Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFormal Developments for Lorentz-Violating Dirac Fermions and Neutrinos
73
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The current paper is a technical work that is focused on Lorentz violation for Dirac fermions as well as neutrinos, described within the nonminimal Standard-Model Extension. We intend to derive two theoretical results. The first is the full propagator of the single-fermion Dirac theory modified by Lorentz violation. The second is the dispersion equation for a theory of $N$ neutrino flavors that enables the description of both Dirac and Majorana neutrinos. As the matrix structure of the neutrino field operator is very involved for generic $N$, we will use sophisticated methods of linear algebra to achieve our objectives. Our main finding is that the neutrino dispersion equation has the same structure in terms of Lorentz-violating operators as that of a modified single-fermion Dirac theory. The results will be valuable for phenomenological studies of Lorentz-violating Dirac fermions and neutrinos.
rate research
Read More
The current article reviews results on vacuum Cherenkov radiation obtained for modified fermions. Two classes of processes can occur that have completely distinct characteristics. The first one does not include a spin flip of the radiating fermion, whereas the second one does. A r{e}sum{e} will be given of the decay rates for these processes and their properties.
Lorentz-violating neutrino parameters have been severely constrained on the basis of astrophysical considerations. In the high-energy limit, one generally assumes a superluminal dispersion relation of an incoming neutrino of the form E ~ |p|v, where E is the energy, p is the momentum and $v = sqrt(1 + delta) > 1. Lepton-pair creation due to a Cerenkov-radiation-like process (nu -> nu + e^- + e^+) becomes possible above a certain energy threshold, and bounds on the Lorentz-violating parameter delta can be derived. Here, we investigate a related process, nu_i -> nu_i + nu_f + bar_nu_f, where nu_i is an incoming neutrino mass eigenstate, while nu_f is the final neutrino mass eigenstate, with a superluminal velocity that is slightly slower than that of the initial state. This process is kinematically allowed if the Lorentz-violating parameters at high energy differ for the different neutrino mass eigenstates. Neutrino splitting is not subject to any significant energy threshold condition and could yield quite a substantial contribution to decay and energy loss processes at high energy, even if the differential Lorentz violation among neutrino flavors is severely constrained by other experiments. We also discuss the SU(2)-gauge invariance of the superluminal models and briefly discuss the use of a generalized vierbein formalism in the formulation of the Lorentz-violating Dirac equation.
Asymptotic single-particle states in quantum field theories with small departures from Lorentz symmetry are investigated perturbatively with focus on potential phenomenological ramifications. To this end, one-loop radiative corrections for a sample Lorentz-violating Lagrangian contained in the Standard-Model Extension (SME) are studied at linear order in Lorentz breakdown. It is found that the spinor kinetic operator, and thus the free-particle physics, is modified by Lorentz-violating operators absent from the original Lagrangian. As a consequence of this result, both the standard renormalization procedure as well as the Lehmann-Symanzik-Zimmermann reduction formalism need to be adapted. The necessary adaptations are worked out explicitly at first order in Lorentz-breaking coefficients.
Topological semimetals have recently attracted extensive research interests as host materials to condensed matter physics counterparts of Dirac and Weyl fermions originally proposed in high energy physics. These fermions with linear dispersions near the Dirac or Weyl points obey Lorentz invariance, and the chiral anomaly leads to novel quantum phenomena such as negative magnetoresistance. The Lorentz invariance is, however, not necessarily respected in condensed matter physics, and thus Lorentz-violating type-II Dirac fermions with strongly tilted cones can be realized in topological semimetals. Here, we report the first experimental evidence of type-II Dirac fermions in bulk stoichiometric PtTe$_2$ single crystal. Angle-resolved photoemission spectroscopy (ARPES) measurements and first-principles calculations reveal a pair of strongly tilted Dirac cones along the $Gamma$-A direction under the symmetry protection, confirming PtTe$_2$ as a type-II Dirac semimetal. The realization of type-II Dirac fermions opens a new door for exotic physical properties distinguished from type-I Dirac fermions in condensed matter materials.
In this work we have used a Hov{r}ava-Lifshitz scaling to rewrite a Lorentz-violating higher-order derivative electrodynamics controlled by a background four-vector $n_{mu}$. The photon propagator was obtained and we have analyzed the dispersion relation and the observational results of gamma-ray burst (GRB) experiments were used. The limits of the critical exponent were discussed in the light of the GRB data and the physical implications were compared with the current GRB-Lorentz-invariance-violation literature. We show that the bound for the Lorentz-violating coupling for dimension-six operators, obtained from a Hov{r}ava-Lifshitz scaling, is eight orders of magnitude better than the result found without considering a Hov{r}ava-Lifshitz scaling, also this bound is nearby one, which is expected to be relevant phenomenologically.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
