Parameter estimation for a Lorentz invariance violation

Abstract

We employ techniques from quantum estimation theory (QET) to estimate the Lorentz violation parameters in the 1+3-dimensional flat spacetime. We obtain and discuss the expression of the quantum Fisher information (QFI) in terms of the Lorentz violation parameter σ0 and the momentum k of the created particles. We show that the maximum QFI is achieved for a specific momentum kmax. We also find that the optimal precision of estimation of the Lorentz violation parameter is obtained near the Planck scale.

Higgs Field-Induced Triboluminescence in Binary Black Hole Mergers

“…Note that the gravitational deformation of dispersion relations assumes an effective violation of the Lorentz invariance. Several models predict a departure from exact Lorentz invariance [79][80][81][82], when the free particle dispersion relation exhibits extra momentumdependent terms, apart from the usual quadratic one occurring in the Lorentz invariant dispersion relation. Most of the studies were performed in the QED, gravity, and for some of the SM particles, where strong constraints on the Lorentz invariance violating terms were obtained [79][80][81][82].…”

“…Several models predict a departure from exact Lorentz invariance [79][80][81][82], when the free particle dispersion relation exhibits extra momentumdependent terms, apart from the usual quadratic one occurring in the Lorentz invariant dispersion relation. Most of the studies were performed in the QED, gravity, and for some of the SM particles, where strong constraints on the Lorentz invariance violating terms were obtained [79][80][81][82]. However, not many studies were performed for the Higgs sector [83][84][85][86], especially on curved backgrounds.…”