at $F^{c(s)}_{l=1}=-1$, preventing a Pomeranchuk instability from taking place. For an order parameter with a generic $l=1$ form-factor, the vertex function is not expressed in terms of $F^{c(s)}_{l=1}$, and a Pomeranchuk instability does occur when $F^{c(s)}_1=-1$. We argue that for other values of $l$, a Pomeranchuk instability occurs at $F^{c(s)}_{l} =-1$ for an order parameter with any form-factor

CPT and Lorentz violation in the electroweak sector

Long ago, Carroll, Field and Jackiw introduced CPT-violation in the photon sector by adding a dimension-3 gauge-invariant term parametrized by a constant four-vector parameter kAF to the usual (Maxwell) Lagrangian, deriving an ultra-tight bound from astrophysical data. Here, we will discuss recent work studying the extension of this term to the full electroweak gauge sector of the Standard Model. In the context of the Standard Model Extension, CPT and Lorentz violation arises from two gauge-invariant terms parametrized by the four vectors k1 and k2. First we will show how upon spontaneous breaking of the electroweak gauge symmetry these two terms yield Lorentz-violating terms for the photon and the W and Z bosons. As it turns out, the resulting modified dispersion relations for the W bosons yield spacelike momentum for one of its propagating modes at sufficiently large energy. This in turn allows for the possibility of Cherenkov-like W-boson emission by high-energy fermions such as protons, provoking their decay. Analysis of ultra-high-energy cosmic ray data allows for bounding the previously unbound parameter k2, and, by combination with the ultra-tight bound on kAF, the parameter k1.

Graphene and high energy physics

We briefly comment upon the parallel between graphene and high energy fermions and explore the possibility of using the former as a test bed for the latter. We also point out that there are parallels to quantum gravity approaches, which indeed provide a novel explanation for such effects as the Fractional Quantum Hall Effect (FQAE).

The Knees-Ankles-Toe in Cosmic Rays and the Periodic Table of Elementary Particles

This paper posits the discovery of the new elementary particles from the energy spectrum for the knees-ankles-toe of cosmic rays. The energy spectrum from 109 eV to 1020 eV appears to follow a single power law except few breaks at the knees-ankles-toe. The power index increases at the first knee and the second knee, and decreases at the ankle. Above 4 × 1019 eV, the power index increases as the “toe”. The fine structure of the cosmic ray spectrum shows that an ankle with decrease in power index is in between the first knee and the second knee, resulting in two knees, two ankles, and one toe. This paper posits that the knees-ankles-toe are explained by the very high-energy fermions and bosons in the periodic table of elementary particles that places all known leptons, quarks, gauge bosons, and the Higgs boson in the table with the calculated masses in good agreement with observed values. In the periodic table, some high-energy dimensional fermions (Fd where d= dimensional orbital number from 5 to 11) and bosons (Bd) are involved in the knees-ankles-toe. At the knees and the toe, some parts of the energies from the energy sources of cosmic rays are spent to generate Fd and Bd, resulting in the increase of power index. The ankles are the the middle points (midpoints) between the adjacent dimensional fermions and bosons. At a midpoint, the energy is too high to keep the thermally unstable high-energy dimensional particle,resulting in the decay and the decrease of power index. The calculated masses of B8, the midpoint, F9, the midpoint, and B9, are 1.7 × 1015, 2 × 1016, 2.4 × 1017, 2.8 × 1018, and 3.2 × 1019 eV, respectively, which are in good agreement with observed 3 × 1015, 2 × 1016, 3 × 1017, 3 × 1018, and 4 × 1019 eV for the first knee, the first ankle, the second knee, the second ankle, and the toe, respectively. The mass of F10 is 4.4 × 1021 eV beyond the GZK limit, so F10 and above are not observed.

Interacting anyonic fermions in a two-body color code model

We introduce a two-body quantum Hamiltonian model of spin $\frac{1}{2}$ on a two-dimensional spatial lattice with exact topological degeneracy in all coupling regimes. There exists a gapped phase in which the low-energy sector reproduces an effective color code model. High-energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. The model exhibits a ${\mathbf{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbf{Z}}_{2}$ gauge-group symmetry and string-net integrals of motion, which are related to the existence of topological charges that are invisible to moving high-energy fermions.

Anomalous spin excitation spectrum of the Heisenberg model in a magnetic field.

Making the assumption that high-energy fermions exist in the two dimensional spin- 1/2 Heisenberg antiferromagnet, we present predictions based on the pi-flux ansatz for the dynamic structure factor when the antiferromagnet is subject to a uniform magnetic field. The main result is the presence of gapped excitations in a momentum region near (pi,pi) with energy lower than that at (pi,pi). This is qualitatively different from spin-wave theory predictions and may be tested by experiments or by quantum Monte Carlo.

CP-Violating Reflection of High Energy Fermions during a First-Order Phase Transition

We study the high energy behaviour of fermions hitting a general wall caused by a first-order phase transition. The wall profile is introduced through general analytic and nonanalytic functions. The reflection coefficient is computed in the high energy limit and its connection with the analytic properties of the wall profile function is shown. The high energy behaviour of the fermions hitting the wall is determined either by the leading singularity, i.e., the closest pole to the real axis when the profile function is analytic, or by the first noncontinuous derivative on the real axis in the nonanalytic case. CP-violating wall profiles are studied and it is shown that the respective symmetry properties of the CP-conserving and CP-violating profile functions play an important role on the size of the CP asymmetry.

Relativistic quantum scattering of high energy fermions in the presence of a phase transition

We study the high energy behaviour of fermions hitting a general wall caused by a first-order phase transition. The wall profile is introduced through a general analytic function. The reflection coefficient is computed in the high energy limit and expressed in terms of the poles of the wall profile function. It is shown that the leading singularity gives the high energy behaviour.

Chiral bosonization in non-abelian gauge theories

The chiral bosonization in non-abelian gauge theories is described starting directly from the QCD functional. For a given mass scale Λ, QCD may be equivalently represented by colour chiral fields, gauge fields and high energy fermions. The effective action for colour chiral fields may admit the existence of a colour skyrmion-boson with baryon number 2/3.

Fermions in general relativity

A discussion is given of the interaction of Fermions with linearized gravitational fields in general relativity by means of the covariant Dirac equation. A formulation of the Dirac equation is used in which the “spin-spin” interaction terms do not appear. The trajectories of the Fermions in a gravitational field are found by means of a WKB type limit. The resulting equations of motion are comparable to those of previous authors and lack certain ambiguities of the equations for classical spinning bodies. Although massless particles must follow null geodesics, massive particles exhibit nongeodetic motion. Any effect on the result of an Eötvös-Dicke type experiment would be of at least second order in the gravitational field strengths, but anomalous deflections are found for high energy Fermions passing near a massive body.