Lorentz and CPT tests with clock-comparison experiments

Abstract

Clock-comparison experiments are among the sharpest existing tests of Lorentz symmetry in matter. We characterize signals in these experiments arising from modifications to electron or nucleon propagators and involving Lorentz-and CPT-violating operators of arbitrary mass dimension. The spectral frequencies of the atoms or ions used as clocks exhibit perturbative shifts that can depend on the constituent-particle properties and can display sidereal and annual variations in time. Adopting an independent-particle model for the electronic structure and the Schmidt model for the nucleus, we determine observables for a variety of clock-comparison experiments involving fountain clocks, comagnetometers, ion traps, lattice clocks, entangled states, and antimatter. The treatment demonstrates the complementarity of sensitivities to Lorentz and CPT violation among these different experimental techniques. It also permits the interpretation of some prior results in terms of bounds on nonminimal coefficients for Lorentz violation, including first constraints on nonminimal coefficients in the neutron sector. Estimates of attainable sensitivities in future analyses are provided. Two technical appendices collect relationships between spherical and cartesian coefficients for Lorentz violation and provide explicit transformations converting cartesian coefficients in a laboratory frame to the canonical Sun-centered frame.

Gauge field theories with Lorentz-violating operators of arbitrary dimension

“…Also, while precision studies of d = 5 operators in the electron sector are less broadly constrained [9,49,50], they nonetheless also lie below the DIS sensitivities estimated below. In contrast, in the d = 5 proton sector the coefficients a (5)µαβ p are only partially bounded [50], and the existing DIS sensitivities are roughly comparable to those estimated below. Since the structure of the proton is nontrivial and little is known about Lorentz and CPT violation in the strong binding by the gluons and sea species, we treat the coefficients a (5)µαβ f and a (5)µαβ p as independent here.…”

“…Note in particular that existing limits on d = 5 operators in the photon sector lie far below DIS sensitivities [9,48]. Also, while precision studies of d = 5 operators in the electron sector are less broadly constrained [9,49,50], they nonetheless also lie below the DIS sensitivities estimated below. In contrast, in the d = 5 proton sector the coefficients a (5)µαβ p are only partially bounded [50], and the existing DIS sensitivities are roughly comparable to those estimated below.…”

Lorentz and CPT violation in partons

“…Cosmic-ray observations imply a few additional bounds on ultrarelativistic combinations of quarksector coefficients [54]. Other constraints on d = 5 spin-independent CPT violation have been extracted from experiments with neutrinos, charged leptons, and nucleons [54][55][56][57][58][59][60].…”

Exact Foldy-Wouthuysen transformation for a Dirac theory revisited

“…The study of the possible candidates to break CPT-Lorentz symmetry is very important nowadays [1]. There are a large study been developed during the last ten years that shows the possible experiments that could give the more prominent physical effect to measure one of these fields [2].…”